CHEM

Identify the wrong statement in the following :

Answer

1 Greenhouse effect is responsible for global warming

2 Ozone layer does not permit infrared ratiation from the sun to reach the earth

3 Acid rain is mostly because of oxides of nitrogen and sulphur

4 Chlorofluorocarbons are responsible for ozone layer depliction

Question 2 of 20 Previous Next

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Which one of the following pairs of species have the same bond order?

Answer

1 NO+ and CN+

2 CN– and CN+

3 CN– and NO+

4 O2– and CN–


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The vapour pressure of water at 20º C is 17.5 mm Hg. If 18g of glucose (C6H12O6) is added to 178.2 g ofwater at 20° C, the vapour pressure of the resulting solution will be

Answer

1 17.325 mm Hg

2 16.400 mm Hg

3 17.675 mm Hg

4 15.750 mm Hg


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The coordination number and the oxidation state of the element 'E' in the complex [E(en)2(C2O4)] NO2(when (en) is ethylene diamine) are, respectively,

Answer

1 6 and 3

2 6 and 2

3 4 and 3

4 4 and 2


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Which one of the following is the correct statement ?

Answer

1 Beryllium exhibits coordination number of six

2 Boric acid is a protonic acid

3 B2H6.2NH3 is known as 'inorganic benzene'

4 Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase


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Four species are listed below:i. HCO3

– ii. H3O+

iii. HSO4–

iv. HSO3F

Which one of the following is the correct sequence of their acid strength?

Answer

1 ii < iii < i < iv

2 iii < i < iv < ii

3 i < iii < ii< iv

4 iv < ii < iii < i Question 7 of 20

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Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in thepresence of H2SO4. The titration gives unsatisfactory result when carried out in the presence of HCl,because HCl

Answer

1 gets oxidised by oxalic acid to chlorine

2 oxidises oxalic acid to carbon dioxide and water

3 furnishes H+ ions in addition to those from oxalic acid

4 reduces permanganate to Mn2+ Question 8 of 20

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The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol–1. The energy required to excite theelectron in the atom from n = 1 to n = 2 is

Answer

1 6.56 × 105 J mol–1

2 9.84 × 105 J mol–1

3 8.51 × 105 J mol–1

4 7.51 × 105 J mol–1


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In which of the following octahedral complexes of Co (at no. 27), will the magnitude of ?0 be the highest?

Answer

1 [Co(H2O)6]3+

2 [Co(CN)6]3–

3 [Co(NH3)6]3+

4 [Co(C2O4)3]3– Question 10 of 20

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Which one of the following constitutes a group of the isoelectronic species?

Answer

1 NO+, C22–, CN–, N2

2 C22–, O2–, CO, NO

3 CN–, N2, O22–, C2

2–

4 N2, O2–. NO+, CO


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The hydrocarbon which can react with sodium in liquid ammonia is

Answer

1 CH3CH2CH2C = CCH2CH2CH3

2 CH3CH2C = CCH2CH3

3 CH3CH = CHCH3

4 CH3CH2 C= CH


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Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The

correct order of their protective powers is

Answer

1 C < B < D < A

2 B < D < A < C

3 A < C < B < D

4 D < A < C < B Question 13 of 20

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In a compound, atoms of element Y form ccp lattice and those of element X occupy 2/3rd of tetrahedralvoids. The formula of the compound will be

Answer

1 X4Y3

2 X2Y

3 X3Y4

4 X2Y3 Question 14 of 20

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The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueoussolution of the corresponding salt, BA, will be

Answer

1 9.58

2 9.22

3 7.01

4 4.79 Question 15 of 20

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The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

Answer

1 –CONH2, –CHO, –SO3H, –COOH

2 –COOH, –SO3H, –CONH2, –CHO

3 –CHO, –COOH, –SO3H, –CONH2

4 –SO3H, –COOH, –CONH2, –CHO Question 16 of 20

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The treatment of CH3MgX with CH3C = C – H produces

Answer

1 H H | |

CH3- C = C - CH

2 CH3C = C – CH3

3 CH4

4 CH3–CH = CH2 Question 17 of 20

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Among the following substituted silanes the one which will give rise to cross linked silicone polymer onhydrolysis is

Answer

1 RSiCl3

2 R3SiCl2

3 R2SiCl2

4 R4Si Question 18 of 20

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In context with the industrial preparation of hydrogen from water gas (CO +H2), which of the following isthe correct statement?

Answer

1 CO is removed by absorption in aqueous Cu2Cl2 Solution

2 H2 is removed through occlusion with Pd

3 CO is oxidized to CO2 with steam in the presence of a catalyst followed by absorption of CO2 in alkali

4 CO and H2 are fractionally separated using differences in their densities


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Given E0Cr3+ /Cr = – 0.72 V, E0

Fe2+ / Fe = – 0.42 V.The potential for the cell Cr |Cr3+ (0.1 M) | |Fe2+ (0.01 M) | Fe is

Answer

1 0.339 V

2 – 0.26 V

3 – 0.339 V

4 0.26 V Question 20 of 20

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Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the mainreason being

Answer

1 more reactive nature of the actinoids than the lanthanoids

2 lesser energy difference between 5f and 6d than between 4f and 5d orbitals

3 more energy difference between 5f and 6d than between 4f and 5d orbitals

4 4f orbitals more diffused than the 5f orbitals

ANSWERQuestion 1 of 20

Next

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Answer

1 Greenhouse effect is responsible for global warming

2 Ozone layer does not permit infrared ratiation from the sun to reach the earth (Correct Answer)




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Answer

1 NO+ and CN+

2 CN– and NO+ (Correct Answer)

3 O2– and CN–

4 CN– and CN+ Question 3 of 20

Previous Next

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Answer

1 17.675 mm Hg

2 17.325 mm Hg (Correct Answer)

3 15.750 mm Hg

4 16.400 mm Hg Question 4 of 20

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The coordination number and the oxidation state of the element 'E' in the complex [E(en)2(C2O4)] NO2(when (en) is ethylene diamine) are, respectively,

Answer

1 4 and 3

2 6 and 2

3 6 and 3 (Correct Answer)

4 4 and 2


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Answer

1 Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase (Correct Answer)

2 Beryllium exhibits coordination number of six


4 Boric acid is a protonic acid Question 6 of 20

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– ii. H3O+

iii. HSO4–

iv. HSO3F


Answer

1 iv < ii < iii < i

2 iii < i < iv < ii

3 i < iii < ii< iv (Correct Answer)

Solution : The decreasing order of acidic strength is

HSO3F > H3O+ > HSO4– > HCO3

–

4 ii < iii < i < iv Question 7 of 20

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Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in the presence of H2SO4. The titration gives unsatisfactory result when carried out in the presence of HCl,because HCl

Answer


2 reduces permanganate to Mn2+ (Correct Answer)


4 furnishes H+ ions in addition to those from oxalic acid

Question 1 of 20 Next

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The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

Answer

1 –CONH2, –CHO, –SO3H, –COOH

2 –SO3H, –COOH, –CONH2, –CHO

3 –CHO, –COOH, –SO3H, –CONH2

4 –COOH, –SO3H, –CONH2, –CHO (Correct Answer)

Solution : The correct decreasing order of priority for the functional groups according to IUPAC nomenclature is –

CO2H > –SO3H > –CONH2 > –CHO Question 2 of 20

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Given E0Cr3+ /Cr = – 0.72 V, E0

Fe2+ / Fe = – 0.42 V.The potential for the cell Cr |Cr3+ (0.1 M) | |Fe2+ (0.01 M) | Fe is

Answer

1 0.339 V

2 – 0.26 V

3 0.26 V (Correct Answer)

4 – 0.339 V Question 3 of 20

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Among the following substituted silanes the one which will give rise to cross linked silicone polymer onhydrolysis is

Answer

1 RSiCl3 (Correct Answer)

2 R2SiCl2

3 R3SiCl2

4 R4Si Question 4 of 20

Previous Next

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Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the mainreason being

Answer

1 4f orbitals more diffused than the 5f orbitals

2 more reactive nature of the actinoids than the lanthanoids

3 lesser energy difference between 5f and 6d than between 4f and 5d orbitals (Correct Answer)

4 more energy difference between 5f and 6d than between 4f and 5d orbitals Question 5 of 20

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Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in thepresence of H2SO4. The titration gives unsatisfactory result when carried out in the presence of HCl,because HCl

Answer



3 reduces permanganate to Mn2+ (Correct Answer)

4 furnishes H+ ions in addition to those from oxalic acid Question 6 of 20

Previous Next

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The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol–1. The energy required to excite theelectron in the atom from n = 1 to n = 2 is

Answer

1 9.84 × 105 J mol–1 (Correct Answer)

2 7.51 × 105 J mol–1

3 8.51 × 105 J mol–1

4 6.56 × 105 J mol–1 Question 7 of 20

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The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueoussolution of the corresponding salt, BA, will be

Answer

1 9.22

2 4.79

3 9.58

4 7.01 (Correct Answer)


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In context with the industrial preparation of hydrogen from water gas (CO +H2), which of the following isthe correct statement?

Answer

1 H2 is removed through occlusion with Pd

2 CO is oxidized to CO2 with steam in the presence of a catalyst followed by absorption of CO2 in alkali (Correct Answer)

3 CO and H2 are fractionally separated using differences in their densities

4 CO is removed by absorption in aqueous Cu2Cl2 Solution The hydrocarbon which can react with sodium in liquid ammonia is

Answer

1 CH3CH2 C= CH (Correct Answer)

2 CH3CH2C = CCH2CH3

3 CH3CH2CH2C = CCH2CH2CH3

4 CH3CH = CHCH3


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Answer

1 17.675 mm Hg

2 17.325 mm Hg (Correct Answer)

3 15.750 mm Hg

4 16.400 mm Hg Question 11 of 20

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In a compound, atoms of element Y form ccp lattice and those of element X occupy 2/3rd of tetrahedralvoids. The formula of the compound will be

Answer

1 X3Y4

2 X2Y

3 X2Y3

4 X4Y3 (Correct Answer) In which of the following octahedral complexes of Co (at no. 27), will the magnitude of ?0 be the highest?

Answer

1 [Co(C2O4)3]3–

2 [Co(NH3)6]3+

3 [Co(H2O)6]3+

4 [Co(CN)6]3– (Correct Answer) Question 13 of 20

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Answer


2 Ozone layer does not permit infrared ratiation from the sun to reach the earth (Correct Answer)


4 Greenhouse effect is responsible for global warming Question 14 of 20

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– ii. H3O+

iii. HSO4–

iv. HSO3F


Answer

1 iii < i < iv < ii

2 ii < iii < i < iv

3 i < iii < ii< iv (Correct Answer)

Solution : The decreasing order of acidic strength is

HSO3F > H3O+ > HSO4– > HCO3

–

4 iv < ii < iii < i


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The coordination number and the oxidation state of the element 'E' in the complex [E(en)2(C2O4)] NO2

(when (en) is ethylene diamine) are, respectively,

Answer

1 4 and 2

2 6 and 2

3 4 and 3

4 6 and 3 (Correct Answer) Question 16 of 20

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Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. Thecorrect order of their protective powers is

Answer

1 C < B < D < A

2 B < D < A < C

3 D < A < C < B

4 A < C < B < D (Correct Answer)

Question 17 of 20

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Which one of the following constitutes a group of the isoelectronic species?

Answer

1 C22–, O2–, CO, NO

2 NO+, C22–, CN–, N2 (Correct Answer)

Solution : Isoelectronic species possess same number of electrons. NO+, C2 2-, CN- and N2, each have 14 electrons

and thus are isoelectronic.

3 N2, O2–. NO+, CO

4 CN–, N2, O22–, C2

2– Question 18 of 20

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Answer

1 Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase (Correct Answer)


3 Boric acid is a protonic acid

4 Beryllium exhibits coordination number of six Question 19 of 20

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Answer

1 NO+ and CN+

2 CN– and NO+ (Correct Answer)

3 O2– and CN–

4 CN– and CN+ Question 20 of 20

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The treatment of CH3MgX with CH3C = C – H produces

Answer

1 CH4 (Correct Answer)

2 H H | |

CH3- C = C - CH

3 CH3–CH = CH2

4 CH3C = C – CH3

MATHEMATICSQuestion 1 of 20

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The conjugate of a complex number is 1 / i-1 . Then that complex number is

Answer

1 1 / (i + 1)

2 -1 / (i + 1)(Correct Answer)

3 1 / (i - 1)

4 -1 / ( i - 1)


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How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which nottwo S are adjacent ?

Answer

1 6. 8. 7C4

2 8. 6C4 . 7C4

3 6. 7. 8C4

4 7. 6C4 . 8C4 (Correct Answer)


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The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to

Answer

1 2 / 3

2 1 / 3

3 4 / 3(Correct Answer)

4 5 / 3


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A parabola has the origin as its focus and the line x =2 as the directrix. Then the vertex of the parabola is at

Answer

1 (0, 1)

2 (2, 0)

3 (1, 0) (Correct Answer)

4 (0, 2) Question 5 of 20

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A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1 / 2. Then the length of the semi-major axis is

Answer

1 4 / 3

2 5 / 3

3 8 / 3(Correct Answer)

4 2 / 3


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The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then apossible value of k is

Answer

1 2

2 1

3 -4 (Correct Answer)

4 -2


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The quadratic equationsx2 – 6x + a = 0and x2– cx + 6 = 0have one root in common.The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

Answer

1 2 (Correct Answer)

2 4

3 3

4 1


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Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such thatx = cy + bz, y = az + cx, and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to

Answer

1 -1

2 3

3 2

4 1 (Correct Answer) Question 9 of 20

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Let A be a square matrix all of whose entries are integers. Then which one of the following is true ?

Answer

1 If det A ≠ ± 1 , then A–1 exists and all its entries are non-integers

2 If det A = ± 1, then A–1 exists but all its entries are not necessarily integers

3 If det A = ± 1, then A–1 need not exist

4 If det A = ± 1, then A–1 exists and all its entries are integers (Correct Answer) Question 10 of 20

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The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is48. If the terms of the geometric progression are alternately positive and negative, then the first term is

Answer

1 4

2 -12 (Correct Answer)

3 12

4 -4


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Let R be the real line. Consider the following subsets of the plane R × R :S = {(x, y): y = x + 1 and 0 < x < 2}T = {(x, y) : x – y is an integer}.Which one of the following is true ?

Answer

1 S is an equivalence relation on R but T is not

2 Neither S nor T is an equivalence relation on R

3 T is an equivalence relation on R but S is not (Correct Answer)

4 Both S and T are equivalence relations on R


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How many real solution does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have ?

Answer

1 8

2 5

3 4

4 1 (Correct Answer) Question 13 of 20

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Let f : N → Y be a function defined as f(x) = 4x + 3 whereY = |y ∈ N : y = 4x + 3 for some x ∈ N|. Show that f is invertible and its inverse is

Answer

1 g(y) = (y-3) / 4(Correct Answer)

2 g(y) = 4 + (y+3)/3

3 g(y) = (3y + 4) / 3

4 g(y) = (y+3)/4


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A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that thenumber obtained is less than 5. Then P(A ∪ B) is

Answer


2 3 / 5

3 2 / 5

4 0


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The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

Answer

1 (y – 2)2 y2 = 25 – (y – 2)2 (Correct Answer)

2 (y – 2) y2 = 25 – (y – 2)2

3 (x – 2) y2 = 25 – (y – 2)2

4 (x – 2)2 y2 = 25 – (y – 2)2


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Answer

1

2

3 (Correct Answer)


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The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the followinggives possible values of a and b ?

Answer

1 a = 1, b = 6

2 a = 5, b = 2

3 a = 0, b = 7

4 a = 3, b = 4 (Correct Answer)


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The statement p → (q → p) is equivalent to

Answer

1 p → (p → q)

2 p → (p ↔ q)

3 p → (p ∧ q)

4 p → (p ∨ q) (Correct Answer)


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The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y –3 = 0 is

Answer

1 (3, – 4)

2 (3, 4)

3 (–3, 4)

4 (–3, –4) (Correct Answer)

Question 20 of 20 Previous

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Answer

1 f is differentiable at x = 0 but not at x = 1 (Correct Answer)

2 f is neither differentiable at x = 0 nor at x = 1

3 f is differentiable at x = 0 and at x = 1

4 f is differentiable at x = 1 but not at x = 0

PHYSICS

Instructions

Your test contains 20 multiple choice questions.

You can mark any question for later using 'Mark for Later' options.

You can review 'Mark for Later' questions any time using 'Review Marked for Later' button.

You can Finish this test any time using 'Finish & Show Result' button.

Once finished you get a chance to review all question with correct answers and their solutions.

You will be awarded three (3) marks each for indicated correct response of each question. One (1) mark will be deducted for indicated incorrect response of each question. No deduction from the total score will be made if no response is indicated for a question.

Question 1 of 20 Next

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A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is

Answer

1 20 m /s

2 40 m /s (Correct Answer)

3 30 m /s

4 10 m /s


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Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

Answer

1

2

3 1.5 N

4 0.5 N (Correct Answer)


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A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. If the motion of the particle takes place in a plane, it follows that

Answer

1 it moves on a straight line

2 its acceleration is constant

3 its velocity is constant

4 its kinetic energy is constant (Correct Answer)


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A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms–1 to 20 ms–1 while passing through a distance 135 m in t second. The value of t is

Answer

1 1.8


Solution : Using v2 – u2 = 2as

202 – 102 = 2 × a × 135

300 / 270 = a = 10 / 9

Using v – u = at20 – 10 = 10 / 9 × t

t = 9 sec

3 10

4 12 Question 5 of 20

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A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle land on the level ground the magnitude of the change in its momentum will be

Answer

1 Zero

2 (Correct Answer)

3 2 mv

4


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If the error in the measurement of radius of a sphere is 2 %, then the error in the determination of volumeof the sphere will be

Answer

1 2%

2 8%

3 6% (Correct Answer)

4 4%


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A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point

Answer

1 C (Correct Answer)

Solution : V maximum velocity point means point at which

dx / dt = slope is maximum==>> ‘C’

2 B

3 D

4 A


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Thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

Answer

1 ML2 / 4

2 ML2 / 24

3 ML2 / 12(Correct Answer)

4 ML2 / 6


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Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period ofoscillation is 0.05 sec and the velocity of the wave is 300 m/sec. What is the phase difference betweenthe oscillation of two points ?

Answer

1 π

2 π / 6

3 2π / 3(Correct Answer)

4 π / 3


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On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points ofwater are 39°W and 239°W respectively. What will be the temperature on the new scale, correspondingto a temperature of 39°C on the Celsius scale ?

Answer

1 78°W

2 139°W

3 117°W (Correct Answer)

4 200°W Question 11 of 20

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Which two of the following five physical parameters have the same dimensions ?(a) Energy density(b) Refractive index(c) Dielectric constant(d) Young’s modulus(e) magnetic field

Answer

1 (c) and (e)

2 (a) and (d) (Correct Answer)

Solution : [Energy density] =

[W] / L3 = [F][L] / [L3][L] = [F] / [L3] = [P] = [Y]

3 (a) and (e)

4 (b) and (d)


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A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 × 109 m and its mean distance from the earth is 1.5 × 1011 m. What is the diameter of the sun’s image on the paper ?

Answer

1 9.2 × 10–4 m (Correct Answer)

Solution : 1 / O = v / u

O = 1.39 × 109 mv = 0.1m

u = 1.5 × 1011 m

I = 9.2 × 10–4 m

2 12.4 × 10–4 m

3 6.5 × 10–5 m

4 6.5 × 10–4 m


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If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closedcycle process, then

Answer

1 Q = 0

2 E = 0

(Correct Answer)

Solution : For a cyclic process ΔU=0or E = 0

3 Q = W = 0

4 W = 0


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A roller coaster is designed such that riders experience “weightlessness” as they go round the top of a hillwhose radius of curvature is 20 m. The speed of the car at the top of the hill is between

Answer

1 15 m/s and 16 m/s

2 14 m/s and 15 m/s (Correct Answer)

3 16 m/s and 17 m/s

4 13 m/s and 14 m/s Question 15 of 20

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A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy.The initial velocity of the shell is

Answer

1 100 ms–1 (Correct Answer)

Solution : 4V + 0.2 v = 0

1/2 * 4 * V2 + 1/2 * .2 * v2

Solving above

v = 100 m/s

2 120 ms–1

3 80 ms–1

4 40 ms–1 Question 16 of 20

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A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?

Answer

1 7.2 J

2 1200 J

3 120 J

4 3.6 J (Correct Answer)

Question 17 of 20

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Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictionalforces are 10 % of energy. How much power is generated by the turbine ? (g = 10 m/s2)

Answer

1 7.0 kW

2 8.1 kW (Correct Answer)

Solution : P generated = P input * 90 /100

= (Mgh / t ) * ( 90 / 100 ) = (15 * 10 * 60 / 1 ) * ( 90 / 100 )

= 8.1 KW

3 10.2 kW

4 12.3 kW Question 18 of 20

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Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m /s will be

Answer

1 Mv / 2 newton

2 Zero

3 2 Mv newton

4 Mv newton (Correct Answer)

Solution : F = d(mv) / dt = v ( dm / dt ) as V = constant

F = Mv Previous Next


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The velocity of electromagnetic radiation in a medium of permittivity ε0 and permeability μ0 is given by

Answer

1

2 (Correct Answer)

3

4

Question 20 of 20 Previous

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The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms–2, in the third second is

Answer

1 6 m

2 19/3 m

3 10 / 3 m(Correct Answer)

4 4 m

Question 35. when rain is accompained by thuder storm the collected rain water has pH

of (A)slightly lower than that of rain water than the thunder

storm (B)slightly higher than that of

the thuder storm (C)no change in pH

(D)depends on amount of dust in air

Answer: [A] 'coz during thunderstorm the bonds between nitrogen r

broken,resulting in formation of nitric oxides,and nitric

acid,hence pH decreases...

Posted By: Kavya .R Answer Count : [1] Post Your Answer

Question 36. a spy jumps from an airplane with the parachute the spy accelerate downward for some time when the parachute

opens the acceleration is suddenly

checked and the spy slowly falls on the ground explain the action of parachute in checking the acceleration?

Answer: when the parachute is opened an upward buoyant force acts on the man apart from earths gravitational pull and the frictional

force which acts upwards(and can be neglected for all practical purposes).This buoyant force deccelerates the mans velocity and

thus he reaches ground safely.

Posted By: shraddha jaiswal Answer Count : [2] Post Your Answer

Question 37. according to newtons third law each team pulls the opposite team with equal force in a tug of war why then one team

wins and other loses

Answer: The ground exerts a force on the people on both teams.This force

has a horizontal component.whichever team's horizontal component is greater wins.


Question 38. suppose you are running fast in afield when u suddenly find a snake in front of you. you stop quickly. which

force is responssible for your deceleration?

Answer: Accrding to me musceles apply extra force on the ground which increases friction in the direction opposite to motion and thus we

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stop


Question 39. Let R be the real line. Consider the following subsets of the plane R × R.

S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x - y is an integer}. Which one of the following is true?

(1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

Answer: 4 is correct answer.

Posted By: Singh Is King Answer Count : [3] Post Your Answer

Question 40. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of - 0.03 mm while measuring the

diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the

main scale as 35. The diameter of the wire is

(1) 3.32 mm (2) 3.73 mm (3) 3.67 mm (4) 3.38 mm

Answer: 4 is correct.

Diameter = M.S.R. + C.S.R × L.C. + Z.E. = 3 + 35 × (0.5/50) + 0.03 = 3.38 mm


Question 41. An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment

distance are measured by

(1) a vernier scale provided on the microscope (2) a standard laboratory scale

(3) a meter scale provided on the microscope (4) a screw gauage provided on the microscope

Answer: 1 is correct..


Question 42. A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss

during the collision is














(1) 0.16 J (2) 1.00 J (3) 0.67 J (4) 0.34 J



Question 43. A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found

between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following

is true for the transistor?

(1) It is an npn transistor with R as base (2) It is a pnp transistor with R as collector (3) It is a pnp transistor with R as emitter

(4) It is an npn transistor with R as collector



Question 44. This question contains Statement -1 and Statement-2. Of the four choices given after the statements,

choose the one that best describes the two statements.

Statement – I: Energy is released when heavy nuclei undergo fission or light

nuclei undergo fusion.

and

Statement – II For heavy nuclei, binding energy per nucleon increases with

increasing Z while for light nuclei it decrease with increasing Z.

(1) Statement – 1is false, Statement – 2 is true.

(2) Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

(3) Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

(4) Statement – 1 is true, Statement – 2 is False.



Question 45. While measuring the speed of sound by performing a resonance column experiment, a student gets the first










resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then

(1) 18 > x (2) x >54

(3) 54 > x > 36 (4) 36 > x > 18



Question 46. Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason

being

(1) 4f orbitals more diffused than the 5f orbitals (2) lesser energy difference between 5f and 6d than between 4f

and 5d orbitals (3) more energy difference between 5f and 6d than between 4f

and 5d orbitals (4) more reactive nature of the actinoids than the lanthanoids


Being lesser energy difference between 5f and 6d than 4f and 5d orbitals.


Question 47. Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

(1) 2,4,6-trinitrobenzene (2) o-nitrophenol (3) p-nitrophenol (4) nitrobenzene



Question 48. Identify the wrong statements in the following:

(1) Chlorofluorocarbons are responsible for ozone layer depletion (2) Greenhouse effect is responsible for global warming

(3) Ozone layer does not permit infrared radiation from the sun to reach the earth

(4) Acid rains is mostly because of oxides of nitrogen and sulphur


Ozone layer does not allow ultraviolet radiation from sun to reach earth.











Question 49. Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is

diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

(1) mixture of o- and p-bromotoluenes (2) mixture of o- and p-dibromobenzenes

(3) mixture of o- and p-bromoanilines (4) mixture of o- and m-bromotoluenes



Question 50. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and

negative, then the first term is

(1) –4 (2) –12 (3) 12 (4) 4

Answer: 2 is correct answer


Question 51. Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the

statement “x is a rational number iff y is a transcendental number”.

Statement –1: r is equivalent to either q or p

Statement –2: r is equivalent to ~ (p ? ~ q).

(1) Statement -1 is false, Statement -2 is true (2) Statement -1 is true, Statement -2 is true, Statement -2 is a

correct explanation for Statement -1 (3) Statement -1 is true, Statement -2 is true; Statement -2 is not

a correct explanation for Statement -1. (4) Statement - 1 is true, Statement - 2 is false.

Answer: 4 is correct


Question 52. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible

values of a and b?

(1) a = 0, b = 7













(2) a = 5, b = 2 (3) a = 1, b = 6 (4) a = 3, b = 4



Question 53. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the

parabola is at

(1) (0, 2) (2) (1, 0) (3) (0, 1) (4) (2, 0)



Question 54. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the

semi-major axis is

(1) 8/3 (2) 2/3 (3) 4/3 (4) 5/3

Answer: 1 is correct answer


Question 55. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number

obtained is less than 5. Then P (A ? B) is

(1) 3/5 (2) 0 (3) 1

(4) 2/5



Question 56. Sir, I want to know the career prospects of studying B Tech PLASTIC ENGINEERING TECHNOLOGY conducted by CENTRAL INSTITUTE FOR PLASTIC ENGINEERING TECHNOLOGY.(CIPET). Whether this

course is suitable for girls. What is the rate of placement of CIPET.

Answer:













Jaya,

B.Tech. in PLASTIC ENGINEERING TECHNOLOGY is a good career option. Demand for plastic engineering is good in market. There

are various jobs in India and abroad in this field. This course is suitable for girls.

Applications of integration

Question 1 of 20|Match the characteristics given in column I, with the curves given in column II.

Column I Column II

(A) Subtangent is constant (P) Exponential

(B) Subnormal is equal to abscissa (Q) Parabola

(C) Subnormal is constant (R) Rectangular hyperbola

(D) Portion of tangent intercepted between the co-axes is bisected at the point of tangency

(S) Hyperbolas

1. A P, B R, S, C Q, D R, S

2. A R, S, B R, S, C Q, D P

3. A R, S, B Q, C R, S, D P

4. A Q, B R, S, C P, D R, S

Question 2 of 20|

If , then the correct statement is

1.

2.

3.

4. none of these

Question 3 of 20|A function f: (0, ) R describes a curve y = f(x), f(1) = 0. P(x, y) is a point on the curve. Subtangent at the point P is the semi harmonic mean of abscissa and ordinates of the point P.

The correct statement about f(x) is

1. f(x) has one point of local maxima

2. f(x) has one point of local minima

3. f(x) has no point of global minima

4. none of these


is

1. 0

2. e

3.

4. does not exist


Area bounded by y = f(x), xe = 1, y = 0 is

1.

2.

3.

4. none of these

Question 6 of 20|

Differential equation of a curve is its eccentricity e is given by

1. e = 0

2. e (0, 1)

3. e = 1

4. e (1, )

Question 7 of 20|

A function y = f(x), satisfies , ef(e) = 1 then,

1. x2 y1 + xy – 1 = 0

2. x2y2 + 3xy1 + y = 0

3. x2y2 + 3xy1 + y = 1

4. x2y1 – xy + 1 = 0

Question 8 of 20|

Self orthogonal curve(s) is/are ( is a parameter)

1. ax2 + 2hxy + by2 =

2.

3.

4. x2 + ax + by + = 0

Question 9 of 20|A point P(x, y) is taken on orthogonal trajectory of a family of curves, whose differential equation is y2dy + 2xydx – x2dy = 0. Find the value of

1.

Question 10 of 20|If e is eccentricity of all those curves whose tangents at any point make with co-axes triangles of constant area, what is the value of [e2]? (where [.] denotes g.i.f.)

1.

Question 11 of 20|

Solution of differential equation is

1. xy tanxy = c

2. xy cotxy = c

3. xy secxy = c

4. none of these

Question 12 of 20|

If solution of differential equation is

, what is the value of ?

1.

Question 13 of 20|P(x, f(x)) is a variable point on the curve y = f(x), which passes through the origin and the

slope of normal at the point P is

If then

1. h(2) > h(1)

2. h(– 2) > h(– 1)

3. |h(t)| > 2

4. none of these

Question 14 of 20|P(x, f(x)) is a variable point on the curve y = f(x), which passes through the origin and the

slope of normal at the point P is

Area bounded by y = f(x), y = 0, x = 0, x = 1 is

1.

2.

3.

4. none of these

Question 15 of 20|

P(x, y) is a point on the curve y = f(x), which passes through the point and satisfies the differential equation (x2y3 + y)dx – xdy = 0.

The probability for the point P(x, y) to lie in the Ist quadrant is

1.

2.

3. 1

4. not sure

Question 16 of 20|


Number of real solution(s) of the equation ef(x) = 1 is(are)

1. 0

2. 2

3. 4

4. none of these

Question 17 of 20|


If (k, f(k)) is a point of extrema on the curve, then the area bounded by |x| = k, |y| = f(k) is

1. 1

2. 2

3. 4

4. none of these

Question 18 of 20|

A function f: R R, satisfies (1 + x2)dy + (y – etan–1 x)dx = 0 and f(0) =

Equation of the curve is

1. 2y =

2. y =

3.

4. none of these

Question 19 of 20|


f(x) is

1. one one into

2. many one into

3. one one onto

4. many one onto

Question 20 of 20|


Number of asymptote(s) of the curve is(are)

1. 0

2. 1

3. 2

4. none of these

INTEGRATION

Question 1 of 15|Directions:The following question has four choices, out of which ONLY ONE is correct.

Let and are real function such that

1.

2.

3.

4.


Let and are real function such that

The wrong statement about g(x) is

1. g(x) is discontinuous exactly at one point

2. g(x) is many one

3. at finitely many points

4. g(x) has no point of local minima


Let and be real function such that

Area bounded by y = g(x), y = 0, x = 0 is

1.

2.

3. 2

4. area is not bounded


Let be a differentiable function satisfying the functional relation

and

The value of is

1. 0

2. 4

3.

4. none of these



and

The area enclosed by with x-axis between the ordinates and is

1.

2. 2

3. 4

4.



and

The area enclosed by the tangent at the curve at (1, 2) and the coordinate axe is

1.

2.

3. there exists no such area

4.

Question 7 of 15|Directions:The answer to the following question is a single digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.

If , then find the value of

1.


Let then K =

1. there exist no such K

2.

3.

4.


If

1.


If where C is constant of integration and f(x) is positive, then has the value equal to

1.

2.

3.

4.


, where [.] denotes the greatest integer function, is equal to ;

1. 0

2. greater than ln2

3. ln2

4. none of these


If find the value of b + c

1.


Let {.} denotes f.p.f., then

1. 50

2. 100

3. 200

4. none of these

Question 14 of 15|Directions:Match the statements / expressions in column-I with the statements / expressions in column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.

Match the following:

Column – I Column – II

A

If

then

where [.] denotes g.i.f.

P – 3

B

where [.] g.i.f.

Q 3

C

If then n =

R 0

D S 1

1. A S; B S; C Q; D P

2. A S; B R; C Q; D P

3. A R; B S; C Q; D P

4. A S; B S; C P; D Q




A P

B Q

C R

D S

T

1. A R ; B Q; C S; D P

2. A R ; B Q; C S; D P

3. A R ; B Q; C S; D P

4. A R ; B Q; C S; D P

SOLUTIONS OF TRIANGLES

Question 1 of 16|Directions: The following question has four choices, out of which ONE or MORE is/are correct.

The side of a triangle ABC satisfy the relationsa + b – c = 2, 2ab – c2 = 4, 2ab – c2 = 4

and f(x) = ax2 + bx + c.

If r, r1, R are in radius, ex-radius opposite to angle A, circum radius of triangle ABC then wrong statement is

1. r =

2. r1 =

3. R =

4. none of these

Question 2 of 16|Directions:The answer to following question is a single digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.

In a triangle ABC a = 4 and b = 3, the medians AD and BE are mutually perpendicular to

the triangle. Find the value of .

1.

Question 3 of 16|Directions:Match the statements / expressions in Column-I with the statements / expressions in Column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.

ABC be a triangle with a = 3, b = 4, c = 5 then match the following:

Column I Column II

A. Distance between circumcentre and orthocentre

P.

B. Distance between centroid and circumcentre

Q.

C. Distance between centroid and incentre

R.

D. Distance between centroid and orthocentre

S.

1. A Q, B R, C P, D S

2. A R, B Q, C S, D P

3. A S, B P, C Q, D S

4. A P, B S, C R, D Q


In ABC, let M be the mid point of segment AB and let D be the foot of the bisector of

C. Then the

1.

2.

3.

4.


In a triangle ABC, a, c, A are given b2 = 2b1, where b1 and b2 are two values of the third side

and 3a = , then =

1. a

2. b

3. c

4.


In a triangle ABC, if 3a = 2b and tan2 A = , then the two values of the third side are

1.

2.

3.

4. none of these


A triangle, the lengths of whose sides are a, b and c is placed so that the middle points of the sides are on the axes. If the equation to the plane of the triangle lx + my + nz = 1, then find

the value of bc l2 cosA + ca m2 cosB + ab n2 cosC.

1.

Question 8 of 16|Directions:The following question has four choices, out of which ONE or MORE is/are correct.

If the sines of the angles A and B of a triangle ABC satisfy the equation c2x2 – c(a + b)x + ab = 0, then the triangle

1. is acute angled

2. is right angled

3. is obtuse angled

4. satisfies sin A + cos A =


In a ABC sin C + cos C + sin (2B – C) – cos (2B + C) = 2 , then ABC is

1. equilateral

2. isosceles

3. right angled

4. none of these

Question 10 of 16|Directions: The following question has four choices, out of which ONLY ONE is correct.

If the vertices of a variable acute angled triangle ABC lie on a circle of radius R such that

. Then =

1.

2.

3.

4. none of these


If the number of sides of two regular polygons having the same perimeter be n and 2n respectively. Which one(s) is/are not the ratio of their areas?

1.

2.

3.

4. none of these


The area of the circle and area of a regular polygon of n-sides and its perimeter equal to that of the circle are in the ratio

1.

2.

3.

4. none of these


Suppose a, b, c are sides of a triangle which are in G.P with common ratio r.

If log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P. then least side of the triangle is

1. a

2. b

3. c

4. none of these


Suppose a, b, c are sides of a triangle which are in G.P with common ratio r.

In the above part the greatest angle of the triangle is

1. 135°

2. 90°

3. 120°

4. none of these

Question 15 of 16|In a triangle PQR, R = /2. If tan (P/2) and tan (Q/2) are the roots of the equation ax2 + bx + c = 0 where a 0, then

1. a + b = c

2. b + c = a

3. a + c = b

4. b = c

Question 16 of 16|If a, b, c be the sides of ABC and equations ax2 + bx + c = 0 and 5x2 + 12x + 13 = 0 have both the roots common, then C is equal to

1. 60º

2. 90º

3. 120º

4. 45º

INVERSE TRIGONOMETRY


Find the value of where [.] denotes g.i.f.

1.


Find the least value of n N for which (n – 2)x2 + 8x + (n + 4) > sin–1 (sin 12) + cos–1 (cos 12), x R .

1.


Suppose x1, x2, x3 and x4 are roots of the equation x4 – x3 sin 2 + x2 cos2 – x cos – sin = 0

equals

1.

2. –

3.

4.


Consider the equation tan–1 y = 4 tan–1 x

In the above equation y is defined if tan–1x

1.

2.

3.

4.



y as algebraic function of x, is given by

1.

2.

3.

4.



is a root of the equation

1. x4 – x2 – 6 = 0

2. x2 – 6x +1 = 0

3. x2 – x –1 = 0

4. x4 – 6x2 + 1 = 0



Column I Column II

A.

P. 2 tan–1 x

B.

Q. – 2 tan–1 x

C.

R. – 2 tan–1 x

D.

S. + 2 tan–1 x

1. A Q, B P, C S, D P

2. A Q, B P, C S, D R

3. A Q, B R, C S, D P

4. A P, B R, C S, D Q

Question 8 of 16|Directions: The answer to following question is a single digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.

Find the value of where [.] denotes g.i.f.

1.


Find the number of integral values of x satisfying .

1.


The is

1.


Find number of real solution of

1.


Let If M and m are the maximum and minimum values of then their arithmetic mean is equal to

1.

2.

3.

4. none of these


If then, find the number of integral values of x.

1.


If b satisfies the equation b + b2(cos–1 x)–1 – 2 cos–1 x = 0 and k : 6 are chances for b to be positive, then find the value of k.

1.


If a1, a2, a3,…,an is A.P. with common difference d, then

is equal to

1.

2.

3.

4.

Question 16 of 16|Directions: Match the statements / expressions in Column-I with the statements / expressions in Column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.

If [.] denotes g.i.f. match the following

Column I Column II

A. If |x| 1, then

is

P. 0

B. x 0, then

is

Q. 1

C.

R. 2

D. If are angles of a triangle then [ ] =

S. 3

1. A Q, B P, C S, D R

2. A R, B S, C P, D Q

3. A S, B R, C Q, D P

4. A P, B Q, C S, D R

TRIGNOMETRIC FUNCTIONS & EQUATIONS

Question 1 of 10|Directions: Statement: Let S1 be the set of all those solutions of the equation (1 + a) cos cos (2 – b) = (1 + a cos 2 ) cos ( – b) which are independent of a and b and S2 be the set of all such solutions which are dependent of a and b. Then:

All the permissible values of b, if a = 0 and S2 is the subset of (0, ):

1. b (– n , 2n ), n Z

2. b (– n , 2 – n ), n Z

3. b (– n , n )

4. None of these


The conditions that should be imposed on a and b such that S2 is non-empty:

1. < 1

2. 1

3. |a sin b| 1

4. None of these


The set S1 and S2 are:

1. {n , n Z} and {n + (– 1)n (a sin b); n Z}

2. and {n + (– 1)n sin–1 (a sin b); n Z}

3. abd {n + (– 1)n sin–1 ; n Z}’

4. None of these


If n = find the value of

1.


Consider the system of equations .

x + 2y is equal to

1.

2.

3.

4.

Question 6 of 10|Directions: Match the statements / expressions in column-I with the statements / expressions in column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.

Match the equations in column I with their numbers of real solutions in column II


A P 0

B


Q 1

CIf c

has real roots,

then number of value(s) of k is (are)

R 3

D S 4

1. A Q ; B Q; C S; D R

2. A R ; B Q; C S; D Q

3. A S ; B Q; C P; D R

4. A Q ; B P; C S; D R


Let S be a square of unit area. Consider any quadrilateral which has one vertex on each side of S. If a, b, c and d denote the lengths of the sides of the quadrilateral. Find the sum of least and greatest values of (a2 + b2 + c3 + d2).

1.




A If , then = P

B , then Q

C

If then

R

D In a right angled triangle, the hypotenuse is four times as long as the perpendicular from opposite vertex, then tangents of its acute angles are

S

T

1. A P,Q,R,S,T ; B P,Q,R,S,T ; C P, R, S ; D P,Q,R,S

2. A P,Q,R,S ; B P,Q,R,S,T ; C P, R, S ; D P,Q,R,S,T

3. A P, R, S ; B P,Q,R,S,T ; C P,Q,R,S,T ; D P,Q,R,S

4. A P,Q,R,S,T ; B P,Q,R,S,T ; C P,Q,R,S ; D P, R, S


If , then

1. a = 16

2. b = –20

3. d = 0

4. b + 4c = 1


If and , find the ratio of the greatest and least value of .

1.

DIFFERENTIAL CALCULUS II


If the line 3x – 2y + 1 = 0 touches a curve y = f(x) at x = 0, then

1. 0

2. 1

3. 2

4. 3


1.

2.

3.

4.

Question 3 of 20|Directions: The answer to the following question is a single digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.

Three functions f, g and h are defined by:

,

,

, Find the number of points of non-differentiability of h(x).

1.


A function f is defined by where [.] denotes g.i.f., then

1. the function is continuous on its domain

2. the function is not continuous at x = 0

3. f(x) has infinitely many points of discontinuities

4. f(x) has finitely many points of discontinuities


Let us define two sequences and such that

answer the following question.

Which of the following statements is true?

1. is increasing, is decreasing.

2. is decreasing, is increasing

3. is increasing, is non-monotonic.

4. is decreasing, is non- monotonic.

Question 6 of 20|

Directions:The following question has four choices, out of which ONLY ONE is correct.

Let us define two sequences and such that

answer the following question.

1. does not exist

2.

3. 0

4. 1


If , then the period of f(x) is

1. 2

2.

3. /2

4. not defined




A If the quadratic function f(x) = x2 + 19x + 92 is a perfect square, then the number of integral value(s) of x is (are)

P 0

B If f(x) = Sgn(x), g(x) = x (x2 – 5x + 6) Q 1

then fog(x) is discontinuous at x =

C If f is continuous R and

then f(0) =

R 2

D The number of real solution(s) of the equation

is (are)

S 3

1. A R; B P,R,S; C Q; D S

2. A S; B P,R,S; C Q; D R

3. A Q; B P,R,S; C R; D S

4. A R; B S; C Q; D P,R,S


1. 1

2. 2

3. 0

4. none of these


1.

2.

3.

4. none of these


The value of is

1. – a2

2. 0

3. a2

4. none of these


The value of

1.

2. 1

3. n

4. none of these


If a function is defined by (where [.] denotes g.i.f.), then

1.

2.

3.

4. x


Let be a function such that the vectors

are coplanar, then the function is

1. one – one

2. many one

3. invertible

4. periodic with period 2


Number of critical points of the function are

1.

Question 16 of 20

|Directions:The following question has four choices, out of which ONLY ONE is correct.

The wrong statement is

1.

2.

3.

4.


(1) f(x) has one point of inflexion;

(2) g(x) has one point of inflexion

(3) f(x) has one point of local minima,

(4) g(x) has one point of local maxima,

then which one of the following statements is correct

1. (1) is true (2) is false

2. (1) is false (2) is true

3. (3) and (4) both are true

4. (1) and (2) both are true


If u = f–1(x), v = g–1 (x) then wrong statement is

1.

2.

3.

4. None of these


If f(x) = ({x} – 1)2, x [–3, 4] (where {.} is f.p.f.), then find the number of points of discontinuities of f(x).

1.


If f(x) = (where [.] is g.i.f.) then the wrong statement(s) is/are

1. the function is discontinuous at x = 1

2. the function is continuous at x = – 1

3. the function is discontinuous at x = 0

4. the function is not-differentiable at x = 0

DIFFERENTIAL CALCULUS I


If the vertices of a variable acute angled triangle ABC lie on a circle such that

, then find sum of in-radius and circum-radius of triangle ABC.

1.


Match the following functions with its behaviour, [.] denotes the g.i.f.


A P f(x) is continuous at x = 0

B [x] [1 – x] Q f(x) is discontinuous at x = 0

C (sgnx) [2 – x] [1 + |x|]

R f(x) is continuous at x = 1

D [cos x] S f(x) is discontinuous at x = 1

1. A P, S ; B Q, S; C Q, S ; D Q, R

2. A Q, R ; B Q, S; C Q, S ; D P, S

3. A Q, S; B P, S; C Q, S ; D Q, R

4. A S ; B Q; C P; D R

Question 3 of 10|

Directions:The following question has four choices, out of which ONLY ONE is correct.

A function describes a curve such that

, P (x,y) is a point on the curve

The function is

1. one-one on to

2. one-one into

3. many one onto

4. many one into


The area of the triangle made by tangent at point P with lines and is

1.

2. 1

3. 2

4. 4


The three points inscribed the given curve. Which centre lies on the curve?

1. centroid

2. orthocentre

3. circumcentre

4. incentre


Let ,

The points of non differentiability of y = |f|x|| are

1. 3

2. 4

3. 5

4. 6


Let ,

Number of real solution of the equation is

1. 3

2. 4

3. 5

4. 6


Let ,

Number of real solution of the equation is

1. 5

2. 6

3. 7

4. 8


Find number of real solution(s) of the equation where [.] denotes g.i.f., {.}denotes f.p.f.

1.


If , then h(x) =

1. f(x)

2. g(x)

3.

4. are in H.P.

VECTOR & 3 D


If the vectors

are reciprocal to each other then the number of ordered pairs of such vectors for

are

1. 2

2. 3

3. 8

4. 16


Let ABC is a triangle, BC = a, CA = B, AB = C, for the following conditions which of the centre o is match :


A P Centroid

B Q Orthocenter

C R Circumcentre

D S Incentre

1. A S ; B P ; C Q ; D R

2. A Q ; B P ; C Q ; D R

3. A R ; B P ; C Q ; D S

4. A P ; B R ; C Q ; D S


The unit vectors are perpendicular and the unit vector be inclined at an angle to

both . If then

1.

2.

3.

4.


Match the following :


A Let be three non-coplanar vectors such that

then 1 + 2 + 3 =

P -1/2

B If f(x) = x3 + 3x2 +4x + b sinx + c cosx x R is a one-one function, then b2 + c2 =

Q ½

C

If (where [.] is g.i.f.) then

R 3

D

If then m + n =

S 1

1. A R; B Q, S; C P ; D Q

2. A Q; B Q, S; C P ; D R

3. A S; B Q, R; C P ; D Q

4. A P; B Q, S; C R ; D Q


Let PM be perpendicular from the point P(1, 2, 3) to x – y plane. If OP makes an angle with the positive direction of the z-axis and OM makes an angle with the positive direction of x-axis, where O is the origin then

( and are acute angles).

1.

2.

3. tan = 2

4.




A

If , then

P

B

If

gof(x) is invertible then x

Q

C

If where [.] denotes g.i.f. then x

R

DIf then

S

1. A Q, S; B P,Q,R; C R; D P,Q,R,S

2. A P,Q,R,S; B P,Q,R; C R; D Q, S

3. A R; B P,Q,R; C Q, S; D P,Q,R,S

4. A P,Q,R; B Q, S; C R; D P,Q,R,S




A

If


P

Then number of point(s) of non differentiability of f(x) on [0, 2] is (are)

B

If

Q 1

C If [.] denotes g.i.f. and {.} denotes f.p.f.

then,

R 2

D

If

y = f(x) is discontinuous at x =

S 4

1. A Q; B P; C P; D P,Q,R

2. A S; B P; C P; D P,Q,R

3. A S; B P; C Q; D P,Q,R

4. A R; B P; C P; D P,Q,R




A If are the position vectors of the vertices of the triangle ABC

P 0

respectively. M is the mid point of BC and D is the mid point of AC such that

B If x1, x2, x3 are the roots of the equation

x3 + 2x – 3 = 0, then

=

Q 1

C A straight line intersects the sides AB, AC and AD of a parallelogram ABCD at points B1, C1 and D1 respectively such

that

then a =

R 2

D The area of a triangle with position vectors of vertices as

where are constants and x

S 3

T 4

1. A T; B P; C Q; D P

2. A T; B R; C Q; D P

3. A S; B P; C Q; D P

4. A T; B S; C Q; D P

Question 9 of 20

|Directions:The answer to following question is a single digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.

In the triangle, OAB, . A point P is taken OA such that and a point

Q is taken on OB such that . If the lines AQ and BP are perpendicular and

then find the value of .

1.


If x, y, z are real numbers and 4x2 + y2 + 9z2 – 20x – 12 y – 24 z + 77 = 0. Find the value of (2x + 3z – y).

1.


Three pairs of lines are(i)

(ii) and

(iii) 2x – y – 5 = 0 = 3y – 2z + 5, x – y – 3 = 0 = y – 2z + 3

then correct statement(s) is (are)

1. (i) and (ii) are skew lines

2. (ii) and (iii) are coplanar lines

3. (i) are skews and (ii) are coplanars

4. (i), (ii) and (iii) are coplanars


If the angle between the vectors is given by

, then find the value of , where [.] is g.i.f.

1.


If are the angles between and , and , and respectively,

, then find the number of values of where [.] denotes g.i.f.

1.


If , are the roots of the quadratic equation ax2 + bx + c = 0 and the plane is passing through the line of intersection of the two planes and then ‘b’

1. is a negative number

2. is zero

3. is a positive number

4. cannot be determined


A force of unit acts along the line . The moment of this force about the point (4, 1) along positive z – axis is

1. 0

2. 5

3. – 5

4. none of these


ABC is a triangle right angled at A, the resultant of the forces acting along and

with magnitudes and respectively, is a force along AD, where D is the foot perpendicular from A on to BC, the magnitude of resultant force is

1.

2.

3.

4. none of these


Let A, B and C be three points on a circle. If the forces acting along and are such that their magnitudes are inversely proportional to AB and BC respectively. If the resultant forces make an angle with normal at B to the circle. Then find the value of [ ] where [.] denotes g. if.

1.

Question 18 of 20

|Directions: The answer to following question is a single digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.

If the vectors and are reciprocal to each other, then find the value which is independent of a.

1.


The two points and lie on the plane in which (2, 3, 2) and (1, 2, 1)

are mirror images of each other, find the number of integral values of

1.


Let 0 < a < b < c < d and a, b, c, d are in A.P. If the shortest distance of the plane ax + by +

cz + d = 0 from the origin is unity, then find the value of

1.

PARABOLA ELLIPSE & HYPERBOLA


A point moves on the ellipse whose semi-axes are 4 m. and 3m. with constant speed 1m/sec.

The point shadow of the moving point seems to move an major axis. If v is speed of shadow of the point on the major axis when its distance from the major axis is 1m. Find the value of 11v2.

1.


P and Q are two points on a parabola, if tangent P and Q intersect at right angles then

1. chord PQ always passes through a fixed point

2. chord PQ always intersects the let us rectum

3. the minimum angle subtended by chord PQ at the vertex is

4. the minimum length of chord PQ = length let us rectum


Let us consider family of trajectory where a is a parameter P, Q, R are three points on it such that normal at Q and R meet at P.

Locus of circum centre of triangle PQR is

1.

2.

3.

4.


Let us consider family of trajectory where a is a parameter P, Q and R are three points on it such that normal at Q and R meet at P.

If tangents drawn at the points P, Q, R taken in pairs meet at the points A, B and C, then

is

1.

2. 2

3. 1

4. epending on the positions of the points P, Q and R


Let us consider family of trajectory where a is a parameter P, Q and R are three points on it such that normal at Q and R meet at P.

If tangents drawn at the points Q and R intersect at t and the chord QR touches then locus of the point t is

1.

2.

3.

4. a circle


The line 2x – y = 1 intersects the parabola at points A and B.

Normals at A and B intersect at G. If a third normal two the parabola through G meets the parabola at the point C. Find double of the area of the triangle made by normal at C with coaxes.

1.


A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. If is the angle in radian between the tangents at P and Q, then find [ ] (where [.] is g.i.f.)

1.


The ordinates of two points on the parabola y2 = 12 x are in the ratio 1 : 2, if the locus of the

point of intersection of normals at these points is x = then find the value

of .

1.


Let the 2x + y = 4 line intersect the X-axis at R. If a line through R intersect the hyperbola xy = 4 at S and T, then find the least value of RS . RT

1.

Question 10 of 10|A bar of length 20 cm moves along with its extremities on two fixed straight lines (take as axes) at right angles. If a marked point on it is at 4 cm from one end, then eccentricity of ellipse described by the marked point is

1. 5/4

2.

3. 6

4.

PERMUTATION & COMBINATION

Question 1 of 20|Directions:The following question has four choices out of which only one is correct.

The probability for the line y = mx to intersect the circle

is

1.

2.

3.

4. None

Question 2 of 20|Directions:The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.

A bag contains (P + 1) balls. Now a ball is drawn from the bag and replaced in the bag with one more ball. This process is repeated till (P – 1) more balls are placed in the bag. If the probability of drawing a ball is ln when the bag contains (P + 1) or more balls as

, then find the value of .

1.


Three tangents are drawn at random to a given circle. If the odds against the circle being inscribed in the triangle formed by them be K : 1, find K.

1.

Question 4 of 20|

Directions:The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.

Each of the ‘n’ urns contains 4 white and 6 black balls. The (n + 1)th urn contains 5 white and 5 black balls. One of the (n + 1) urns is chosen at random and two balls are drawn from it without replacement. Both the balls turn out to be black. If the probability that the (n +1)

th urn was chosen to draw the balls is , then find the value of n – 1.

1.


An artillery target may be either at point I with the probability or at point (II) with the

probability . There are 21 shells each of which can be fired either at point I or II. Each

shell may hit the target independently of the other shell with the probability . If n is the maximum number of shells that must be fired at point I to hit the target with the maximum probability, then find value of n – 4.

1.


Four positive integers are taken at random and are multiplied together. Then the probability that the product ends with an odd digit other than 5 is

1.

2.

3.

4. none of these

Question 7 of 20

|Directions: Match the statements / expressions in column-I with the statements / expressions in column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.


Column I Column II

A Probability if

is

P

B Probability if

is

Q 1

C

Let the probability if

is

R

D Probability if

is

S

1. A S, B P, C Q, D P

2. A S, B P, C Q, D R

3. A S, B R, C Q, D P

4. A R, B P, C Q, D S

Question 8 of 20|Directions:The following question has four choices out of which one or more is/are correct.

'n' balls of different colours are placed in n boxes whose colours are same as that of the

balls. If Pn is the probability that no ball goes into the box of its own colour then

1. 1

2. e

3. e–2

4. e–1


A quadratic equation is chosen from the set of all quadratic equations which are unchanged by squaring their roots. The chances that the chosen equation has equal roots is

1.

2.

3.

4. None of these


Let S(n) denote the number of ordered pairs (x, y) satisfying , where n > 1 and x, y, n N. Find the value of S(6).

1.

Question 11 of 20|

Directions:The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.

A fight of stairs has 10 steps. A person can go up the steps one at a time, two at a time, or any combination of 1’s and 2’s. If n is the number of ways in which a person can go up the stairs, then find the value of 90 – n

1.


The length of the sides of a triangle are log1012, log1075 and log10n, where n N. If m is the

number of all possible values of n, then find

1.


Three numbers a, b and c are selected by tossing three six faces dice. If k : 216 are the chances that a polynomial of the form x3 + ax2 + bx + c is divisible by x2 + 1, then find k.

1.


The value of is

1. n2+2n – 2Cn

2. n2 2nCn – 2

3. (n + 1)2 – 1

4. none of these

Question 15 of 20|Directions:The following question has four choices out of which ONLY ONE is correct.

For 1 the value of is

1. nCr+1

2. n+1Cr

3. n+1Cr+1

4. none of these


In a multiple choice question there are five choices of which one or more than one is correct. A candidate will get marks on the question only if he ticks the correct answers. The candidate ticks the answers at random. For the probability of the candidate getting marks on

the question, to be greater than or equal to , what is the least number of changes he should be allowed?

1.

Question 17 of 20| Directions: The following question has four choices out of which only one is correct.

A natural number n is chosen from first 100 natural numbers, the probability that nn is a perfect square is

1.

2.

3.

4. none of these

Question 18 of 20|Directions: The following question has four choices out of which only one is correct.

From 31 tickets consecutively numbered, three are selected at random, the probability that the numbers are in AP is

1.

2.

3.

4. none of these

Question 19 of 20| Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.

Let A1, A2, …, be independent events such that find the value

of

1.

Question 20 of 20|Directions: The following question has four choices out of which only one is correct.

Let S be a set containing n elements and two subsets A and B of S are selected at random then the probability that A B = S and ism

1.

2.

3.

4. none of these

LINES & CIRCLES

Question 1 of 10|Directions: The following question has four options, out of which one or more is/are correct.

If such that then

1. the least value of is 5

2. the greatest value of is 25

3. has 20 natural values

4. is solution of the equation

Question 2 of 10|Directions:The following question has four options out of which one or more is/are correct.

and are two concentric circles, the radius of is the double of . From a point

P on tangents PA and PB are drawn to the circle , which of the centre of the

triangle PAB lies on the circle ?

1. The centroid

2. The orthocentre

3. The circum centre

4. The incentre


and are two circles with lying inside . Another circle S lying inside ,

touches internally and externally. The locus of centre S is a / an

1. parabola

2. circle

3. ellipse

4. hyperbola


The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is.

1.




A ABC is a triangle, P is a point inside it such that the areas of the triangles PBC, PCA and PAB, all are equal then P is

P Centroid

BIf are position vectors of the points A, B and C respectively such that

then point P is

Q Orthocentre

CIf are position vectors of the points A,

B and C respectively and is a point in the plane of triangle ABC such that

then P is

R In-centre

D The straight lines

.

form a triangle, then which of the centre lies inside the triangle

S Circumcentre

1. A Q ; B P; C Q ; D P, Q, R, S

2. A P ; B P; C Q ; D P, Q, R, S

3. A P ; B Q; C Q ; D P, Q, R, S

4. A R ; B P; C Q ; D P, Q, R, S


The circles and intersects at two distinct points A and B. A line through A meets the one circle at P and a parallel line through B meets the other circle at Q. then,

1. the radical axis of the circles is Y axis

2. a and b may be of alternate sign

3. the centre of the locus of the mid point of PQ is

4. the two circles represent two families of circles provided


If (a,0) is a point on a diameter of the circle , then has

1. exactly one real root in (-1,0)

2. exactly one real root in [2,5]

3. distinct roots less than

4. distinct roots less than 5


A conic passing through the point A(1, 4) is such that the segment joining a point P(x, y) on the conic and the point of intersection of the normal at P with the abscissa of the coordinate axis is bisected by y-axis. If (g, f) is the centre of the circle touching the conic at A(1, 4) and passing through its focus, then find greatest value of (g + f)

1.


From a point P outside a circle with centre at C tangents PA and PB are drawn such that

, then length of chord AB is

1. 8

2. 12

3. 16

4. 10


If f(x + y) = f(x) + f(y) – xy – 1 and f(1) = 1 then find

1.

BINOMIAL THEOREM & LOGARITHM

Question 1 of 10|Directions: The following question has four choices out of which ONLY ONE is correct.

n N satisfies the inequality

and E = .

Two dice are tossed, the probability that the sum of the numbers be n is

1.

2.

3.

4. none of these



and E = .

The sum of coefficients in the expansion E is

1.

2.

3.

4. none of these

Question 3 of 10

|Directions: The following question has four choices out of which ONLY ONE is correct.


and E = .

The terms independent of x in the expansion of E are in

1. A.P.

2. G.P.

3. A.G.P.

4. none of these


A function f is defined by f(x) = 7 – xPx – 3 and .

If A = {(x, y) : y = f(x)}, then n(A) equals

1. 6

2. 4

3. 9

4. none of these



The number of rational terms in the expansion of E are

1. 15

2. 10

3. 35

4. none of these



The number of irrational terms in the expansion of E are

1. 35

2. 30

3. 10

4. none of these

Question 7 of 10|Directions: The answer to following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.

If |x| < 1, then find the value of

, where [.] denotes g.i.f.

1.


Let S = (x – 1)10 + (x – 1)9 (x + 1) + (x – 1)8 (x + 1)2 + …….+ (x + 1)10

The number of dissimilar terms in S is

1. 11

2. more than 100

3. 6

4. none of these


Let S = (x – 1)10 + (x – 1)9 (x + 1) + (x – 1)8 (x + 1)2 + …….+ (x + 1)10

Which one is not the constant in expansion of E

1. 2

2. 2. 11C1

3. 11C10

4. 1


Let S = (x – 1)10 + (x – 1)9 (x + 1) + (x – 1)8 (x + 1)2 + …….+ (x + 1)10

If O is the sum of coefficients of odd powers of x and E is the sum of the coefficients of even powers of x, then the wrong statement is

1. E = 211

2. E = O

3. O = 211

4. E = 210

MATRICES & DETERMINANTS


If , then . Find the value of k.

1.


If , , then find the number of real solutions of the system of equations

, , :

1.

Question 3 of 20|Directions: The following question has four choices out of which ONE or MORE is/are correct.

If , where a2 + b2 + c2 = 1, then:

1. F( ) is independent of a, b, c

2. F( ) is periodic with period

3.

4. F( ) < 0


If (1 + x + x2)n = a0 + a1x + a2x2 + ………+ a2nx2n, then the system of equations

an – 3 x + an – 1 y + an + 1 z = 0

an – 6 x + an – 3 y + an + 3 z = 0

an – 14 x + an – 7 y + an + 7 z = 0 has

1. trivial solution only

2. finitely many solutions

3. infinitely many solutions

4. integral solutions

Question 5 of 20|Directions:The following question has four choices out of which ONE or MORE is/are correct.

If A = n N, then

1.

2.

3. trace of

4. trace of


If A = and A3 + aA2 + bA + cI = 0, f(x) = ax2 + bx + c, then the equation f(x) = 0 has

1. a pair of irrational roots

2. a pair of complex roots

3. unequal roots

4. real roots


AIf A =

P 3

B There are 7 green bottles and 8 blue bottles

(assume all bottles to be alike except

for the colour) arranged in a row.

If exactly one pair of green bottles is side

by side in 7m. 3n. 2r ways then the value of m + n + r =

Q 2

C

If is primitive cube root of unity, then period of is

R 6

D If a, b, c are sides of a triangle satisfying

a2 + b2 + c2 – ac – ab = 0, then

S 5

1. A Q; B R; C P; D P

2. A Q; B R; C S; D P

3. A Q; B R; C P; D S

4. A R; B Q; C P; D S

Question 8 of 20|Directions: Match the statements / expressions in Column-I with the statements / expressions in Column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.



A The number of real roots of the equation

is (are)

P 0

BIf the equation has at least

one real solution in , then possible values of a is (are)

Q 1

C If

then

R 8

D

If then

S 9

T 4

1. A Q; B R,S; C S D P

2. A Q; B R,S; C P D R

3. A Q; B R,S; C P D P

4. A Q; B ; P C P D R,S

Question 9 of 20| Directions: Match the statements / expressions in Column-I with the statements / expressions in Column-II and indicate your answer by selecting the appropriate option. Any statement in column -I can correctly match with one or more statement(s) in column –II.


A Determinants of order 2 × 2 are formed using the numbers 0, 1, 2, 3. Then, sum of values of all such determinants is

P –1

B

If is orthogonal,

then the value of

Q 2

C

If Where [.] denotes g.i.f, then

R –2

D

Product of all value of is

S 0

T 1

1. A S; B T; C P,R,S; D P

2. A R; B T; C P,R,S; D S

3. A S; B T; C P,R,S; D R

4. A Q; B T; C P,R,S; D P


Column I Column II

A

If

and then find the value of 5a + b

P 5

B If

and B is inverse of A, then =

Q 1

C If

, then value of c + d is

R 4

D

If A = ,

, then =

S 3

1. A Q, B P, C P, D S

2. A P, B Q, C P, D S

3. A R, B P, C Q, D S

4. A S, B P, C R, D Q


If A = , then

1. A = 0

2. A is an odd function of

3. A = 0 for

4. A is independent of


If A and B are 3 3 matrices such that AB = B and BA = A, then

1. A2 = A and B2 B

2. A2 A and B2 = B

3. A2 = A and B2 = B

4. A2 A and B2 B


If (b – 1)2 > 4ac, then the system of equations

has

1. no real solution

2. one real solution

3. n real solutions

4. two real solutions


The value of the determinant is:

1.

2. – 1

3. 0

4. none of these

Question 15 of 20|Directions:> The following question has four choices out of which ONE or MORE is/are correct.

If , and then wrong statement(s) is/are

1. A(z) = A(x) + A(y)

2. A(z) = A(x) – A(y)

3. A(z) = A(x) (A(y))–1

4.


If A = and B = A + A2 + A3 + A4, then

1. B is symmetric

2. B is invertible

3. AB = BA

4. A is periodic

Question 17 of 20|Directions:The answer to following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.

If is orthogonal, then find the number of ordered triplets of (x, y, z)

1.

Question 18 of 20|Directions:The following question has four choices out of which ONE or MORE is/are correct.

Let A be a 3 3 hermitian matrix with complex elements while P and Q be two 3 3 matrices with real elements. If A = P + iQ,

1. P must be symmetric

2. Q must be symmetric

3. P must be skew symmetric

4. Q must be skew symmetric


Let g(x) = where is a constant, then

1. 0

2. 1

3. – 1

4. None of these


Suppose , , , R are such that sin , sin , sin 0 and

, then cannot exceed

1. 1

2. 0

3.

4. none of these

CHEM

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