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INSTRUCTIONS:1. Answer ALL the questions in a separate answer booklet.2. The question paper consists of four sections and 33

questions.3. There is an internal choice in Section – IV.4. Write answers neatly and legibly.

SECTION – I

Note: i) Answer ALL the questions.

ii) Each question carries 12 mark. 12 12 = 6

1. Find the HCF of 32 and 54.

p2q32. Expand log

r4

3. Write the set builder form of {1, 4, 9, 16, 25, ……100}.

4. Let A = {2, 5, 6, 8}, B = {5, 7, 9, 1}, Find A B.

5. Write the general form of a cubic polynomial in one variable x?

6. Check whether the pair of linear equations 2x 3y = 5 and4x 6y = 15 are consistent?

7. Find the discriminant of 2x2 4x + 3 = 0.

8. The product of two consecutive positive integers is 306.Represent the situation in the form of quadratic equation tofind the integers?

9. Find the 10th term of the AP 5, 1, 3, 7,…………...

10. Write the GP, if a = 256, and r = 12 .

11. Find the volume of right circular cone with radius 3 cm andheight 7 cm.

12. Match the following.

Group A Group B

i) L.S.A. of hemisphere a) 4r2

ii) T.S.A. of hemisphere b) 2r2

iii) T.S.A. of sphere c) 3r2

A) i – a, ii – b, iii – c B) i – b, ii – a, iii – c

C) i – a, ii – c, iii – b D) i – b, ii – c, iii – a

SECTION – II Note: i) Answer ALL the questions.

ii) Each question carries ONE mark. 8 1 = 8

13. Without actually performing the long division, state 77210

will

have a terminating decimal expansion or non-terminating

repeating decimal expansion.

14. Show A B in Venn diagram, where A = {1, 3, 5, 7} andB = {2, 3, 5, 7}.

15. Find the sum and product of the zeroes of the polynomial4x3 + 3x2 + 2x.

16. Give an example for quadratic polynomial whose sum of thezeroes is zero.

17. Cost of 2 kgs brinjal and 4 kgs tomato is Rs.120. After twodays the cost of 4 kgs brinjal and 5 kgs tomato is Rs.160.Express this situation in linear equation.

18. Discuss the nature of the roots of 2x2 + 5x + 2 = 0.

19. Find the 30th term of the AP: 10, 7, 4,………

20. If the total surface area of a cube is numerically equal to itsvolume. Find its lateral surface area?

SECTION – III

Note: i) Answer ALL the questions. ii) Each question carries TWO marks. 8 2 = 16

21. Solve 3x = 5x2.

22. A = {Quadrilaterals}, B = {Square, Rectangle, Trapezium,Rhombus}. State whether A B or B A. Justify youranswer.

23. Find the zeroes of the following graph?

24. Solve the following pair of linear equations usingelimination method.

3x + 2y = 11 and 2x + 3y = 4

25. For what value of ‘k’ the pair of equations 3x + 4y + 2 = 0and 9x + 12y + k = 0 represent coincident lines?

26. Find two numbers whose sum is 27 and product is 182.

27. Which term of the GP : 2, 22, 4, ….. is 128.

28. Find the volume of a sphere of radius 4.2 cm.

SECTION – IV

Note: i) Answer ALL the questions.ii) Each question carries FOUR marks.iii) There is an internal choice for each question.

5 4 = 2029. a) The length, breadth and height of a hall are 8 m. 25 cm.,

6 m. 75 cm. and 4 m. 50 cm. respectively. Determine thelongest rope which can measure the three dimensions ofthe hall exactly.

(OR)

b) A motor boat whose speed is 18 km/h in still water. Ittakes 1 hour more to go 24 km up stream than to returndownstream to the same spot. Find the speed of thestream.

30. a) A = {x : x is a prime number less than 20}, B = {x : x isan odd positive integer less than 10} and C = {x : x is aneven positive integer less than 15} then find

i) (A B) C ii) (A – B) (B – A)

iii) (B – C) (A – B) iv) (A B) C

(OR)

b) Divide p(x) = x4 – 3x2 + 4x + 5 by q(x) = x2 – 2 and findthe quotient and remainder.

31. a) The ratio of incomes of two persons is 9 : 7 and the ratioof their expenditures is 4 : 3. If each of them managesto save Rs.2000 per month, find their monthly income.

(OR)

b) A rectangular park is to be designed whose breadth is3 m less than its length. Its area is to be 4 square metresmore than the area of a park that has already beenmade in the shape of an isosceles triangle with its baseas the breadth of the rectangular park and of altitude12 m. Find its length and breadth.

32. a) A sum of Rs.700 is to be used to give seven cash prizesto students of a school for their overall academicperformance. If each prize is Rs.20 less than its precedingprize. Find the value of each of the prizes.

(OR)

b) From a cylindrical wooden log of length 30 cm and baseradius 7

2 cm. a biggest cuboid of square base is

made. Find the volume of wood wasted.

33. a) Draw the graph of p(x) = x2 – 6x + 9 and find the zeroesof the polynomial.

(OR)

b) Ten students of class X took part in Mathematics quiz. Ifthe number of girls is 4 more than the number of boys.Represent this situation graphically.

SUMMATIVE ASSESSMENT - 2

MATHEMATICS PAPER - I

Time: 2 Hrs. 45 Min. (English Version) Max. Marks: 50

TENTH CLASS MODEL PAPER

2020New

Pattern

1. Find any rational number between thenumbers 10/3 and 11/3.

2. Write 103 = 0.001 in the logarithmic form.3. Write the prime factorization of 343.4. Give example for disjoint sets.5. The value of n(A B) + n(A B) is equal

to ...... 6. Define quadratic polynomial.7. Write a cubic polynomial with zeroes ,

and .8. The graph of the polynomial f(x) = 3x – 7

is a straight line which intersects the x - axis at exactly one point. Name thatpoint.

9. Write the value of 'k' for which the systemof equations x + y = 4 and 2x + ky = 3 hasno solution.

10. If am bl, then how many solutions havethe system of equations ax + by = c and lx + my = n

11. Find the area of the triangle formed by thelines y = x, x = 6 and y = 0.

12. Find the roots of the equation 3x2 – 2

6x + 2.

13. If , are the roots of 6x2 + 42x – 3 = 0,

then find 2+ 2.14. Assertion: The expression 3x4 – 4x3/2 + x2 2

is not a polynomial because the term– 4x3/2 contains a rational power of ‘x’.Reason: The highest exponent in variousterms of an algebraic expression in onevariable is called its degree.

a) both assertion and reason are true andreason is the correct explanation ofassertion.

b) both assertion and reason are true butreason is not the correct explanation ofassertion.

c) assertion is true but reason is false.

d) assertion is false but reason is true.15. Write the general form of a G.P. in which

the first term is ‘r’ and common ratio is ‘a’.

16. A magician triples the chocolates in his tinin every minute. So the number of choco-lates at every minute interval can beexpressed in which progression.

17. If the sum of 3 numbers in an A.P. is 30. Ifthe greatest number is 13, then find itscommon difference?

18. Match the followingGroup A Group B

41. Volume of a cylinder (a) r3

31

2. Volume of a cone (b) r2h3

3. Volume of sphere (c) r2hA. 1a, 2b, 3c B. 1b, 2a, 3cC. 1c, 2b, 3a D. 1a, 2c, 3b

19. Can we say the volume of a sphere is r3times to its total surface area? Justify.

20. Write the combining parts of “Cricket bat”21. Explain why (13 11 3) + (13 11 5)

is a composite number?

22. Without actual division, State whether

rational number 64455

is terminating or non-

terminating, repeating decimal.23. Expand Log 625

2524. Write the set builder form of A B and

A – B25. If A = {5, 6, 7, 8} and B = {7, 8, 9, 10} then

find n(A B) and n (A B)26. Define Division Algorithm for Polynomials.27. Check whether – 2 and 2 are the zeroes of

the polynomial x2 1628. Write the set of values of ‘a’ and ‘b’ for

which the following system of equationshas infinitely many solutions. 2x + 3y = 7and 2ax + (a + b)y = 28.

- T.S.V.S. Suryanarayna Murthy

12 Mark Questions

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1. The d.r’s of the normal to the plane passingthrough the point (2, 1, 3) and the line ofintersection of the planes x + 2y + z = 3 and2x y z = 5 is1) 13, 6, 1 2) 6, 13, 1 3) 1,6,13 4) 1, 13, 6

x22. Let f : R R be defined by f(x) = ,

x4 +1xR then the range of f is

1 11) (0, ) 2) [0, ] 3) [0, ) 4) [0, 2]2 2

3. The equation of the common tangentdrawn to the curves y2 = 8x and xy = 1 is 1) y = 2x + 1 2) 2y = x + 63) y = x + 2 4) 3y = 8x + 2

4. The product of first n odd natural numbersequals

1 n1) 2nCn

nPn 2) () 2nCn nPn2

1 n3) () 2nCn

2nPn 4) 2n 2nCn

2nPn4

5. The length of the tangent drawn from any

point on the circle x2 + y2 + 2gx + 2fy + = 0

to the circle x2 + y2 + 2gx + 2fy + = 0 is

1) 2)

3) 4)

6. The area bounded by the curve y = 8 x2

and the straight line 8x 4y + 11 = 0 is125 32 9 1) 2) 3) 36 4)

6 3 27. A GP consists of an even number of terms.

If the sum of all the terms is five times thesum of those terms occupying the oddplaces, then common ratio is 1) 2 2) 3 3) 4 4) 6

xdx8. The value is

0 4 cos2 x + 9 sin2 x2 2 2 2

1) 2) 3) 4) 12 4 6 3

9. If f(x) = x2 + 2bx + 2c2 and g(x) = x2 2cx +b2 are such that min f(x) > max g(x), then relation between b and c is

b1) no relation 2) 0 c 2

b3) c 4) c

2 b

210.Which of the following is false

1) pp is tautology2) (p) p is tautology3) (p(p q)) p is a tautology4) p p is a controdiction

11.The system of equations 2x + y + z = a, x2y + z = b, x + y 2z = c is consistent. If1) a + b + c = 0 2) a + b + c = 13) a + b + c 0 4) a + b + c 0

12.If a = 3 i

+ 3 j

+ 3 k

, b

= i

+ k

, c =

3 i

+ 3 j

+ k

are coplanar then the

non zero vector b c =

1) 3 i

+ (3 1) j+

3 k

2) 3 i

+ (1 3) j+

3 k

3) 3 i

+ (3 1) j

3 k

4) 3 i

+ (3 1) j+

3 k

sin [x] , [x] 013.If f(x) = [ [x] where [.] denotes

0, [x] = 0

G.I.F then Lt f (x) equalsx 0

1)1 2) 0 3) –1 4) does not exist14. If log (a + c), log (a c), log(a - 2b + c) are

in A.P then 1) a, b, c are in A.P 2) a2, b2, c2 are in A.P.3) a, b, c are in G.P 4) a, b, c are in H.P.

15.If sin, cos, tan are in G.P then cos9+cos6+ 3cos5 1 is equal to1) 1 2) 0 3) 1 4) 2

16.If A is a 3 4 matrix and B is a matrix suchthat ATB and BAT are both defined thenorder of B is 1) 3 4 2) 3 3 3) 4 4 4) 4 3

17.Out of numbers 1, 2, 3,……9, two numbersare choosen at random, so that their sumis an even number, the probability for thetwo choosen numbers to be odd is

3 5 3 21) 2) 3) 4) 8 8 55 5

18.The distance of the point on y = x4 + 3x2 +2x which is nearest to the line y = 2x 1 is

4 3 2 11) 2) 3) 4) 5

5

5

5

dy19.The solution of x2 + (x 2)y = x2e

2x is

dxx2

1) xye2x = x2 + c 2) xye

2x = + c

2x2 x2

3) xy2e2x = + c 4) 2xye

2x = + c

2 2x4 + 1 B

20. If dx = Alog x + + Cx(x2 + 1)2 1 + x2

where C is the constant of integration then1) A = 1, B = 1 2) A = 1, B = 13) A = 1,B = 1 4) A = 1, B = 1

21. In a series of 2n observations, half ofthem equal to 'a' and remaining halfequals to 'a'. If the standard deviation ofthe observations is 2 then a equal to

22. If the 6th term in the expansion of 1

8( + x2logx10) is 5600. Then the value of x is

x8/3

23. If P1, P2, P3, .... Pn are n points on the liney = x all lying in the first quadrant, suchthat (OPn) = n(OPn1)(O is origin), OP1 = 1

and , Pn = ( 2520 2, 2520

2 ) then n =

24. If & are the roots of the equationx2 2x + 4 = 0 then the value of 6 + 6 is

25. The distance of the point (1, 2, 3) fromthe plane x y + z = 5 measured parallel

x y zto = = is

2 3 6

Physics26. In a practical wheat stone bridge circuit as

shown, when one more resistance of 100 is connected in parallel with unknown

l1resistance ‘x’, then ratio become ‘2’. AB l2

is a uniform wire. Then value of ‘x’ must be?

1) 50 2) 100 3) 200 4) 400 27. A 40 F capacitor in a defibrillator is

charged to 3000 V. The energy stored inthe capacitor is sent through the patientduring a pulse of duration 2 ms. Thepower delivered to the patient is :

1) 45 kW 2) 90 kW 3) 180 kW 4) 360 kW

28. A soap bubble (surface tension = T) ischarged to a maximum surface density ofcharge = . When it is just going to burst?Its radius R is given by

2 T1) R = 2) R = 80 80T 2

80T

3) R = 4) R = 80T 2

29. Two point charges q and + q2

are situatedat the origin and at the point (a, 0, 0)respectively. The point along the x-axiswhere the electric field vanishes is

a1) x = 2) x =

2a

2

2a

2a

3) x = 4) x = 2 1

2 + 1

30. A thin convex lens made from crown glass 3( = ) has focal length f. When it is mea2

sured in two different liquids having refrac

4 3tive indices and , it has the focal

3 2lengths f1 and f2 respectively. The correctrelation between the focal lengths is 1) f2 f and f1 becomes negative 2) both f1 and f2 become negative3) f1 = f2 f4) f1 f and f2 becomes negative

31. A metal conductor of length 1 m rotatesvertically about one of its ends at an angu-lar velocity 5 radians per second. If the hor-izontal component of the earth’s magneticfield is 0.2 104 T, then the emf developedbetween the two ends of the conductor is 1) 5 V 2) 50 V 3) 5 mV 4) 50 mV

32. Photoelectric emission is observed from ametallic surface for frequencies v1 and v2of the incident light rays (v1 v2). If themaximum values of kinetic energy of thephotoelectrons emitted in the two casesare in the ratio of 1 : k, then the thresholdfrequency of the metallic surface is

v1 v2 kv1 v21) 2) k 1 k 1

kv2 v1 v2 v13) 4) k 1 k

33. Half-lives of two radioactive elements A andB are 20 minutes and 40 minutes, respec-tively. Initially, the samples have equal num-ber of nuclei. After 80 minutes, the ratio ofdecayed numbers of A and B nuclei will be1) 1 : 16 2) 4 : 1 3) 1 : 4 4) 5 : 4

34. A TV tower has a height of 100 m. Howmuch population is covered by TV broad-cast, if the population density around thetower is 1000/km2 nearly?

1) 39.5 105 2) 19.5 × 106

3) 29.5 107 4) 9 104

35. Two particles A and B start moving from thesame point along the same straight line. Amoves with constant velocity and B moveswith constant acceleration 'a'. During thetime that elapses before B catches A, themaximum distance between the particles is

v2 v2 2v2 v21) 2) 3) 4)

a 2a a 4a36. In the cube of side ‘a’

shown in the figure, thevector from the centralpoint of the face ABODto the central point ofthe face BEFO will be:

1 1 1) a (k i ) 2) a ( i k)

2 21 1

3) a ( j i ) 4) a ( j k) 2 2

37. After perfectly inelastic collision betweentwo identical particles moving with samespeed in different directions, the speed ofthe particles becomes half the initialspeed. The angle between two velocitiesbefore collision is 1) 30 2) 60 3) 90 4) 120

38. Two masses m1 and m2 are placed at adistance L1 apart. The centre of mass ofthe system is at O, m1 is displaced by 'a'towards O and m2 is displaced by 'b' awayfrom O. The distance between the newCOM and point O is

a + b m2a + m1b1) 2)

2 m1 + m2m1 + m2 a m1a + m2b

3) ( ) 4) m1 m2 b m1 + m2

39. A rigid uniform rod of mass 'M' and length'L' is resting on a smooth horizontal table.Two marbles each of mass 'm' and travel-ling with uniform speed 'V' collide with twoends of the rod simultaneously and inelastically as shown. The marbles getstruck to the rod after the collision and

Mcontinue to move with the rod. If m = 6

and V = L mts/sec, then the time taken by the rod to rotate through is2

1) 1s 2) 2s 3) 3s 4) s2

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No. of Questions: 75 Max. Marks: 300 Time: 180 Minutes

JEE Main - 2020 (January)Model Paper

NewPattern

Mathematics

V

m

m

l/2

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