ICSE class 10 Maths question paper - 2016 by Prasenjit Dutta | Practice Test to Test Your Knowledge
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ICSE class 10 Maths question paper - 2016

ICSE class 10 Maths question paper - 2016

This mock test includes actual ICSE Class 10 Maths board exam questions from the year 2016, helping students understand exam trends and practice real paper format

2025-08-13
Prasenjit Dutta Prasenjit Dutta
Class 10 Grade 10 2016 Mathematics ICSE

Duration

50 min

Questions

50

Marking

Negative

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Questions Preview

Using remainder theorem, find the value of k if on dividing $2x^3+3x^2-kx+5$ by x - 2, leaves a remainder 7.

A
k = 30
B
k = 32
C
k = 28
D
k = 25

Given matrices $A=\begin{bmatrix}2&0\ -1&7\end{bmatrix}$ and $I=\begin{bmatrix}1&0\ 0&1\end{bmatrix}$. If $A^2=9A+mI$, find the value of m.

A
m = -14
B
m = 14
C
m = 5
D
m = -5

The mean of the following numbers is 68. Find the value of 'x': 45, 52, 60, x, 69, 70, 26, 81, and 94. Then, estimate the median.

A
x = 73, Median = 70
B
x = 73, Median = 69
C
x = 69, Median = 70
D
x = 69, Median = 69

The slope of a line joining P(6,k) and Q(1-3k,3) is 1/2. Find the value of k and the midpoint of PQ.

A
k = -1, Midpoint = (5, 2)
B
k = -1, Midpoint = (4, 1)
C
k = 1, Midpoint = (4, 1)
D
k = 1, Midpoint = (5, 2)

Without using trigonometric tables, evaluate: $cosec^2 57^o - tan^2 33^o + cos 44^o cosec 46^o - \sqrt{2}cos 45^o - tan^2 60^o$.

A
-2
B
-1
C
1
D
2

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.

A
27 cones
B
54 cones
C
81 cones
D
108 cones

Solve the following inequation: $-3(x-7) \ge 15-7x > \frac{x+1}{3}$, where x is a real number. Write the solution set and represent it on the number line.

A
x \ge -3 \text{ and } x < 2.5 \implies x \in [-3, 2.5)
B
x \le 3 \text{ and } x < 2.5 \implies x \in (-3, 2.5]
C
x \le -3 \text{ and } x > 2.5 \implies \text{No solution}
D
x \ge 3 \text{ and } x > 2.5 \implies x \in (2.5, \infty)

In a circle with diameter AD and center O, AD is parallel to BC and $\angle CBD = 32^o$. Find the value of $\angle ABD$.

A
$32^o$
B
$58^o$
C
$64^o$
D
$45^o$

If $(3a+2b) : (5a+3b) = 18 : 29$, find the ratio $a:b$.

A
3:2
B
4:3
C
2:3
D
3:4

A game of numbers has cards marked with 11, 12, 13, ..., 40. A card is drawn at random. What is the probability that the number on the card is a perfect square?

A
3/30
B
4/30
C
5/30
D
6/30

A game of numbers has cards marked with 11, 12, 13, ..., 40. A card is drawn at random. What is the probability that the number on the card is divisible by 7?

A
4/30
B
5/30
C
6/30
D
3/30

A line AB meets X-axis at A and Y-axis at B. P(4,-1) divides AB in the ratio 1:2. Find the coordinates of A and B.

A
A(6,0), B(0,-3)
B
A(4,0), B(0,2)
C
A(6,0), B(0,-2)
D
A(0,6), B(0,-2)

A line AB meets X-axis at A and Y-axis at B. P(4,-1) divides AB in the ratio 1:2. Find the equation of the line through P and perpendicular to AB.

A
y = 2x - 9
B
y = 3x - 13
C
y = 2x + 9
D
y = 3x + 13

Mr. Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate the rate of interest.

A
5.5%
B
6.0%
C
6.5%
D
7.0%

Mr. Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate the amount at the end of the second year, to the nearest rupee.

A
Rs. 5670
B
Rs. 5671
C
Rs. 5669
D
Rs. 5672

Solve the quadratic equation $x^2 - 3(x+3)=0$, giving the answer correct to two significant figures.

A
x = 4.8, -1.8
B
x = 4.8, 1.8
C
x = 1.8, -4.8
D
x = 3.0, -3.0

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually?

A
1 year
B
2 years
C
3 years
D
4 years

In the given figure, PQRS is a cyclic quadrilateral. PQ and SR produced meet at T. If $TP=18$ cm, $RQ=4$ cm and $TR=6$ cm, find SP.

A
6 cm
B
12 cm
C
18 cm
D
10 cm

In the given figure, PQRS is a cyclic quadrilateral. PQ and SR produced meet at T. If area of $\triangle PTS=27 cm^2$, and $TP=18$ cm, $RQ=4$ cm and $TR=6$ cm, find the area of quadrilateral PQRS.

A
$18 cm^2$
B
$20 cm^2$
C
$24 cm^2$
D
$25 cm^2$

Given matrices $A=\begin{bmatrix}4~sin~30^{\circ}&cos~0^{\circ}\ cos0^{\circ}&4~sin~30^{\circ}\end{bmatrix}$ and $B=\begin{bmatrix}4\ 5\end{bmatrix}$. If $AX=B$, find the matrix 'X'.

A
$X=\begin{bmatrix}1\\ 2\end{bmatrix}$
B
$X=\begin{bmatrix}2\\ 1\end{bmatrix}$
C
$X=\begin{bmatrix}1\\ -2\end{bmatrix}$
D
$X=\begin{bmatrix}-2\\ 1\end{bmatrix}$

An aeroplane at an altitude of 1500 metres finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are $45^{\circ}$ and $30^{\circ}$ respectively. Find the distance between the two ships.

A
$1500(\sqrt{3}-1)m$
B
$1500(\sqrt{3}+1)m$
C
$1500(2-\sqrt{3})m$
D
$1500(2+\sqrt{3})m$

If $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$, show that $\frac{x^3}{a^3}+\frac{y^3}{b^3}+\frac{z^3}{c^3}=\frac{3xyz}{abc}$ is a true statement.

A
The statement is not provable.
B
This can be proved by letting each ratio equal to k and substituting it back into the equation.
C
The equation is only true for specific values of a, b, c.
D
This is true only if x, y, z are equal to a, b, c respectively.

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of VAT is 6%, find the price paid by the shopkeeper including the tax.

A
Rs. 5724
B
Rs. 5824
C
Rs. 5720
D
Rs. 5700

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of VAT is 6%, find the VAT paid by the dealer.

A
Rs. 240
B
Rs. 252
C
Rs. 260
D
Rs. 270

A model of a ship is made to a scale 1:300. The length of the model of the ship is 2 m. Calculate the length of the actual ship.

A
600 m
B
0.006 m
C
60 m
D
300 m

A model of a ship is made to a scale 1:300. The area of the deck of the actual ship is 180,000 $m^2$. Calculate the area of the deck of the model.

A
2 $m^2$
B
1.5 $m^2$
C
1 $m^2$
D
0.5 $m^2$

A model of a ship is made to a scale 1:300. The volume of the model is 6.5 $m^3$. Calculate the volume of the actual ship.

A
$1.755 \times 10^9$ $m^3$
B
$1.755 \times 10^8$ $m^3$
C
$1.755 \times 10^7$ $m^3$
D
$1.755 \times 10^6$ $m^3$

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity, find the monthly installment.

A
Rs. 750
B
Rs. 800
C
Rs. 850
D
Rs. 900

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity, find the amount of maturity.

A
Rs. 20400
B
Rs. 21400
C
Rs. 22400
D
Rs. 23400

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced by 10 km/h and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be x km/h, form an equation and solve it to evaluate 'x'.

A
$x^2 - 10x - 1200 = 0$, x = 40
B
$x^2 - 10x - 1200 = 0$, x = 30
C
$x^2 + 10x - 1200 = 0$, x = 40
D
$x^2 + 10x - 1200 = 0$, x = 30

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475, find the number of shares he bought.

A
800
B
825
C
900
D
950

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475, find the market value of each share.

A
Rs. 30
B
Rs. 31
C
Rs. 32
D
Rs. 33

The histogram represents scores of 25 students. Frame a frequency distribution table from the given histogram.

A
0-10: 2, 10-20: 5, 20-30: 8, 30-40: 4, 40-50: 6
B
0-10: 2, 10-20: 5, 20-30: 8, 30-40: 6, 40-50: 4
C
0-10: 2, 10-20: 5, 20-30: 7, 30-40: 4, 40-50: 6
D
0-10: 10, 10-20: 20, 20-30: 30, 30-40: 40, 40-50: 50

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Determine the modal class.

A
10-20
B
20-30
C
30-40
D
40-50

The figure shows a kite with a circular and a semicircular motif. The radius of the circle is 2.5 cm and the semicircle is 2 cm. The diagonals AC and BD are 12 cm and 8 cm respectively. Find the area of the shaded part, correct to the nearest whole number.

A
$20 cm^2$
B
$25 cm^2$
C
$28 cm^2$
D
$30 cm^2$

The figure shows a kite with a circular and a semicircular motif. The radius of the circle is 2.5 cm and the semicircle is 2 cm. The diagonals AC and BD are 12 cm and 8 cm respectively. Find the area of the unshaded part.

A
$12 cm^2$
B
$20 cm^2$
C
$25 cm^2$
D
$15 cm^2$

The table shows the distribution of the scores obtained by 160 shooters. Use the data to estimate the median score.

A
45
B
48
C
50
D
52

The table shows the distribution of the scores obtained by 160 shooters. Use the data to estimate the interquartile range.

A
20
B
25
C
30
D
35

The table shows the distribution of the scores obtained by 160 shooters. Use the data to estimate the number of shooters who obtained a score of more than 85%.

A
6
B
7
C
8
D
9

Prove that $\frac{cos~A}{1+sin~A}+tan~A=sec~A$.

A
The statement is true and can be proved by converting all terms to sine and cosine.
B
The statement is false.
C
The statement is only true for specific values of A.
D
The statement is true only if the angle A is in degrees.

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the height of the balloon from the ground.

A
6($\sqrt{3}$ + 1) m
B
6($\sqrt{3}$ - 1) m
C
6($\sqrt{3}$ + 3) m
D
12($\sqrt{3}$ + 1) m

A manufacturer sells an article to a wholesale dealer at a profit of 20%. The wholesale dealer sells it to a shopkeeper at a profit of 25%. The shopkeeper sells it to the customer at a profit of 30%. The marked price is 10% more than the price at which the article is sold by the shopkeeper. If the customer pays Rs. 450 for the article, find the cost price of the article for the manufacturer.

A
Rs. 200
B
Rs. 225
C
Rs. 250
D
Rs. 275

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the horizontal distance between the man and the balloon.

A
6($\sqrt{3}$) m
B
6($\sqrt{3}$+1) m
C
6($\sqrt{3}$-1) m
D
6 m

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the distance between the man and the balloon.

A
6 m
B
6($\sqrt{2}$) m
C
6($\sqrt{3}$) m
D
12 m

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the distance between the platform and the balloon.

A
6($\sqrt{3}$) m
B
6($\sqrt{3}$+1) m
C
6($\sqrt{3}$-1) m
D
6 m

The mean of the numbers 45, 52, 60, x, 69, 70, 26, 81, and 94 is 68. Find the median of the numbers.

A
70
B
69
C
68
D
60

The mean of the numbers 45, 52, 60, x, 69, 70, 26, 81, and 94 is 68. Find the value of x.

A
73
B
70
C
69
D
68

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the height of the platform.

A
3 m
B
6 m
C
9 m
D
12 m

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the height of the balloon above the man on the platform.

A
6($\sqrt{3}$) m
B
6($\sqrt{3}$ - 1) m
C
6($\sqrt{3}$ + 1) m
D
6($\sqrt{3}$ + 3) m

A man stands on a platform 6 metres high from the ground. He observes the angle of elevation of a balloon to be $30^o$. Another man on the top of the balloon observes the angle of depression of the man on the ground to be $45^o$. Find the distance between the two men.

A
6($\sqrt{3}$) m
B
6($\sqrt{2}$) m
C
6($\sqrt{3}$ + 1) m
D
12($\sqrt{3}$ + 1) m