About Mr Prashant Gohil
• Mr Prashant Gohil is a Mathematics Examiner for IB Mathematics since Jan 2007.
• He corrects IB Diploma Mathematics Answer Scripts of a number of International Schools.
• He is working as the IB Diploma Coordinator for a prestigious School in South Mumbai. He is
also the Head of Mathematics Department at this School.
• He has attended a number of Workshops conducted by the IBO. He has attended Workshops at
Seoul (South Korea), Ching Mai (Thailand) and Hongkong.
• He conducts Graphic Display Calculator Workshops for Cranes Software (Authorized distributors
for Texas Instruments). He has conducted a GDC workshop at Navrachna School, Baroda and
Dhirubhai Ambani International School, Mumbai.
• He has also completed a training workshop for IGCSE Mathematics (Cambridge).
• His earlier assignments include:
o IB Mathematics Teacher at BD Somani International School,
o ISC Physics and Calculus AP Teacher at Cathedral and John Connon School
o ICSE Mathematics Teacher at Bombay International School
o ICSE Mathematics and Physics teacher at Palm Beach School
• He has been tutoring students, since 1990, at various University, Pre-university and High School
Level. He has trained students for
o Mathematics and Statistics module at University Level (London School of Economics,
Nottingham University, University of Illinois etc.)
o IB Mathematics Higher Level and Standard Level ( Dhirubhai Ambani International
School, Ecole Mondiale, B.D Somani, Jamnabai Narsee, Fazlani, D.Y. Patil etc)
o HSC Mathematics(Std 11 and 12),
o ICSE Mathematics and Physics (Std 9 and 10)
• He has also tutored students for a number of entrance tests such as
o SAT
o SAT Subject Tests- Mathematics and Physics
o GMAT
• He was a Merit List holder and received a National Scholarship for his performance at B.Sc.
Examinations at University of Mumbai.
• Presently, he is pursuing M.Ed from IGNOU.
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
Last Minute Revision 2011
1. The list price of an article is Rs.4,750. A rebate of
5% is given on it. After the rebate sales tax at the
rate of 6% is charged on it. Find the total cost of
the article to be paid by the buyer.
2. If x + 2y − z
3a − b=
y + 2z − x
3b − c=
z + 2x − y
3c − a
show that each fraction = x + y + z
a + b + c.
3. In the figure [not drawn to scale,] LM is parallel
to BC. BA=12 cm, AL=4 cm and AC=18 cm.
Calculate : (i) the length of CM. (ii)the value
of ratio and then
4. In the given figure AC is the diameter of the semi
circle. BM is perpendicular to AC. If AM = 16cm
and the diameter of the circle is 25 cm, calculate 1
BM 2 Area of the shaded part. use =3.142.
5. Solve the following inequation and represent the
solution set on a number line. 30 − 4(2x−1) > −8
and x ∈ { positive integers}
6. On what sum of money will the difference between
the simple interest and the compound interest for 2
years at 5% p.a will be Rs 75?
7. A part of Rs 5110 was invested in 8% Rs 100
shares quoted at Rs 98 and the rest in 9 % shares
quoted at Rs 105. If the total dividend received
from both is Rs 430, find the sum invested in 8%
shares.
8. Mr Soni invested Rs 9000 in 15% (Rs 10) shares
selling at Rs.45 After a year he sold these shares
at Rs 40 each and invested the proceeds in 10%
(Rs20) shares selling at Rs25. Calculate: -
(i) the number of shares purchased,
(ii) the income from the first investment,
(iii) the income from the second investment;
(iv) percentage return on his original investment in
the second investment.
9. Car A travels x km for every litre of petrol, While
car B travels (x+5) km for every litre of petrol. (i)
Write down the number of litres of petrol used by
car A and car Bin covering a distance of 400 km.
(ii)iIf car A uses 4 litres of petrol more than car B
in covering the 400 km, write down an equation in
x and solve it to determine the number of litres of
petrol used by car B for the journey.
10. A certain sum of money amounts to Rs 6600 in 1
year and to Rs 7986 in 3 years, at compound
interest. Find the sum and the rate of interest.
11. Given P = { x : 5 < 2x − 1 ≤ 11, x ∈ R}
Q ={ x : −1 ≤ 3 + 4x < 23, x ∈ I}
where R = {real numbers}, I = { integers}
Represent P and Q on number lines. Write down
the elements of P ∩ Q.
12. P is a point on the line joining A(4,3) and B(−2,6)
such that 5AP=2BP.Find the co−ordinates of P.
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13. At what rate per cent per annum C.I. will Rs
2,000 amount to Rs 2,315.25 in 3 years?
14. The scale of a map is 1: 210000. A plot of land of
area 83.79 km2 is to be represented on the map.
Find :
(i) The number of kilometres on the ground which
is represented by 1 centimetre on the map.
(ii) The area in km2 that can be represented by 1
cm2.
(iii) The area on the map that represents the plot of
land.
15. Calculate the annual income of five hundred, 12%
shares bought at Rs.150 at a premium of 25%.
When the market value of these shares rose to a
premium of 50%, he sold some shares, just enough
to raise Rs.18,000. Calculate the number of shares
remaining.
16. A trader bought a number of articles for Rs 1200.
Ten were damaged and he sold each of the rest at
Rs 2 more than what he paid for it, thus getting a
profit of Rs 60 on the whole transaction . Taking
the number of articles he bought a x, form an
equation in x and solve it.
17. Solve the inequation: .
Represent your solution on a number line.
18. Find the ratio in which the line joining A(−2,7)
and B(6,1) is divided by the line y=2. Hence find
the co−ordinate of the point where line AB cuts the
line y=2.
19. Use graph paper for this question. Plot the points
A (8,2) and B(6, 4). These two points are the
vertices of a figure which is symmetrical about x =
6 and y−2=0. Complete the figure o the graph .
Write down the geometrical name of the figure.
20. The weights of 60 boys are given in the following distribution table, find the median, lower quartile,upper
quartile, interquartile range.
Weight in kg 37 39 38 41 40
No. of boys 6 10 14 12 18
21. Furniturewalla buys wood for Rs.17,325 including
5 % VAT. He sells the chair made from that wood
for Rs 24,640 including 12 % VAT.
a) What is the tax paid by him on purchase?
b) What is the tax to be collected by him?
c) What VAT will he have to pay to the
government?
22. Points (3, –4 ) and (9 , –4) are invariants points
under reflection in the line L1. Points (–6 ,5) and
(–6, –8) are invariant points on reflection in line
L2.
(i)Name or write equations for the lines L1 and L2.
(ii)Write down the images of points P (3 ,4 ) on
reflection in L1. Name the images as P′. (iii)Write
down the images of Q(-5,-2) on reflection in L2.
Name the images as Q′.
23. A person invested 20%, 30% and 25% of his
savings in buying shares of three different
companies A, B and C which declared dividends
of 10%, 12% and 15% respectively. If his total
income on account of dividends be Rs 4675, find
his saving and the amount which he invested
buying shares of each company.
24. Find the values of a and b so that the polynomial
x3 −4x2 + ax +b is exactly divisible by x2 + x
− 2.
25. If (x+2) and (x-3) are the factors of x3 + ax + b,
find the values of a and b. With these values of a
and b, factorise the given expression.
26. The product of the digits of a two digit number is
24. If its units digit exceeds twice its tens digit by
2; Find the number.
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27. Given that a,b are the roots of x2−5x + 6 = 0, a>
b, frame the equation whose roots are 2a and
3b.
28. Rs125 is divided equally among a certain number
of children; if there were 25 children more, each
would have received 25 paise less. Find the
number of children.
29. List the solution set of 30 − 4 [ 2x − 1] < 30,
given that x is a positive integer.
30. Find the equation of the perpendicular dropped
from the point (−1,2) onto the line joining the
points (1,4) and (2,3).
31. Find the values of x which satisfy the inequation:
Graph the solution set on the real number line.
32. In the figure alongside,find: (i)Co−ordinates of
A,B and E. , (ii)Slope of CD(// to AE) ,
(iii)Equation of CD , (iv)Co−ordinates of C , D ,
(v)The ratio CB : BD.
33. Find the third proportional to
34. Two circles touch externally. The sum of their
areas is 130 cm2 and the distance between their
centres is 14 cm. Find the radii of the circles.
35. A publisher buys paper for Rs. 28,090 including
6% VAT. He makes 1000 notebooks and sells
them at Rs.50 each. He has to charge VAT at 10%
on the finished goods. What VAT is he liable to
pay to the government?
36. A man borrowed Rs 2048 at 6.25% p.a compound
interest. At the end of the first year he repays Rs.
176 and at the end of the second year he repays
Rs253. How much should he pay (i) at the
beginning of the 3rd year; (ii) at the end of the
third year to settle the loan.
37. The line y = 3x − 2 bisects the join of (a,3) and (2,
−5), find the value of a.
38. Solve the given inequation and graph the solution
on the number line.
2y − 5 < y + 2 ≤ 8y + 9 ; y ∈ R.
39. If A = . Find : i At.A ii A.At, where
At is the transpose of matrix A.
40. Miss Mina purchased the following items for her
mother and her neighbour:
Mother : 5 eggs 4 pies
Neighbour: 4 eggs 3 pies
If eggs are 80 p. each, pies 60p. write the above
information as a matrix product, hence find the
total cost of the bill for her mother and neighbour.
41. A person invests Rs 4368 and buys some
hundred-rupee shares at 91. Shares worth Rs 2400
face value are sold at Rs 95 and the remainder
when they have fallen to 85. Find his gain or loss
on the total transaction.
42. From a solid cylinder whose height is 8 cm and
radius 6 cm, a conical cavity of height 8 cm and
of base radius 6 cm is hollowed out. Find the
volume and the total surface area of the remaining
solid.
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43. Framing quadratic equations from the given roots
3 + , 3 −
44. Solve
45. The catalogue price of a data projector is
Rs.69,000 The shopkeeper gives a discount of 9%
on the listed price. He gives a further off-season
discount of 15% on the balance. However, sales
tax at 13% is charged on the remaining amount.
Find: (i) The amount of sales tax a customer has
to pay.
(ii) The final price he has to pay for the
data projector. (Give all your answers to the
nearest rupee)
46. Find the equation of the line AB, through (3,2) and
perpendicular to the line 2y=3x+5. Thus line AB
meets the x−axis at point P and y−axis at point Q.
Find the co−ordinates of points P and Q. Also,
find the area of triangle OPQ, where O is the
origin.
47. The side AB of an equilateral triangle ABC is
parallel to x-axis. Find the slopes of all its sides.
48. The compound interest on a certain sum of money
for 2 years is Rs 1890 and the simple interest for 2
years at the same rate is Rs 1800. Calculate the
sum and the rate of interest.
49. A solid right circular cone of height 20 cm and
base radius 15 cm is melted and casted into
smaller cones of equal sizes with height 5 cm and
base radius 1.5 cm. Find how many cones are
made.
50. Without solving, comment upon the nature of
roots of each of the following equations:
6x2 − 13x + 4 =0
51. The mean lengths of 25 pencils in a box is 20 cm.
It was later discovered that 5 pencils were not a
part of that box and were removed. The lengths of
the pencils that were removed was 12cm, 10 cm,
8cm, 11cm and 9 cm respectively. Calculate the
average length of the remaining pencils.
52. The line 4x−3y+12=0 meets x−axis at point A.
Find the co−ordinates of A. Further, find the
equation of the line through point A and
perpendicular to 4x−3y+12=0.
53.
54. Find the equation of the line which passes through
the point (−2, 3) and is perpendicular to the line 2x
+ 3y + 4 = 0.
55. Five year’s ago, a woman’s age was the square of
her son’s age. Ten years hence her age will be
twice that of her son’s age. Find:
(i) the age of the son five years ago
(ii) the present age of the woman.
56. The roots of x2 − 6px + 45= 0 are p and 5p. Find
the values of p.
57. If x: y be the sub duplicate ratio of x−a : :y−a ,
prove that
58. (1,5) and (−3,−1) are the co−ordinates of vertices
A and C respectively of rhombus ABCD. Find the
equations of the diagonals AC and BD.
59. Draw an ogive for the following distribution:
Income in Rs 120−140 140−160 160−180 180−200 200−220 220−240
No of
employees
30 72 90 80 70 28
Use the ogive i the median income, iithe number of employees whose income exceeds Rs190.
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th.- MATHS, PHYSICS. Call 2380 00 92.
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60. P is the solution set of 7x − 2 > 4x + 1 and Q is
the solution set of 9x − 45 5 (x − 5); where x
R. Represent: (i) , (ii) P − Q , (iii)
on different number lines.
61. where Mt is transpose of M.
62. The figure alongside
given represents the lines y=x+1 and y= x−1.
Write down the angles that the lines make with the
positive direction of the x−axis. Hence determine
63. Spherical marbles of diameter 1.4 cm are dropped
into cylindrical beaker containing some water and
are fully submerged. The diameter of the beaker is
7 cm. Find how many marbles have been dropped
in it if the water rises by 5.6 cm.
64. The compound interest on a certain sum of money
for the fourth year is Rs.1452 and for the fifth
year is Rs. 1597.20. Find:
a) the rate of interest,
b) the compound interest for the sixth year,
c) the compound interest for the third year.
65. Without solving, comment upon the nature of
roots of each of the following equations:
7x2 − 9x + 2 =0
66. The following table gives the height of the plants in centimeter. if the mean height of the plants is 60.95 cm, find
the value of ‘f’.
Height [cm] 50 55 58 60 65 70 71
No. of plants 2 4 10 f 5 4 3
67. If x3 + ax2 +bx + 6 has x − 3 as a factor and
leaves a remainder 8 when divided by x +1.
Find a and b.
68. A man sells 60, Rs 15 shares of a company paying
12 % dividend, at Rs.21 each and invests the
proceeds in Rs 6 shares of another company at Rs
9 each. Find his change in income, if the second
company pays a dividend of 8 %.
69. A company declares 12% dividend to the
shareholders. If a man receives Rs. 5400 as his
dividend, find the nominal value of his shares.
70. If A= ; find the matrix X
such that 2AX=B.
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th.- MATHS, PHYSICS. Call 2380 00 92.
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71. Describe and draw the following loci
i ) A and B are two fixed points, the locus of a
point P such that angle APB = 90'.
ii) AB is a chord of a circle, the locus of a point in
the circle so that it is equidistant from A and
B.
iii) The locus of a point, which is equidistant from
two fixed points.
iv) The locus of a point, intersecting straight in
which is equidistant from two intersecting
lines.
v ) The locus of the mid-points of all equal chords
in a circle.
vi) The locus of mid-points of all parallel chords
in a circle
vii) The locus of a point equidistant from two
concentric circles.
viii) The locus of the centre of a given circle of
which rolls around the outside of a second
circle and is always touching it.
ix) The locus of the centres of all circles that are
tangent to both sides of a given angle.
x) The locus of the centres of all circles passing
through two fixed points.
xi) The locus of points equidistant from three
given non-collinear points.
xii) The locus of vertices of all isosceles triangles
having a common base.
xiii) The locus of the vertices of all triangles with
a given base and a given altitude.
xiv) The locus of a point P so that AB2 = AP2 +
BP2 where A and B are two fixed points.
xv) The locus of a point P so that ∆ ABP is
constant, where A and B are two fixed points.
xvi) The locus of a point in rhombus ABCD so
that it is equidistant from
72. Solve, 2 significant figures: x2 + 9x + 5 = 0
73. Find the 2×2 matrix X which satisfies the equation
74. At what rate will a sum of money become 1.96
times of itself in 2 years at compound interest?
75. Points (5 , 1) and (−2, 1) are invariants points
under reflection in the line L1. Points (2, −6) and
(2 ,3) are invariant points on reflection in line L2.
Give the equation of line L1 and L2.Write down the
images of P(2,4) and Q (-3,8) on reflection in L2.
Name the images as P′′ and Q′′respectively.
76. Do not use a graph paper. Points A (2, −1) and B
(2 , 4) are invariant when reflected in line L1.
Points C (−3 , 5) and D (4, 5) are invariant when
reflected in line L2. (i) Find the equation of line L1
and L2; (ii) Reflect point A in line L2 (iii) Reflect
point C in line L1.
77. If the speed of a car is increased by 10 km per hr,
it takes 9 minutes less to cover a distance of 18
km. Find the speed of the car.
78. A shopkeeper buys a certain number of books for
Rs.720. If the cost per book was Rs.5 less, the
number of books that could be bought for Rs.720
would be 2 more. Taking the original cost of each
book to be Rs. x, write an equation in x and solve
it.
79. Framing quadratic equations from the given roots
80. In an auditorium, the number of rows was to the
number of seats in each row. When the number of
rows was doubled and the number of seats in each
row was reduced by 10, the total number of seats
increased by 300. How many rows were there?
81. Three consecutive natural numbers are such that
the square of the middle number exceeds the
difference of the squares of the other two by 32.
Assume the middle number to be x and form a
quadratic equation satisfying the above statement.
Hence; find the three numbers.
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th.- MATHS, PHYSICS. Call 2380 00 92.
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82. Mr. Mistry has 120 shares of nominal value of Rs
100 and he decides to sell them when they are at a
premium of 60% . He invests the proceeds in
shares of nominal value of Rs. 50, quoted at 4%
discount, paying 15% dividend annually. Calculate
: (i) the sale proceeds; (ii) the number of shares
he buys; and (iii) the annual dividend from these
shares.
83. The hypotenuse of a right−angled triangle is 17
cm and the sum of other two sides is 23 cm. Find
the lengths of its sides.
84. Find the equation of the mirror line in each of the cases.
Sr. No Point Image Equation of the
mirror line
1 (2 ,4) (2 , 8)
2 (-6 , 8) (4 , 2)
3 (3 , -2) (3 , 0)
4 (2 , 3) (6 , 3)
5 (-3 , 7) (-4 , 0)
6 (2 , 5) (- 1 , 8)
85. Which is a better investment : 12 % at Rs 120 or
8% at Rs 90 ?
86. Calculate the amount and compound interest on
Rs.14500 at 6 % p.a. for 12 months compounded
half yearly.
87. If q is the mean proportional between p are r,
prove that:p2−q2 + r2 = q4
88. The mean age of a class of 40 students is 13
years. The mean age of 25 boys in the class is 13
years 3 months, what is the mean age of the girls
in the class.
89. The roots of x2−4kx + 12 = 0 are k and 3k. Find
the value of k.
90. An article is sold for Rs 810. It was sold after a
discount of 10% on the list price and then adding
sales tax at a rate of 20%. Calculate the list price
of the article.
91. If A and B are square matrices, is ( A+ B)2 = A2 +
2 AB + B2? Explain.
92. The equation of a line is x − y = 4. Find its slope
and y−intercept. Also, find its inclination.
93. In what ratio is the join of (4,3 and (2,−6 divide by
x−axis. also find the co−ordinates of the point of
intersection.
94. A sum of money is lent out at compound interest
for 2 years at 20 % p.a., compound interest being
reckoned yearly. If the same sum of money was
lent out at compound interest at the same rate per
cent per annum, compound interest being reckoned
half-yearly, it would have fetched Rs 482 more by
way of interest. Calculate the sum lent out.
95. The abscissa of a point is four times its ordinate.
Find the co−ordinates of the points if its distance
from (6,2) is units.
96. Lines 2x−by+5=0 and ax+3y=2 are parallel to
each other. find the relation connecting a and b.
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
97. The daily expenditure of 50 students is given below:
Expenditure [Rs.] 10−20 20−30 30−40 40−50 50−60 60−70
No. of students 5 14 a b 11 8
The mean daily expenditure per student is Rs.40.20 p. Find the values of a and b.
98. The points (K, 3), (2, −4) and (−K + 1, −2) are
collinear, Find K.
99. A merchant buys an article for Rs. 44,000/- and
sells it to a customer for Rs.68,000/-. If the VAT
rate is 11%; find the VAT paid by the merchant.
100. In , given A (2 , 4), B (−4, −6) and C (0 ,
8). Find :(1) equation of median AM (2) altitude
BN (3) perpendicular bisector of AB.
101. Find the equation of the line passing through (5,
−3) and parallel to x−3y = 4.
102. Find the positive integers p and q such that
p qÈ
ÎÍÍÍÍ
˘
˚˙̇˙̇
p
q
È
Î
ÍÍÍÍÍÍÍÍÍÍÍÍ
˘
˚
˙̇˙̇˙̇˙̇˙̇˙̇
= 25[ ]
103. Two solid spheres have surface areas of 5 cm2 and
45 cm2 respectively and the mass of the smaller
sphere is 3 kg. Find the mass of the larger sphere.
104. Given A(x+2,−2) and B (11,6). Find x if AB=17.
105. The centre of a circle of radius 13 units is the
point (3,6). P (7,9) is a point inside the circle.
APB is a chord of the circle such that AP=PB.
Calculate the length of AB.
106. Attempt this on a graph paper. (i)Plot A (2 ,2), B (
0 , − 2) and C (4 , − 2). Locate M, the midpoint of
AC. (ii)Complete the figure ABDC, so that it is
symmetrical about the line BC. Write the
coordinates of D. write the geometrical name of
the figure ABDC. (iii)Is the figure ABDC
symmetrical about AD ? Locate , the image of
M on reflection in BC. Write the coordinates of
.
107. Find the equation of the line passing through
(−5,7) and parallel to (i)x − axis (ii)y − axis.
108.
The diagram represents two inequations A and B on real number
lines. (i) Write
down A and B in set builder notation. (ii) Represent A ∩ B,
A ∩ B′ on two different number lines.
109. Salman purchased a pair of shoes for Rs.7920,
which included sales tax. If the rate of sales tax is
10%, find the list price of shoes.
110. Factorise: x3 − 37x − 84.
111. The centre of a circle is (2k −1, 3k +1) and it
passes through the point (−3,−1). Find the value or
values of k, if the diameter of the circle is of length
20 units.
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112. An article is bought at a certain price and a VAT
at a rate of 10% was paid. It was sold for
Rs.1,600 more for which he has to charge 11 %
VAT. If he deposits Rs. 816 as VAT with the
government, find the cost price of the article.
113. If x =a + 3b + a − 3b
a + 3b − a − 3b, prove that 3bx
2 -
2ax + 3b = 0.
114. Draw two intersecting lines to include an angle of
30°. Use ruler and compasses only to locate
points which are equidistant from these lines and
also 2 cm away from their point of intersection.
How many such points exist?
115. Use ruler and compasses only for this question.
Draw a circle of radius 4 cm and mark two chords
AB and AC of the circle of length 6 cm and 5 cm
respectively.
(i) Construct the locus of points, inside the circle,
that are equidistant from A and C. Prove your
construction.
(ii)Construct the locus of points, inside the circle,
that are equidistant from AB and AC.
116. Draw a histogram for the frequency distribution and use it to find the mode. Also, calculate the Arithmetic mean.
Marks 31−40 41−50 51−60 61−70 71−80 81−90 91−100
frequenc
y
5 9 12 18 15 6 3
117. Points A and B have co-ordinates (–1, –5 ) and
(–1 , –1) respectively. Find:
(i)The equation of the mirror line so that A is
image of B.
(ii) the equation of the line in which both the
points are invariant.
118. Find two numbers such that the mean proportional
between them is 12 and the third proportional to
them is 96.
119. Ms. Bachan goes to a shop to buy a walkman,
costing Rs.3638. The rate of sales tax is 7%. She
tells the shopkeeper to reduce the price of the radio
to such an extent that she has to pay Rs 3638
inclusive of sales tax. Find the reduction needed in
the price of the radio.
120.
121. Draw a cumulative frequency table, plot an ogive for the data given below and form the cumulative frequency
curve, find : (i) the median marks, (ii) the lower quartile, (iii) the upper quartile , (iv)Find passing marks if 80%
of students passed, (v)If students scoring more than 75% mark are awarded scholarship, how many get?
Mar
ks
1−10 11−20 21−30 31−40 41−5
0
51−60 61−7
0
71−80 81−
90
91−
100
No.o
f
pupil
s
4 6 7 16 25 21 12 5 3 1
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122. Solve
123. Points (−2,−1) and (1,8) lie on the line y = mx + c.
Find the numerical values of m and c.
124. A map of a country is drawn to the scale 1 :
400000. Calculate: (i) the distance on the map
which will represent an actual country side
distance of 40 km. (ii)the area in cm2 on the map
which would represent an actual area of 64 km2.
125. What point on x−axis is equidistant from points
(7, 6) and (−3,4).
126. Solve :
127. Two numbers are in the ratio 2:5 and if 3 be added
to each, they are in the ratio 5:11. Find the
numbers.
128. Match the equations A, B, C, D with the lines L1 ,
L2 , L3, L4 , whose graphs are roughly drawn in
the adjoining diagram.
Hence, find the point of intersection of B and C.
129. Find the equation of the perpendicular bisector of
the line segment obtained on joining the points
(6,−3) and (0,3).
130. A triangle whose area is 12 cm2 is transformed
under enlargement about a point in space. If the
area of its image is 108 cm2, find the scale factor
of the enlargement.
131. A person invested Rs 16,000 and Rs 20,000 in
buying shares of two companies which later on
declared dividends of 12% and 8% respectively.
He collects the divided and sells out all his shares
at a loss of 2% and 3% respectively on his
investment. Find his total earning from the above
transaction.
132. Solve for matrix X if
133. If (p − 1) x + 2y = 4 is perpendicular to x + y = 3
find p.
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134. Calculate the mean, median and mode:
X 0 2 4 6 8 10
F 2 3 5 7 2 1
135. Points (5 , 0) and (−2, 0) are invariants points
under reflection in the line L1. Points (0, −6) and
(0 ,3) are invariant points on reflection in line L2.
Write down the images of points P (3 ,4) and Q (
−5 , −2) on reflection in L1. Name the images as P′
and Q′ respectively.
136. If 6x2 − 3y2: x2 + y2 is equal to 6:25, find the
value of x:y.
137. If
138. Plot the points A (2,1), B (2,8), C(5,5) and D
(5,−2) on graph paper. (i) Name the figure ABCD;
(ii) Write down the equation of its line of
symmetry. (iii) If P, Q are the images of A and D
when reflected in the line CD. Write down the
co−ordinates of P and Q. Name the completed
figure ABPQD.
139. Mukesh deposited Rs.220/- per month in a bank
for 24 months under the Recurring Deposit
Scheme. What will be the maturity value of his
deposits, if the rate of interest is 7 % per annum
and interest is calculated at the end of every
month?
140. By purchasing Rs 25 auto shares for Rs 40 each a
man gets 4% profit on his investment. What rate
per cent is company paying? What is his dividend
if he buys 120 shares?
141. Complete the following:
Sr. No. P P′ Mirror line Line in which
points are
invariant
1 (2 , 0) (- 4 , 0)
2 (0 , 3) (0 , - 6)
3 (3 , 1) (9 , 1)
4 (2 , 7) (2 , -1)
142. Solve, 2 significant figures: x2 − 10x + 6 = 0
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143. Mr. Pascal invested Rs 8000 in 8% Rs 100 shares
selling at Rs80. After a year he sold these shares
at Rs 75 each and invested the proceeds in Rs 90
shares selling at Rs 100 with a dividend of 12%.
Calculate : (i.)his income from the first
investment; (ii) his income from the second
investment, (iii) the increased percentage return on
his original investment.
144. Without solving, comment upon the nature of
roots of each of the following equations:
25 x2 −10x + 1 = 0
145. A owns 560 shares of a company. The face value
of each share is Rs 25. The company declares a
dividend of 9%. Calculate : (i) the dividend A
would receive; (ii) the rate of interest on his
investment considering that A bought these shares
at Rs 30 per share in the market.
146. In the figure given alongside AB and CD are the
lines 2x−y+6=0 and x−2y=4 respectively.(i) Write
down the co−ordinates of A,B,C and D; (ii) Prove
that triangles OAB and ODC are similar; (iii) Is
the figure ABCD cyclic? Give reasons for your
answer.
147. Prove that : If two triangles are similar the ratio of
their areas equals ratio of the square of their
corresponding sides.
148. A spherical ball of lead has been melted and made
into identical small balls each with radius equal to
half the radius of the original one. How many such
balls can be made?
149. If b is the mean proportional between a and c.
Prove:
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150. Fill in the blanks:
Sr.no. point Reflect in Image
1 (2 , 6) x-axis
2 (3 , −4) y-axis
3 (−2 , 4) y = 0
4 (6 , −2) x = 0
5 (−2 , −4) origin
6 (−3 , 2) (−3, −2)
7 (−3 , 7) (3 , 7)
8 (3 , 4) x = −1
9 (−2 , 3) y = 5
10 (−2 , 8) (−2 , 4)
11 (4 ,−3) (4 , 5)
151. A girl goes to her friends house, which is at a
distance of 12 km. she covers half the distance at a
speed of x km/hr. and the remaining at a speed of
x+2 km/hr. If she takes 2 hrs. 30 minutes to cover
the whole distance, find ‘x’.
152. Draw a triangle ABC in which AB = 6 cm, BC =
4.5 cm and AC = 5 cm.
(i) Draw and label the locus of the centres of all
circles which touch AB and AC,
(ii)the locus of the centres of all the circles of
radius 2 cm which touch AB.
Hence, construct the circle of radius 2 cm which
touches AB and AC.
153. A =0 4
3 0
6
−1
È
Î
ÍÍÍÍÍÍÍÍÍÍÍÍ
˘
˚
˙̇˙̇˙̇˙̇˙̇˙̇
and
B =
sin00
−cot450
−5
tan450
cose c 300
−2cot230
0
È
Î
ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ
˘
˚
˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙̇
,
find if possible (i)AB , (ii) BA , (iii)A2.
154. Use ruler and compasses only for the following
question. Construct triangle BCP where CB = 5
cm , BP = 4 cm and ∠ PBC = 45°,Complete the
rectangle ABCD such that:
(i) P is equidistant from AB and BC; and
(ii) P is equidistant from C and D.
Measure and write down the length of AB.
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155. A is represented on number line as given below.
B is also represented on a number line given below
.
a)Write A in the set builder form.
b) Write B in the set builder form.
c) On the given number line show A ∩ B.
d) On the given number line show A ∪ B
.
e) On the given number line show A ∩ B'.
f) On the given number line show A'∩ B.
156. Parul holds 1350; Rs 100 shares of a company
that pays 15% dividend annually Calculate her
annual dividend. If she had bought these shares at
40% premium, what percentage return does she
get on her investment? Give your answer to the
nearest integer.
157. Points (5 , 0) and (−2, 0) are invariants points
under reflection in the line L1. Points (0, −6) and
(0 ,3) are invariant points on reflection in line L2.
Name or write equations for the lines L1 and L2.
158. A man invests Rs 2,400 for two years at
compound interest. After one year this money
amounts to Rs 2,550. Find the interest for the
second year correct to the nearest paise.
159. In the figure given alongside BC parallel to DE.
Area of triangle ABC = 150 cm2, area of
trapezium BCED = 66 cm2, DE = 42 cm.
Calculate the length of BC.
160. The value of a machinery in 2007 is Rs.29160. If
the rate of depression is 10 % p.a., find the value
of the computer in 2004.
161. A certain sum of money is invested for three years
at 10% p.a., if the compound interest for the
second year is Rs 880, calculate the amount at the
end of three years.
162. The line passing through (−4, −2) and (2, −3) is
perpendicular to the line passing through (a, 5)
and (2, −1). Find a.
163. Two isosceles triangles have equal vertical angles
and their areas are in the ratio 16 : 25. Find the
ratio of their corresponding heights.
164. A foot path of uniform width runs round the inside
of a rectangular field 16m long and 14 m wide. If
the path occupies 56 m2, Find the width of the
path.
165. If A, B and C are 2X2 matrices, is A. (B.C ) =
(A.B) C? Why?
166. The compound interest on a certain sum of money
at a certain rate is Rs 300 for the first year and the
compound interest for 2 years is Rs 612. Find the
sum and the rate of interest.
167. Calculate the co−ordinates of the centre of the
circle which passes through the points (4,2),
(2,−2) and (7,−7). Find the value of its radius.
Also, calculate the centroid of ∆ formed by joining
the three points.
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168. If A and B are square matrices and if A.B = 0,
then A = 0 or B = 0? Why?
169. For what values of a and b, the expression 2x3 +
ax2 + b x + 3 is divisible by
2x2 + x −1.
170. The mean of 1,7,5,3,4 and 4 is m.The numbers
3,2,4,2,3,3 and p have mean m−1 and median q.
Find p and q.
171. If A= , B= and (A+B)2= A2 +
B2, find the value of x.
172. Find the co−ordinates of the points of trisection of
the line joining the points (−3,0) and (6,6).
173. A man invests Rs 46,875 at 4% per annum
compound interest for 3 years. Calculate : (i) The
interest for the 1st year; ( ii) The amount
standing to his credit at the end of the second year;
(iii) The interest for the 3rd year.
174. If x =
175. By investing Rs 7500 in a company paying 10%
dividend an income of Rs.500 is received. What
price is paid for each Rs 100 share?
176. Find the ratio compounded of the reciprocal ratio
of 15:28 , the sub−duplicate ratio of 36:49 and
triplicate ratio of 5 :4.
177. Solve :
178. Lines mx+3y+7=0 and 5x−ny−3=0 are
perpendicular to each other. find the relation
connecting m and n.
179. A motor boat whose speed is 15 km/hr in still
water goes 30 km downstream and comes back in
a total of 4 hour 30 minutes. Determine the speed
of the stream.
180. In what time will Rs 1500 yield Rs 496.50 as
compound interest at 20% per compounded
semi-annually?
181. Using the information in the given histogram,
calculate the mean.
182. A model of a missile is made to a scale of 1:600.
(i) The length of the model is 6 m; calculate the
length of the missile.
(ii) The area of the surface of the missile is
7,200,000 m2; find the surface area of the model.
(iii) The volume of the model is 200 litre;
calculate the volume of the missile is m3.
183. Prove that the points A(−5,4),B(−1,−2) and C(5,2)
are vertices of an isosceles right angled triangle.
Find the co−ordinates of D so that ABCD is a
square.
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184. The results of an examination are tabulated below:
Marks less than 10 20 30 40 50 60 70 80 90 100
No. of candidates 0 25 42 65 95 120 128 135 148 150
Draw an ogive for the above data and find :(i) the number of candidates who got less than 45; (ii) the number of
candidates who got more than 75.
185. If [2x−1] : [5x+15] be in the duplicate ratio of 3 :
5, find x.
186. A can do a piece of work in ‘x’ days and B can do
the same work in x+8 days . If both working
together can do it in days; Calculate ‘x’.
187. The marks obtained by 19 boys are given :
27,36,22,31,25,26,33,24,37,32,29,28,36,35,27,26
,32,35,28, find the (i) median, (ii) lower quartile,
(iii) upper quartile and (iv) Interquartile range.
188. The machinery of a particular factory is valued at
Rs 18400 at the end of 1990. If it is supposed to
depreciate each year at 8% of the value at the
beginning of the year, calculate the value of the
machinery at the end of 1989 and 1991.
189. Calculate the mean from the following ogive.
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190. In the given ∆ PQR, LM is parallel to QR and
PM:MR = 3:4.Calculate the value of ratio:(i)
and then . (ii) . (iii)
, (iv ) .
191. If x + a is a common factor of expressions
f(x) = x2 + px + q and g(x)=x2 +mx + n; show that
.
192. If .
193. John deposited Rs.260/- per month in a bank for 9
months under the Recurring Deposit Scheme. If
the maturity value of his deposits is Rs.2437.5,
what is the rate of interest given that the interest is
calculated at the end of every month?
194. If
195. The following data gives the frequency distribution for the no. of apples in the farm:
Weight.in grams 60−64 65−69 70−74 75−79 80−84
No. of apples 7 11 22 16 4
Calculate: (a) the mean weight of the apples in grams,(b) If the weight of each apple is increased by 5 gm, what
will be the new mean weight be? (c) the total weight of all the apples in the above table. (d) if the number of
apples in each category is doubled, what is the new mean weight (e)the medial class of the above data. (f) the
modal class of the above data.
196. A page from the pass book of Mr. Shah is given below. Find the interest for the period January to December
1998 at 4.5% per annum.
Date Particulars Debit (Rs.) Credit (Rs.) Balance (Rs.)
Jan. 1 Balance B/F 7,500 = 00
March 7 By Cheque 1,875 = 00
March 10 To Cash 625 = 00
July 17 To Self 3,250 = 00
Oct. 5 By Cheque 2,160 = 00
Dec. 19 To Cheque 1,340 = 00
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197. By selling at Rs 77, some 2 ¼ % shares of face
value Rs 100 and investing the proceeds in 6%
shares of face value Rs 100 selling at Rs 110 a
person increased his income by Rs 117 a year.
Find : (i) How many shares did he sell? (ii) How
many shares did he buy? (iii)What was his original
income?
198. Framing quadratic equations from the given roots
a, −b
199. Framing quadratic equations from the given roots
−1 ± 2
200. Factorise the following, using Factor theorem:
x3 − 4x2 + x +6.
201. Solve : x2 = 25
202. Find the equations of the lines passing through
point (−2,0) and equally inclined to the
co−ordinate axes.
203. Given . Find x
and y.
204. One pipe can fill a cistern in 3 hours less than the
other. The two pipes together can fill the cistern in
6 hours 40 minutes. Find the time that each pipe
will take to fill the cistern.
205. Evaluate x and y if ;
206. A circus tent is cylindrical to a height of 4 m and
conical above it. If it is diameter is 105 m and its
slant height is 80 m, calculate the area of canvas
required. Also find the total cost of canvas used at
Rs.15 per metre if the width is 1.5 m.
207. Find the order of matrix M and hence, find matrix
M in each of the following
M×
208. The compound interest, calculated yearly, on a
certain sum of money for the second year is Rs
630 and for the third year is Rs 661.50. Calculate
the rate of interest and the sum.
209. Solve :x2 − 5x = 0
210. A sector of radius 35 cm is cut out of a thin
cardboard with angle 1440. It is folded into a cone
of maximum size. Find the curve surface and the
volume of the cone. Take = 22/7.
211. Find the ratio in which the line joining (3,4) and
(−2,8) is divided by the line x-=1.
212. Mr. Ashok has an account in the Central Bank of India. The following entries are from his pass book:
Date Particulars Withdrawals Deposits Balance
01.01.05 B/F 1200.00
07.01.05 By cash 500.00 1700.00
17.01.05 To cheque 400.00 1300.00
10.02.05 By cash 800.00 2100.00
25.02.05 To cheque 500.00 1600.00
20.09.05 By cash 700.00 2300.00
21.11.05 To cheque 600.00 1700.00
05.12.05 By cash 300.00 2000.00
If Mr.Ashok gets Rs.167.50 as interest at the end of the year where the interest is compounded annually,
calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December, 2005.
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2011 LMR contd
213. A card is drawn from a well-shuffled pack of 52
cards. Find the probability that the card drawn is:
(i)a spade (ii)a red card (iii)a face card (iv)5 of
heart or diamond (v)Jack or Queen (vi) ace and
king (vii)a red and a king (viii)a red or a king
Read carefully and answer fully showing all steps
of working
214. An aeroplane flying horizontally 1 km above the
ground is observed at an elevation of 600. After 10
seconds, its elevation is observed to be 300; find
the uniform speed of the aeroplane in km per hour.
215. Quad OABC is a parallelogram. Calculate
∠OAB.
216. Prove : sin (90−A)cos (90−A)=tanA cos2A
217. The length of the direct common tangent to two
circles of radii 12 cm and 4 cm is 15 cm.
Calculate the distance between their centres.
218. A person standing on the bank of a river observes
that the angle of elevation of the top of a tree
standing on the opposite bank is 600. He moves 40
m away from the bank, he finds the angle of
elevation to be 300, find : i the height of the tree;
iithe width of the river.
219. A copper wire when bent in the form of a square
encloses an area of 121 cm2. If the same wire is
bent into the form of a circle, find the area of the
circle.
220. The area of a circle, inscribed in an equilateral
triangle, is 154 cm2. Find perimeter of the triangle.
Take = 1.73. Give answer correct to one
decimal place. Calculate the area of circumcircle
to the above triangle.
221. Given that two circles intersect at T and S. BA
and CD are produced to meet at P.
i Prove that PATD is a cyclic quadrilateral.
iiProve PA PB = PC PD.
iiiIf PA = 3 cm, AB = 7 cm, PD = 4 cm, Find PC.
222. Evaluate: sin 150 cos 750 + cos 150 sin 750
223. The height of a tree is times, the length of its
shadow. Find the angle of elevation of the sun.
224. In the given figure ∠XYZ = 52° and ∠YZX =
70°. Calculate ∠ABC, ∠BAC, ∠ACB.
225. Prove :
226. In a circle with centre O. Chords BA and DC are
produced to meet at a point P. If PA=2 cm,
AB=7cm and PC=3 cm. Find CD.
227. The given diagram represents the area swept by
the wiper of a car with the dimensions given in the
diagram, calculate the shaded area swept by the
wiper. Take
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228. The angles of elevation of the top of a tower from
two points on the ground at distances a and b
metres from the base of the tower and in the same
straight line with it are complementary. Prove that
the height of the tower is metre.
229. In a circle with centre O, diameter AB is produced
to point T. TC is tangent to the circle, if∠CAB =
24°,
Calculate ∠CTB.
230. In the adjoining diagram chords AB and CD of
the circle are produced to meet at O. Prove that
triangle ODB and OAC are similar. Given that
CD = 2 cm, DO = 6 cm and BO = 3 cm, Calculate
AB.
231. An equilateral triangle of side 8 cm is inscribed in
a circle. Find the radius of the circle.
232. In the given figure, AB is a side of a regular five
sided polygon and AC is a side of a six sided
polygon inscribed in the circle, centre S. Calculate
the sizes of i∠ASB; ii∠ACB; iii∠ABC.
233. Evaluate: sin420sin480−cos420cos480
234. In the diagram I is the incentre of triangle XYZ,
XI produced meets the circum circle of triangle
XYZ at W. ∠YXZ = 50°, ∠XYZ=70°. Calculate :
i∠WYZ;
ii∠IYZ;
iii∠YIW.
235. A chord AB subtends an angle of 1210 at the
centre O of the circle. If the length of the chord is
20 cm; calculate the radius of the circle.
236. At a point on level ground, the angle of vertical
tower is found to be such that its tangent is 5/12.
On walking 192 metres towards the tower, the
tangent of the angle is found to be 3/4. find the
height of the tower.
237. Calculate the circumference of a circle whose area
is equal to the sum of areas of the circles with
diameters 24 cm, 32 cm and 96 cm.
238. Prove :
239. The upper part of tree, broken over by the wind,
makes on angle of 450 with ground ; and distance
from the root to the point where the top of the tree
touches the ground, is 15m. What was the height
of the tree before it was broken?
240. Prove :
241. In the figure PT is a tangent to the circle. PA = 2
cm and AB = 16 cm. Prove that PT2 =PA. PB.
Hence, find PT.
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242. From the top of a light house, it is observed that a
ship is sailing directly towards it and the angle of
depression of the ship changes from 300 to 450 in
10 minutes. Assuming that ship is traveling at
uniform speed, calculate how long will it take to
reach the light house.
243. A chord of length 24 cm is at a distance of 5 cm
from the centre of the circle. Find the length of the
chord of the same circle which is at a distance of
12 cm from the centre.
244. AB and CD are two chords in a circle that
intersect at P. If AP = 2 cm ,DP= 3 cm and CP= 5
cm. Find BP.
245. Evaluate: tan 100 tan 150 tan750 tan 800
246. Draw a line AP = 7.5 cm. Mark a point Q on AP
such that PQ = 4 cm. Using a ruler and
compasses only, construct:
(1) a circle of radius 2.5 cm to pass through A and
Q.
(2) a tangent to the above circle from P. Measure
its length.
247. Calculate the length of the radius of the
circumcircle and the incircle of a right angled
triangle of side 5 cm and 12 cm, that contain the
right angle. .
248. In the diagram, if the length of the chord is 30 cm
and CE:AB=5:6, find the radius of the circle.
249. O is the centre of the circle, PQR is an isosceles
triangle inscribed in a circle PQ = PR = 25 cm and
QR = 14 cm. Calculate the radius of the circle.
250. ABCD are the vertices of a rectangle in the given
figure, on the circumference of a circle. If the
length of the rectangle is 24 cm and the width is 7
cm. Find the area of the shaded region. Take π =
3.14
251. In the adjoining diagram AB and CD are two
chords intersecting at P. If CD = 9 cm, find CP
and PD.
252. If 00 < A < 900 , solve the following eqns: (i)sin
3A = cos 2A ,(ii) tan 5A = cot A , (iii) sin (3A−4)
= cos (5A+6) ,(iv) sin2 300 + cos2 (2A + 20)=1
253. A piece of card board is in the shape of quarter of
a circle of a radius 7 cm, bounded by
perpendicular radii OX and OY, points A and B
lie on OX and OY respectively such that OA = 3
cm and OB = 4 cm. The triangular part is
removed. Calculate the area and the perimeter of
the remaining piece.
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254. Construct a regular pentagon of side 4cm.
Construct all the lines of symmetry for this
pentagon.
255. Two circles of radii 25 cm and 9 cm touch each
other externally. Find the length of the direct
common tangent.
256. If tan A + sin A = m and tan A – sin A = n ;
prove that ; m2 – n2 = 4
257. A vertical tower is 20m high. A man at some
distance from the tower knows that the cosine of
the angle of elevation of the top of the tower is
0.53. How far is he standing from the foot of the
tower.
258. From the top of a cliff, 60 metres high the angle of
depression of the top and bottom of a tower are
observed to be 300 and 600. Find the height of the
tower.
259. The figure given below shows a circle with centre
O in which diameter CD bisects the chord AB at
point E. If AE = EB = 8 cm and ED = 4 cm, find
the radius of the circle.
260. Construct triangle ABC, ∠B=60°, ∠A = 45° and
the circumradius = 4 cm. Hence, complete cyclic
quadrilateral ABCD such that D is equidistant
from A and C.
261. AC, BQ and BP are the tangents to the circle.
Prove that BQ= semi−perimeter of ∆ABC.
262. In the figure alongside, PR is a diameter of the
circle, PQ = 7 cm, QR = 6 cm and RS = 2cm.
Calculate the perimeter of the cyclic quadrilateral.
263. Two parallel chords are drawn in a circle of
diameter 30 cm. The length of one chord is 24 cm
and the distance between the two chords is 21 cm;
find the length of another chord.
264. Prove : sec 700 sin 200 + cosec 700cos200 =2.
265. Prove :
266. A boy of height 1.7 m is standing 20m away from
a flag staff on the same level ground. He observes
that the angle of elevation of the top of the
flagstaff is 240. Calculate the height of the
flagstaff.
267. In the area enclosed between the concentric circles,
is 770 cm2. Given that the radius of the outer
circle is 21 cm. Calculate the radius of the inner
circle. ( )
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268. From a boat, 300 m away from a vertical cliff, the
angles of elevation of the top and the foot of a
vertical concrete pillar at the edge of the cliff are
55040′ and 54020′ respectively. find the height of
the pillar correct to the nearest metre.
269. A kite is flying at a height of 175 metres from the
level ground, attached to a string inclined at 600 to
the horizontal. Find the length of the string to the
nearest metre.
270. Prove :
271. In a circle with centre O, given that AB is parallel
to diameter CD. If ∠ABC = 25°. Calculate
∠AEB.
272. The angle of elevation of a stationary cloud from a
point 25m above a lake is 150 and the angle of
depression of its reflection in the lake is 450. What
is the height of the cloud above the lake−level?
273. The length of common chord of two intersecting
circles is 30 cm. If the diameters of two circles be
50 cm and 34 cm, calculate the distance between
their centres.
274. The radii of two concentric circles are 17 cm and
10 cm ; a line PQRS cuts the larger circle at P and
S and the smaller circle at Q and R. If QR = 12
cm. Calculate PQ.
275. In the figure the tangent PT = 8 cm. PA = 5 cm,
find the length of the chord AB.
276. PA = 10 cm, find AB. If PT is a tangent as shown,
find its length.
277. Prove : cos4 A – sin4 A = 2 cos2 A – 1
278. Given that O is the centre of a circle. Chord QP is
produced to any point R such that ∠TRQ= 26°.
Also given that ∠OQP = 48°. Calculate ∠PTQ
and ∠TPQ.
279. MN is a diameter of a semicircle with centre O. P,
Q, and R are points on the circumference such that
PM = PQ. If ∠QRN = 136°. Calculate ∠MPQ
and ∠PNQ. Prove that OP is parallel to QN.
280. In the given diagram chord AB and CD of a circle
intersect at E. (i)Prove that triangle ADE and
CBE are similar. ( ii)Given DC = 12 cm, DE = 4
cm and AE = 16 cm, Calculate the length of BE.
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281. Given two circles that intersect at points B and E.
HEC and AEG are straight lines.
Prove ∠AHE + ∠EGC = 180°.
282. The perimeter of a semi−circle is 90 cm. Calculate
its area.
283. Draw a circle of radius 3 cm. Mark P, any point
on the circle. Construct a tangent to the circle at
point P. Mark point A on the tangent such that AP
= 4.5 cm, construct another tangent to the circle
from point A.
284. The angle of elevation of a cloud from a point
20m above lake level is xo, where tan xo= and
the angle of depression of its reflection in the lake
water is yo where tan yo= . Calculate the height
of the cloud above the lake level, correct to the
nearest m.
285. Two parallel chords of lengths 16 cm and 12 cm
are drawn in a circle of diameter 20 cm. Find the
distance between the chords, if both the chords are
ion the same side of the centre, (ii) on the opposite
sides of the centre.
286. In the figure AB is a diameter of the circle, centre
O ,CD // AB. If angle CAB = x , find the value of
i ∠COB ii∠DOC ,iii∠DAC ,iv∠ADC.
287. Prove :
288. Three spheres of diameters x, 8 cm and 10 cm are
melted and recasted into a single sphere of
diameter 12 cm. Calculate the value of x.
289. O is the centre of the circle. TP bisects ∠OPQ.
i Prove TO // PQ
ii if ∠POQ = 64°,
calculate ∠TQR.
290. Prove :sec2 A cosec2 A = tan2 A + cot2 A + 2
291. A box contains 150 bulbs out of which 15 are
defective. It is not possible to just look at a bulb
and tell whether or not it is defective. One bulb is
taken out at random from this box. Calculate the
probability that the bulb taken out is :
(i)a good one
(ii)a defective one
292. In the given figure, if
∠ACE = 430
and ∠CAF = 620 find the values of
a, b and c.
293. Find the values of x which satisfy the inequation:
Graph the solution set on the real number line.
294. Prove that :sin2A + cos
2A = 1
295. The mid point of the line segment joining (2a , 4)
and (-2 , 2b) is (1 , 2a + 1). Find the values of a
and b.
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296. An article is bought at a certain price. It is marked
up by 30% on the purchased price. A discount of
10% is given on the marked price. A sales tax of
10% is marked on the discounted price and the
article is sold for Rs 3861.Find:
a) the cost price of the article;
b) the marked price on the article.
297. Let a, b, c and d be integers such that a < b,
b < c and c = d.
The mode of these four numbers is 11.
The range of these four numbers is 8.
The mean of these four numbers is 8.
Calculate the value of each of the integers a,
b, c, d.
298. An inverted cone of height 10 cm and base radius
6.4cm contains water to a depth of 5 cm,
measured from the vertex. Calculate the volume of
water in the cone.
299. An archery target has three concentric regions.
The diameters of the regions are in the ratio 1:2:3.
Find the ratio of their areas.
300. (i)If A and B are two complementary events then
what is the relation between P(A) and P(B)?
(ii)If the probability of happening of an event A is
0.46. What will be the probability of not
happening of the event A?
301. Using a ruler, construct a triangle ABC with BC =
6.4 cm, CA = 5.8 cm and ∠ABC = 600. Draw its
incircle. Measure and record the radius of the
incircle.
302. Two dice are rolled together. Find the probability
of getting:
(i)a total of at least 10
(ii)a multiple of 2 on one die and an odd number
on hte other die
303. In a single throw of a die, find the probability of
getting :
(i)5 (ii)8 (iii)a number less than 8 , (iv) a prime
number.
304. If P(E) = 0.39; find P (not E).
305. A bag contains 3 white, 5 black and 2 red balls, all
of the same shape and size. A ball is drawn from
the bag without looking into it, find the probability
that the ball drawn is:
(i)a black ball ,
(ii)a red ball ,
(iii) awhite ball,
(iv)not a red ball,
(v)not a black ball
306. In a single throw of two dice, find the probability
of :
(i)a doublet
(ii)a number less than 3 on each die
(iii)an odd number as a sum
(iv)a total of at most 10
(v)an odd number on one die and a number less
than or equal to 4 on the other die.
307. An inverted cone of height 15cm and base radius 4
cm contains water to a depth of 10 cm. Calculate
the volume of water in the cone.
308. Draw a circle of radius 4 cm. Draw two tangents
to this circle so that the angle between the tangents
is 45°. Measure distance of centre from exterior
point.
309. A card is drawn from a pack of 100 cards
numbered 1 to 100. Find the probability of
drawing a number which is a square.
310. Two dice are thrown simultaneously. Find the
probability that :
(i)both the dice show the same number,
(ii)the first die shows 6,
(iii)the total (sum) of the numbers on the dice is 9,
(iv)the product of the numbers on the dice is 8,
(v)the total of the numbers on the dice is greater
than 9.
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
311. A straight line passes through the points
P(-1,4) and Q (5,-2). It intersects the
co-ordinate axes at points A and B
respectively. If M is the midpoint of the
segment AB. Find:L
i) the equation of the line,
ii) The co-ordinates of A and B,
iii) The co-oridnates of point M.
312. A shopkeeper buys a camera at a discount of 20%
from the wholesaler, the printed price of the
camera being Rs.1600 and the rate of sales tax is
6%. The shopkeeper sells it to the buyer at the
printed price and charges tax at the same rate.
Find :
(i)The price at which the camera can be bought.
(ii)The VAT (Value Added Tax) paid by the
shopkeeper.
313. A pair of dice is thrown. Find the probability of
getting a sum of 10 or more, if 5 appears on the
first die.
314. Use a ruler and compass only in this question.
(i) Draw a circle, centre O and radius 4 cm.
(ii) Mark a point P such that OP = 7cm.
Construct the two tangents to the circle from P.
Measure and record the length of the tangents.
315. In the given figure, AB is a diameter. The tangent
at C meets AB produced at Q.
If find: (i) (ii)
316. An inverted cone of height 12cm and base radius
6cm contains 20 cm3 of water. Calculate the depth
of water in the cone, measured from the vertex.
317. In the given figure, ABC is a triangle. DE is
parallel to BC andAD
DB=
3
2.
(i) Determine the ratios AD
AB,DE
BC
(ii) Prove that DEF is similar to CBF.
Hence, find EF
FB.
(iii) What is the ratio of the areas of
DFE and BFC ?
318. A die is thrown once. Find the probability of
getting: (i)an even number , (ii) a number between
3 and 8 , (iii)an even number or a multiple of 3.
319. From the top of a hill, the angle of depression of
two consecutive kilometer stones, due east are
found to be 300
and 450 respectively. Find the
distance of the two stones from the foot of the bill.
320. Using a ruler and compasses only, construct a
triangle ABC in which
BC = 6 cm, ∠ACB = 45° and perpendicular from
A on BC is 4 cm. Draw an inscribed circle and
measure its radius.
321. In the given figure, AB is the diameter of a circle
with centre O and OA = 7 cm.
Find the area of the shaded region.
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
322. In the figure, and
. Find: (i) (ii) Hence
show that AC is a diameter.
323. The median of the following observations 11, 12,
14, 18, (x + 4), 30, 32, 35, 41 arranged in
ascending order is 24. Find x.
324. A box contains some black balls and 30 white
balls. If the probability of drawing a black ball is
two-fifths of a white ball; find the number of black
balls in the box.
325. A circular paper of radius 20 cm is cut in half and
each half is made into a hollow cone by joining the
straight edges. Find the slant height and base
radius of each cone.
326. Mukesh deposited Rs.400/- per month in a bank
for 39 months under the Recurring Deposit
Scheme. What will be the maturity value of his
deposits, if the rate of interest is 12 % per annum
and interest is calculated at the end of every
month?
327. Three identical coins are tossed together. What is
the probability of obtaining :
(i)all heads (ii)exactly two heads (iii)exactly one
head (iv)at least one head (v)at least two heads
(vi)all tails
328. A single letter is selected at random from the word
‘Probability ‘. Find the probability that it is a
vowel.
329. The price of a TV set including sales tax at
8% is Rs 16,200. Find its marked price. When
the rate of sales tax was increased, the
customer had to pay Rs. 300 more. Find the
new rate of sales tax.
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Last Minute Revision 2011
Answer Section
1. Rs4,783.25
2. show that
3. (i)12cm, (ii)1:9,1:8
4. 12 cm; 95.47 cm2
5. S.S= {1,2,3,4,5}
6. Rs 30, 000
7. Rs 1960
8.
(i)200 , (ii)300 , (iii)640 , (iv)7.11%
9. 16 litres
10. Rs 6000,10%
11. {4}
12. (16/7,27/7)
13. R = 5%
14. (i) 1cm on map represents 210000 cm on the ground = 210000
100000=2.1 km on the ground.
(ii)1 cm2 on map represents ( 2.1)2 km2 on the ground = 4.41 km2 on the ground.
(iii) the area on the map that represents the plot = 83.79
4.41=19 cm2
15. Rs.7,200; 400 shares
16. 100
17. s. s. = x: − 3 < x ≤ 3 ;x ∈ R{ }
18. 5:1;
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
19. square
20. 39.5,38,40,2:
21. Rs.1,815.
22. (i) For L1 as the y-coordinate is the same, the equation of L1 is y = –4.
For L2 as the x coordinate is the same, the equation of L2 is x= –6 .
(ii) P(3,4)y = − 4
→ P’(3,y2) where using midpoint formula we get, y2= –12
(iii)Q(−5,−2)x = −6
→ Q’(x2,-2) where using midpoint formula we get, x2= –7
23. Rs. 50,000; Rs.10,000, Rs 15000; Rs 12,500
24. a = −7, b = 10
25. a=-7, b= -6; (x+2)(x-3)(x+1)
26. 38
27. x2 − 12x + 36 = 0
28. 100
29. S.S= {1,2,3….}
30. y=x+3
31.
s.s. = {1 , 2 , 3}
32. (i) A(−2,4),B(2,6),E(6,0),( ii)− ½ ,( iii) 2y+x=14,( iv) C(0,7, D(14,0(v1:6
33.
Third proportion = xy
34. 11cm , 3 cm
35. Rs.3,410
36. Rs 1872. Rs 1989
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
37. 14
3
38. −1 ≤ y < 7
39.
40.
41. Loss =Rs 48
42. 603.43 cm3 ; 603.4 cm2
43. x2−6x + 7=0
44. x=
45. (i) 6,938 (ii) Rs.60,310.
46. 2x+3y=12; P=(6,0); Q=(0,4); 12 unit2.
47.
48. 9000, 10%
49. 400
50. irrational and unequal
51. 22.5 cm
52. A=(−3,0); 3x+4y+9=0
53. M=
54. 2y = 3x + 12
55. (i) Son;s age 5 years ago is 5 years
(ii) Present age of women = x2 + 5 = 52 + 5 = 30 years.
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
56. ±3
57. ..
58. AC is 2y=3x+7; BD is 2x+3y=4
59. Rs.179,138
60. ..
61. M = [1 2]
62. 15o
63. 150
64. a) 10%, b) Rs. 1756.92, c) Rs. 1320.
65. rational and unequal
66. 12
67. a = −2, b = −5
68. Rs. 40.8 less
69. Rs. 45,000
70.
71. i AB and BC ; ii B and D.
72. {−.60,−8.4}
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
73.
74. 40 %
75. P′′ ( 2 , 4) , Q′′ (7,8)
76. ix=2;y=5; ii (2,11); iii(7,5)
77. 30 km/hr
78. Rs.45
79. 4x2−3=0
80. 30
81. 7 , 8 , 9
82. Rs.19,200; 400; Rs3,000
83. 8cm;15cm
84. ..
85.
first investment is better
86. Rs.883.05.
87. prove
88. 12.58 years
89. ±2
90. Rs. 750
91. False , AB≠BA
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92. 1, −4 and 450
93. 1:2 and (10/3,0)
94. Rs 20,000
95. (4,1) or
96. ab= −6
97. a=8;b=4
98. −
99. Rs.2,640.
100. 3x−4y+10=0; x−2y−8=0; 3x+5y+8=0
101. x−3y−14=0
102. p=3 and q=4 or p=4 and q =3
103. 81 kg
104. 24 and −6
105. 24 units
106. (i) M(3,0);( ii) D(2,−6), rhombus; (iii)Yes,M'(3,−4)
107. i y=7 , iix+5=0
108.
109. Rs 7200
110. (x + 3) ( x− 7) (x + 4 )
111. 2,
112. Rs.64,000.
113. prove
114. DIAGRAM
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
115. l
116. 67 , 64.18
117. (i) Mirror line is the perpendicular bisector of the segment joining the two points, hence the mirror line is y= –3
(ii) The equation of the line in which these points are invariant is the line that passes through both these points,
i.e x = –1
118. 6 and24
119. Rs 238
120. M=
121. (i)47.5,(ii)35.5, (iii)58.5,(iv)33%, (v)6
122. {3 , -2}
123. m=3,c=5
124. (i) 10 cm, ( ii) 4 cm2
125. (3 , 0)
126. x = 0 , 2
127. l2 & 30
128. -D is line L1, C is line L2, A is line L3, and B is L4
129. y = x - 3
130. 3
131. Rs 2600
132.
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
133. p = - 1
134. mean= 4.7, median=5, mode=6
135. P′ (3 , −4) , Q′(−5 , 2)
136. [
137. prove
138. i parallelogram; ii No, lines of symmetry; iii P , 8,8 and Q , 8,1, pentagon.
139.
24 Rs. 5665
140. 6.4 %; Rs.192
141. ..
142. {9.4,.64}
143. Rs 800; Rs 810;
144. real and equal
145. Rs 1260, 7 ½ %
146. iA(0,6);B(−3,0);C(0,−2);D(4,0); iiS−A−S test; iiiYes ABCD is cyclic
147. prove
148. 8
149. prove
150. ..
151. 4
152. DIAGRAM
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Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
153. i
154. l
155. a) A = { x: − 4 < x ≤ 3,x ∈ R}
b) B ={ x: − 3 ≤ x <5,x ∈ R}
c)A ∩ B
d)A ∪ B
e)A ∩ B'
f) A'∩ B
156. Rs 20,250, 11%
157. L1 is x-axis or y = 0; L2 is y-axis or x = 0
158. Rs 159.38
159. In In ABC and ADE
∠BAC=∠DAE ( common angle )
∠ABC = ∠ADE ( corresponding angles)
∴ ABC ∼ ADE (A-A postulate)
ADE= ABC+ trap.BCED = 150 + 66 =216 cm2
ABC
ADE=
BC
DE
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃˜̃˜̃
2
(the ratio of areas of similar triangles equals square of ratio of its sides)
150
216=
BC
42
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃˜̃˜̃
2
⇒ 25 / 36=BC
42⇒
5
6× 42 = BC ∴ BC = 35cm
160. P = Rs.40000
161. Rs.10,648
162. a=3
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163. 4:5
164. 1 m
165. True, multiplication of matrices is associative
166. Rs 7500,4%
167. (7,−2); 5 units
168. False
169. a = −5 , b = - 4
170. 4,3
171. 1
172. (0,2) and (3,4)
173. Rs 1875; Rs 50,700; Rs 2,028
174. show that
175. Rs 150
176. 25
8
177. x=[
178. 5 = m , 3 = n
179. 5 km/hr
180. 1.5 years
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
181. mean=38
182. (i)k =length of the model
length of the missile
1
600=
6
length of the missile⇒ ∴ length of the missile = 600 × 6 = 3600m.
(ii) k2
=area of the model
area of the missile
1
6002
=area of the model
7,200,000⇒ ∴
1
6002
× 7,200,000 = area of the model
∴ area of the model= 20m2.
(iii) k3
=volume of the model
volume of the missile
1
6003
=350
volume of the missile⇒ ∴ volume of the missile = 600
3× 350 = 75,600,000,000 litres.
To
convert litres to m3 we divide by 1000
therefore the volume in m3 is 75,600,000,000
1000=75,600,000 m3
183. (1 , 8)
184. 80,19
185. x = 32
186. 8
187. 29,26,35,9
188. Rs 20,000; Rs16928
189. 38.85 yrs
190. (i)3:7, 3:7 ,(ii)3:7 ,(iii)10:7 , (iv)9:49
191. ..
192. 13 : 1
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
193.
r = 10 %
194. prove
195. (i) 71.92g,( ii)76.92g (iii)4315g, (iv)71.92 g, (v)69.5−74.5 (vi) 69.5−74.5
196. Rs.377.40
197. 60; 42; Rs 135
198. a. x2−:[a−b]x−ab=0
199. x2+ 2x−1=0
200. (x−2)(x−3)(x+1)
201. {5 , -5}
202. y=x+2 and x+y+2=0
203. x=3 and y=2
204. 12 hrs ; 15 hrs.
205. x=3, y=2
206. 14520 sq m and Rs.145200
207. M = [−4 −5]
208. Rs 12000, 5%
209. {0 , 5}
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
210. 1540 cm2; 6587.09 cm3
211. 2:3
212. R = 10% p.a.
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
2011 LMR contd
Answer Section
213. (i)1
4 (ii)
1
2(iii)
3
13 (iv)
1
26(v)
2
13 (vi)0 (vii)
1
26 (viii)
7
3
214. 415.67 km/hr
215. 60 cm
216. prove
217. 17 cm
218. 20 m,20m
219. 154 cm2
220. 72.7 cm
221. 7.5 cm
222. ..
223. 600
224. 76°,64°,40°
225. prove
226. 3 cm
227. 77 cm2
228. prove
229. 42°
230. 13 cm
231.
232. 72°,36°,30°
233. ..
234. 25°,35°,60°
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
235. 11.49 cm
236. 180 m
237.
238. prove
239. 36.21m
240. prove
241. 6 cm
242. 13.66 minutes
243. 10 cm
244. 7.5 cm
245. ..
246. ..
247. 2cm, 6.5 cm
248. 17 cm
249.
250. 322.625 cm2
251. CP 1.15 cm, PD = 7.85 cm
252. (i)180 (,ii) 150 ,(iii) 11o ,(iv) 50
253. 38.5 cm2, 23 cm
254. ..
255. 30 cm
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
256. prove
257. CB=12.5m
258. 40 m
259. 10 cm
260. ..
261. ..
262. 24 cm
263. 18cm
264. prove
265. prove
266. 10.6 m
267. 14 cm
268. 21 m
269. 202 m
270. prove
271. 40°
272. 43.3 m
273. 28cm
274. 9 cm
275. 7.8 cm
276. 4 cm ; 7.75 cm
277. prove
278. 42°,37°
279. 134°,23°
280. 2 cm
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
281. ..
282. 481.2 sq. cm.
283. ..
284. 24.44m
285. i 2 cm, ii 14 cm
286. 2x°; 180−4x; 90−2x; 90+x
287. prove
288. 6 m
289. 61°,
290. prove
291. (i)9
10 (ii)
1
10
292. In
= 1800 – (62 + 43) = 75 (sum of angles of a triangle)
a = 180 – 75 = 105 (opp. angles of cyclic quadrilateral)
In
62 + 105 + b = 180 (sum of angles of a triangle)
b = 13
= 43 + 62 = 105 (exterior angle property)
13 + 105 + c = 180
c = 62
293.
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
294. Using the definition of sin A and cos A we get;
sinA =opp
hyp=
BC
AC; cosA =
adj
hyp=
BA
AC
L. H. S:
sin2A + cos
2A
=BC
AC
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃˜̃˜̃
2
+BA
AC
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃˜̃˜̃
2
=BC
2+ BA
2
AC2
=AC
2
AC2
(By Pythagoras Theorem; BC2
+ BA2
= AC2)
= 1 Hence Proved.
295.
2 = 2a – 2 2(2) + 1 =
2a = 4 10 = 4 + 2b
a = 2 b = 3
296. a) Rs 3000/- ; b) Rs. 3900/-
297. d = 11; c = 11
d – a = 8 therefore
therefore b = 7
298. 53.6 cm
299. 1:3:5
300. (i) 1 , (ii)0.054
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
301. radius of incircle 1.1 cm
302. (i)1
6, (ii)
1
2
303. (i)1
6 (ii)0 (iii)1 (iv)
1
2
304. 0.61
305. (i)1
2 (ii)
1
5 (iii)
3
10 (iv)
4
5(v)
1
2
306. (i)1
6, (ii)
1
9, (iii)
1
2,(iv)
11
12 ,(v)
4
13
307. 74.5 cm3
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
308. 10.5 cm
309. Total number of all possible outcomes = 100
Since required (favourable) outcomes are : 1 , 4, 9 , 16 ,25 , 36 , 49 , 64 , 81 or 100
The number of favourable outcomes = 10
Required probability = Number of favourable outcomes
Totalnumber of outcomes=
10
100=
1
10
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
310. When the two dice are thrown simultaneously, all the possible outcomes are as shown alongside.
Clearly, the total number of all possible outcomes = 62
= 6 × 6 = 36
(i)When both the dice show the same number:
The favourable outcomes are : (1 , 1) , (2 , 2) , (3 , 3) , (4 , 4) , (5 , 5) , (6 , 6)
The number of favourable outcomes = 6
Required probability = 6
36=
1
6
(ii)When the first die shows 6 :
The favourable outcomes are : (6 , 1) , (6 , 2) , (6 , 3) , ( 6 , 4) , (6 , 5) and (6 , 6)
The number of favourable outcomes = 6
Required probability = 6
36=
1
6
(iii)When the total of the numbers on the dice is 9:
The favourable outcomes are : (3 , 6) , (4 , 5) , (5 , 4) and (6 , 3)
The number of favourable outcomes = 4
Required probability = 4
36=
1
9
(iv)When the product of the numbers on the dice is 8:
The favourable outcomes are : (2 , 4) and (4 , 2)
The number of favourable outcomes = 2
Required probability = 2
36=
1
18
(v)When the total of the numbers on the dice is greater than 9:
The favourable outcomes are : (4 , 6) , (5 , 5) , (5 , 6) , (6 , 4) , (6 , 5) and (6 , 6).
The number of favourable outcomes = 6
Required probability = 6
36=
1
6
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
311.
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
312.
313. 1
18
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
314. 5.9 cm
315. (i) ∠BCA = 900 (angle inscribed in a semicircle is 90)
90 + 34 + ∠CBA = 180 (Sum of angles of a triangle)
∴ ∠CBA = 560
(ii) ∠BCQ = 340 (angles in the alternate seg. are equal)
∴ ∠ CBA = ∠BCQ + ∠CQB (ext. angle property of a triangle)
56 = 34 + ∠CQA
∴ ∠CQA = 220
316. 4.24 cm
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
317. (i)
(ii) (vertically opp. angles)
(iii)
318. (i)1
2 (ii)
2
3 (iii)
2
3
319. Let BC= x,
therefore, the distance of the stones from the foot of the hill is 1.366 km and 2.366 km respectively.
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ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
320.
321. area of semicircle CBD = 1
2πr
2
=1
2×
22
7× 7 × 7 = 77 cm
2
area of BCD =1
2b × h =
1
2× 14 × 7 = 49 cm
2
area of semicircle - BCD = 77 - 49 = 28 cm2
radius of circle (smaller) = 3,5 cm
area of small circle = πr2
=22
7× 3.5 × 3.5 = 38.5 cm
2
area of shaded part = 28 + 38.5 = 66.5 cm2
322. (i) ∠BAD + ∠BCD = 1800 (Opp. angles of a cyclic quad. are supplemenrtary)
∴ ∠ BCD = 1150
(ii) In ABD ; 650
+ ∠ADB + 700
= 1800
(Sum of angles of a triangle)
∴ ∠ADB = 180 - 135
= 45
In ADC ; ∠ADC = 45 + 45 = 90
AC is the diameter of the circle. (Converse of angle inscribed in a semicircle is 90)
323. 11 , 12, 14, 18, (x + 4) , 30 , 32 , 35 , 41
N = 9
Median rank = N + 1
2 = 5th observation
x + 4 = 24 = x = 20
324. x = 12
325. 20cm, 10 cm.
326.
monthly deposit= x = Rs.400 ; n = 39 months ; r = 12 %
Interest =n(n + 1)x
2×
r
100×
1
12=
39(39 + 1) × 12
2400= 3120
maturity value = nx + I = 39×400 + 3120 = Rs. 18720 (Ans)
PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS.Experienced IB teacher and IB examiner.
ID: A
Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7.
327. When three coins are tossed together (or , a single coin is tossed three times): the possible outcomes are : HHH ,
HHT , HTH , THH , HTT , THT , TTH , and TTT
i.e., the total number of possible outcomes = 8
For the favourable outcomes, we can form a table as shown below:
Favourable outcomes No. of favourable outcomes
(i)All heads : HHH 1
(ii)Exactly two heads : HHT , HTH , THH 3
(iii)Exactly one head : HTT , THT , TTH 3
(iv)At least one head : HTT , THT , TTH ,
HHT , HTH , THH , HHH
7
(v)At least two heads : HHT , HTH , THH ,
HHH
4
(vi)All tails : TTT 1
(i) P (all heads) = 1
8
(ii)P (exactly two heads) = 3
8
(iii)P(exactly one head) = 3
8
(iv)P (at least one head) = 7
8
(v)P (at least two heads) = 4
8=
1
2
(vi)P (all tails) = 1
8
328. (i) 5
31 (ii)
5
31 (iii)
8
31
329.
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