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Question Papers

Maths ICSE B...

Maths | ICSE Board | Grade 10 | 2013

Q. A box contains some black balls and

30

white balls. If the probability of drawing a black ball is two-fifths of the probability of drawing a white ball, find the number of black balls in the box.

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Q. Salman buys

50

shares of face value Rs.

100

available at Rs.

132

.
(i) What is his investment?
(ii) If the dividend is

7.5 %

, what will be his annual income?
(iii) If he wants to increase his annual income by Rs.

150

, how many extra shares should he buy?

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Q. Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of

8 %

per annum and Mr. Britto gets Rs.

8088

from the bank after

3

years, find the value of his monthly instalment.

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Q. If

(x - 2)

is a factor of the expression

2 x^{3} + a x^{2} + b x - 14

and when the expression is divided by

(x - 3)

, it leaves a remainder

52

, find the valves of

a

and

b

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Q. Find

x + y

[\begin{matrix} x & 3 x y & 4 y \end{matrix}]

[\begin{matrix} 21 \end{matrix}]

= [\begin{matrix} 512 \end{matrix}]

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Q. Given below are the entries in a Savings Bank A/c pass book.

Date	Particulars	Withdrawals	Deposite	Balance
Feb. $8$ .	B/F	-	-	Rs. $8, 500$
Feb. $18$	To self	Rs. $4, 000$	-	-
April $12$	By cash	-	Rs. $2, 230$	-
June $15$	To self	Rs. $5, 000$	-	-
July $8$	By cash	-	Rs. $6, 000$	-

Calculate the interest for six months from February to July at

6 %

p.a.

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Q. The marks obtained by

120

students in a test are given below.

Marks	No. of students
$0 - 10$	$5$
$10 - 20$	$9$
$20 - 30$	$16$
$30 - 40$	$22$
$40 - 50$	$26$
$50 - 60$	$18$
$60 - 70$	$11$
$70 - 80$	$6$
$80 - 90$	$4$
$90 - 100$	$3$

Draw an ogive for the given distribution on a graph sheet. Using suitable scale for ogive to estimate the following:
(i) The median.
(ii) The number of students who obtained more than

75 %

marks in the test.
(iii) The number of students who did not pass the test if minimum marks required to pass is

40

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Q. Without solving the following quadratic equation, find the greater value of

p

for which the given equation has real and equal roots.

x^{2} + (p - 3) x + p = 0

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Q. At what rate

%

p.a. will a sum of Rs.

4000

yield Rs.

1324

as compound interest in

3

years

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Q. In the given figure,

A B

and

D E

are perpendicular to

B C

.
(i) Prove that

△ A B C \sim △ D E C

(ii) If

A B = 6 c m : D E = 4 c m

and

A C = 15 c m

, calculate

C D

.
(iii) Find the ratio of the area of

△ A B C

: area of

△ D E C

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Q. Without using tables evaluate

3 cos 80^{o} . cosec 10^{o} + 2 sin 59^{o} . sec 31^{o}

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A B

is a diameter of a circle with centre

C = (- 2, 5)

. If

A = (4, - 3)

. Find.
(i) The coordinates of

B

.
(ii) equation of tangent

A T

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Q. Solve the following inequation, write the solution set and represent it on the number line:

- \frac{x}{3} \leq \frac{x}{2} - 1 \frac{1}{3} < \frac{1}{6}, x \in R

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Q. In the figure alongside,

O A B

is a quadrant of a circle. The radius

O A = 3.5 c m

and

O D = 2 c m

. Calculate the area of the shaded portion.

(Take π = \frac{22}{7})

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Q. Using a ruler and compass only.
(i) Construct a

△ A B C

with the following data.

A B = 3.5 c m, B C = 6 c m

and

∠ A B C = 120^{\circ}

(ii) In the same diagram, draw a circle with

B C

as diameter. Find a point

P

on the circumference of the circle which is equidistant from

A B

and

B C

.
(iii) Measure

∠ B C P

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Q. In the figure given above, the line segment

A B

meets

X

-axis at

A

and

Y

-axis at

B

. The point

P (- 3, 4)

A B

divides it in the ratio

2 : 3

. Find the coordinates of

A

and

B

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Q. In the given figure,

∠ B A D = 65^{o}, ∠ A B D = 70^{o}, ∠ B D C = 45^{o}

(i) Prove that

A C

is a diameter of the circle.
(ii) Find

∠ A C B

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Q. Find the mean of the following distribution by step deviation method.

Class Interval	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$10$	$6$	$8$	$12$	$5$	$9$

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Q. The median of the following observations

11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47

arranged in ascending order is

24

. Find the value of

x

and hence find the mean.

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Q. In the figure given, from the top of a building AB

= 60 m

high the angles of depression of the top and bottom of a vertical lamp post

C D

are observed to be

30^{\circ}

and

60^{\circ}

respectively. Find: (i) The horizontal distance between

A B

and

C D

. (ii) The height of the lamp post

C D

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Q. A solid sphere of radius

15 c m

is melted and react into solid right circular cones of radius

2.5 c m

and height

8 c m

. Calculate the number of cones recast.

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Q. Using graph paper, plot the points

A (6, 4)

and

B (0, 4)

.
(i) Reflect

A

and

B

in the origin to get the images

A^{'}

and

B^{'}

.
(ii) Write the co-ordinates of

A^{'}

and

B^{'}

.
(iii) State the geometrical name for the figures

A B A^{'} B^{'}

.
(iv) Find its perimeter.

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Q. Given A

= [\begin{matrix} 2 & - 6 2 & 0 \end{matrix}], B = [\begin{matrix} - 3 & 2 4 & 0 \end{matrix}], C = [\begin{matrix} 4 & 0 0 & 2 \end{matrix}]

. Find the matrix X such that

A + 2 X = 2 B + C

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Q. In

Δ

ABC,

A (3, 5), B (7, 8)

and

C (1, - 10)

. Find the equation of the median through

A

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Q. Show that

\sqrt{\frac{1 - cos A}{1 + cos A}} = \frac{sin A}{1 + cos A}

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Q. A shopkeeper purchase a certain number of books for Rs.

960

. If the cost per book was Rs.

8

less, the number of books that could be purchased for Rs.

960

would be

4

more. Write an equation, taking the original cost of each book to be Rs.

x

, and solve it to find the original cost of the books.

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Q. A shopkeeper sells an article at the listed price of Rs.

1, 500

and the rate of VAT is

12 %

at each stage of sale. If the shopkeeper pays a VAT of Rs.

36

to the Government, what was the price, inclusive of Tax, at which the shopkeeper purchased the article from the wholesaler?

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Q. What number must be added to each of the number

6, 15, 20

and

43

to make them proportional?

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Q. Using the properties of proportion, solve for

| x |

, given

\frac{x^{4} + 1}{2 x^{2}} = \frac{17}{8}

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Q. Solve the following equation and calculate the answer correct to two decimal places.

x^{2} - 5 x - 10 = 0

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