Q. In the given Venn diagram $n\left(A\right)$ is

1. 3
2. 1
3. 5
4. 2

Q. Sum of all the first 'n' terms of even natural number is

1. $n(n+1)$
2. $n(n+2)$
3. $n^2$
4. $2n^2$

Q. A boy has 3 shirts and 2 coats. How many different pairs, a shirt and coat can he dress up with?

1. 3
2. 18
3. 6
4. 5

Q. In a random experiment, it the occurrence of one event prevents the occurrence of other event, is

1. A complementary event
2. a certain event
3. Not mutually exclusive event
4. mutually exclusive event

Q. If the polynomial $p\left(x\right)=x^2-x+1$ is divided by $(x-2)$ then the remainder is

1. 2
2. 3
3. 0
4. 1

Q. The distance between a point with coordinates (p, q) and the origin is:

1. $p^2-q^2$
2. $\sqrt{p^2-q^2}$
3. $\sqrt{p^2+q^2}$
4. $q^2-p^2$

Q. The equation of line having slope $3$ and y-intercept $5$ is

1. $3y=4x+3$
2. $5y=3x+5$
3. $y=3x-5$
4. $y=3x+5$

Q. The surface area of a sphere of radius $7$ cm is:

1. $88c{m}^2$
2. $616c{m}^2$
3. $661c{m}^2$
4. $308c{m}^2$

Q. Find the HCF of $14$ and $21.$

Q. The average run scored by a batsman in 15 cricket matches is 60 and standard deviation of the runs is 15. Find the coefficient of variation of the runs scored by him.

Q. Write the degree of the polynomial $f\left(x\right)=x^2-3x^3+2$.

Q. What are congruent circles?

Q. If $sin\theta =\frac{5}{13}$ then write the value of $cosec\theta$.

Q. If $U=\{0,1,2,3,4\}$ and $A=\{1,4\},B=\{1,3\}$ show that $(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$

Q. Find the sum of the series$3+7+11+...........$ to 10 terms.

Q. At a constant pressure certain quantity of water at ${24}^{0}C$ is heated. It was observed that rise of temperature was found to be $4^{0}C$ per minute. Calculate the time required to rise to the temperature of water to ${100}^{0}C$ at sea level by using formula.

Q. A dice numbered 1 to 6 on its faces is rolled once. Find the probability of getting either an even number or multiple of '3' on its top face.

Q. What are the surds and unlike surds?

Q. Rationalise the denominator and simplify:
$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Q. Find the quotient and the remainder when $f\left(x\right)=2x^3-3x^2+5x-7$ is divided by $g\left(x\right)=(x-3)$ using synthetic division.

Q. Solve the equation $x^2-12x+27=0$ by using formula.

Q. Draw a chord of length 6 cm in circle of radius 5 cm. Measure and write the distance of the chord from the center of the circle.

Q. In $△ABC$, $\angle ABC={90}^0$, $BD\perp AC$. If $BD=8cm,AD=4cm.$ Find $CD$ and $AB.$

Q. In $△ABC$, XY || BC and $XY=\frac{1}{2}BC$. If the area of $△AXY=10c{m}^2$, find the area of trapezium XYCB.

Q. Show that , $\cot \theta \cos \theta +\sin \theta =cosec\theta$

Q. A student while conducting an experiment on Ohm's law plotted the graph according to the given data. Find the slope of line obtained.

X-axis I	1	2	3	4
Y-axis V	2	4	6	8

Scale
X-axis: 1 unit =1 cm
Y-axis: 1 unit =1 cm

Q. Draw the plan for the information given below:
Scale 20 m=1cm

	Metre To C
To D 50 To E 30	140 100 60 40	40 to B
	From A

Q. Out of $8$ different bicycle companies, a student likes to choose bicycle from three companies. Find out in how many ways he can choose the companies to buy bicycle.

Q. In a Geometric progression the sum of first three terms is $14$ and the sum of next three terms of it is $112$. Find the Geometric progression.

Q. Marks scored by 30 students of ${10}^{th}$ standard in a unit test of mathematics are given below.

Marks (x)	4	8	10	12	16
No. of students (f)	13	6	4	3	4

Find the variance of the scores.