Q1
mcq
1 mark
If $n(A \times B)=6$ and $A=\{1,3\}$, then $n(B)$ is:
- A. 1
- B. 2
- C. 3
- D. 6
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Q2
mcq
1 mark
If $f : A \to B$ is a bijective function and if $n(B)=7$, then $n(A)$ is equal to:
- A. 7
- B. 49
- C. 1
- D. 14
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Q3
mcq
1 mark
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
- A. 2025
- B. 5220
- C. 5025
- D. 2520
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Q4
mcq
1 mark
An A.P. consists of 31 terms. If its $16^{\text{th}}$ term is $m$, then the sum of all the terms of this A.P. is:
- A. $16m$
- B. $62m$
- C. $31m$
- D. $\frac{31}{2}m$
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Q5
mcq
1 mark
Which of the following should be added to make $\frac{x^4}{16}$ a perfect square?
- A. $4x^2$
- B. $16x^2$
- C. $8x^2$
- D. $-8x^2$
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Q6
mcq
1 mark
Graph of a linear equation is a ________.
- A. straight line
- B. circle
- C. parabola
- D. hyperbola
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Q7
mcq
1 mark
If in $\triangle ABC$, $DE \parallel BC$, $AB=3.6$ cm, $AC=2.4$ cm and $AD=2.1$ cm then the length of $AE$ is:
- A. 1.4 cm
- B. 1.8 cm
- C. 1.2 cm
- D. 1.05 cm
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Q8
mcq
1 mark
How many tangents can be drawn to the circle from an exterior point?
- A. One
- B. Two
- C. Infinite
- D. Zero
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Q9
mcq
1 mark
The area of triangle formed by the points $(-5,0)$, $(0,-5)$ and $(5,0)$ is:
- A. 0 sq. units
- B. 25 sq. units
- C. 5 sq. units
- D. 10 sq. units
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Q10
mcq
1 mark
If $x=a\tan\theta$ and $y=b\sec\theta$, then:
- A. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
- B. $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
- C. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
- D. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=0$
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Q11
mcq
1 mark
The curved surface area of a right circular cylinder of height 4 cm and base diameter 10 cm is:
- A. $40\pi$ sq. units
- B. $20\pi$ sq. units
- C. $14\pi$ sq. units
- D. $80\pi$ sq. units
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Q12
mcq
1 mark
The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is:
- A. 1 : 2 : 3
- B. 2 : 1 : 3
- C. 1 : 3 : 2
- D. 3 : 1 : 2
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Q13
mcq
1 mark
Which of the following values cannot be a probability of an event?
- B. 0.5
- C. 1.05
- D. 1
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Q14
mcq
1 mark
The probability of getting a job for a person is $\frac{3}{x}$. If the probability of not getting the job is $\frac{2}{3}$, then the value of $x$ is:
- A. 2
- B. 1
- C. 3
- D. 1.5
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Q15
short answer
If $A \times B=\{(3,2),(3,4),(5,2),(5,4)\}$ then find $A$ and $B$.
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Q16
short answer
If $f(x)=3x-2$, $g(x)=2x+1$ and $f\circ g=g\circ f$, then find the value of $k$.
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Q17
short answer
‘a’ and ‘b’ are two positive integers such that $\frac{a}{b}\times\frac{b}{a}=800$. Find ‘a’ and ‘b’.
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Q18
short answer
Simplify:
$$\frac{2x^3y^2\times x^z}{2x^{20}y^4z^6}$$
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Q19
short answer
Find the sum and product of the roots for following quadratic equation.
$$x^2-18x-65=0$$
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Q20
short answer
A man goes 18 m due East and then 24 m due North. Find the distance of his current position from the starting point.
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Q21
short answer
If the points $A(-3, 9)$, $B(a, b)$ and $C(4, -5)$ are collinear and if $a-b=1$, then find $a$ and $b$.
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Q22
short answer
Find the equation of a straight line which has slope $-\frac{5}{4}$ and passing through the point $(-1, 2)$.
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Q23
short answer
Prove that $\frac{1+\cos\theta}{\cosec\theta+\cot\theta}=1-\cos\theta$.
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Q24
short answer
If the base area of a hemispherical solid is 1386 sq. metres, then find its total surface area.
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Q25
short answer
Find the volume of cylinder whose height is 2 m and base area is 250 sq. m.
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Q26
short answer
Find the range and coefficient of range of the following data :
25, 67, 48, 53, 18, 39, 44
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Q27
short answer
What is the probability that a leap year selected at random will contain 53 Saturdays ?
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Q29
long answer
Let $A=\{x\in N\mid 1<x<4\}$, $B=\{x\in W\mid 0\le x<2\}$ and $C=\{x\in N\mid x<3\}$. Then verify that $A\times(B\cup C)=(A\times B)\cup(A\times C)$.
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Q30
long answer
Let $A=\{0, 1, 2, 3\}$ and $B=\{1, 3, 5, 7, 9\}$ be two sets. Let $f : A \to B$ be a function given by $f(x)=2x+1$. Represent this function
(i) by arrow diagram (ii) in a table form
(iii) as a set of ordered pairs (iv) in a graphical form
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Q31
short answer
Find the sum of $9\frac{3}{110\frac{3}{1}}\ldots\ldots 21\frac{3}{ }$
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Q32
short answer
Find the square root of $64x^4-16x^3-117x^2-2x+11$.
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Q33
short answer
If $A=\begin{bmatrix}3 & 1\\ 1 & 2\end{bmatrix}$, show that $A^2-5A+2I=0$.
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Q35
short answer
Find the area of quadrilateral whose vertices are at $(-9, -2)$, $(-8, -4)$, $(2, 2)$ and $(1, -3)$.
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Q36
short answer
Find the equation of the perpendicular bisector of the line joining the points $A(-4, 2)$ and $B(6, -4)$.
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Q37
short answer
Two ships are sailing in the sea on either sides of a lighthouse. The angle of elevation of the top of the lighthouse as observed from the ships are $30^\circ$ and $45^\circ$ respectively. If the lighthouse is 200 m high, find the distance between the two ships. $(\sqrt{3}=1.732)$
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Q40
short answer
Find the coefficient of variation of 24, 26, 33, 37, 29, 31.
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Q41
short answer
Two dice are rolled once. Find the probability of getting an even number on the first die or the total of face sum 8.
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Q44
long answer
(a) Draw the graph of $y=2x^2-3x-5$ and hence solve $2x^2-4x-6=0$.
OR
(b) Draw the graph of $xy=24$, $x,y>0$. Using the graph find,
(i) $y$ when $x=3$ and
(ii) $x$ when $y=6$.
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