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.

View Solution

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?

View Solution

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.

View Solution

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

View Solution

Q. Find

x + y

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

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

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

View Solution

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.

View Solution

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

View Solution

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

View Solution

Q. At what rate

%

p.a. will a sum of Rs.

4000

yield Rs.

1324

as compound interest in

3

years

View Solution

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

View Solution

Q. Without using tables evaluate

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

View Solution

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

View Solution

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

View Solution

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})

View Solution

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

View Solution

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

View Solution

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

View Solution

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	$10$	$6$	$8$	$12$	$5$	$9$

View Solution

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.

View Solution

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

View Solution

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.

View Solution

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.

View Solution

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

View Solution

Q. In

Δ

ABC,

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

and

C (1, - 10)

. Find the equation of the median through

A

View Solution

Q. Show that

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

View Solution

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.

View Solution

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?

View Solution

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

6, 15, 20

and

43

to make them proportional?

View Solution

Q. Using the properties of proportion, solve for

| x |

, given

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

View Solution

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

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

View Solution