The decimal expansion of 22/7 is

(a) Terminating

(b) Non-terminating and repeating

(c) Non-terminating and Non-repeating

(d) None of the above

Which of the following is not irrational?

(a) (3 + √7)

(b) (3 – √7)

(c) (3 + √7) (3 – √7)

(d) 3√7

What is the quadratic polynomial whose sum and the product of zeroes is √2,
⅓ respectively?

(a) 3x2-3√2x+1

(b) 3x2+3√2x+1

(c) 3x2+3√2x-1

(d) None of the above

Zeroes of p(x) = x2-27 are:

(a) ±9√3

(b) ±3√3

(c) ±7√3

(d) None of the above

The roots of 100x2 – 20x + 1 = 0 is:

(a) 1/20 and 1/20

(b) 1/10 and 1/20

(c) 1/10 and 1/10

(d) None of the above

The sum of two numbers is 27 and the product is 182. The numbers are:

(a) 12 and 13

(b) 13 and 14

(c) 12 and 15

(d) 13 and 24

If the length of the shadow of a tree is decreasing then the angle of elevation
is:

(a) Increasing

(b) Decreasing

(c) Remains the same

(d) None of the above

The angle of elevation of the top of a building from a point on the ground,
which is 30 m away from the foot of the building, is 30°. The height of the
building is:

(a) 10 m

(b) 30/√3 m

(c) √3/10 m

(d) 30 m
If the height of the building and distance from the building foot’s to a point is
increased by 20%, then the angle of elevation on the top of the building:

(a) Increases

(b) Decreases

(c) Do not change

(d) None of the above

The mode and mean is given by 7 and 8, respectively. Then the median is:

(a) 1/13

(b) 13/3

(c) 23/3

(d) 33

If the mean of first n natural numbers is 3n/5, then the value of n is:

(a) 3

(b) 4

(c) 5

(d) 6

The probability of event equal to zero is called;

(a) Unsure event

(b) Sure Event

(c) Impossible event

(d) Independent event

A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a
marble randomly, then what is the probability of not getting purple marble?

(a) 0.5

(b) 0.66

(c) 0.08

(d) 0.77

11th term of the A.P. -3, -1/2, 2 …. Is

(a) 28

(b) 22

(c) -38

(d) -48

The 21st term of AP whose first two terms are -3 and 4 is:

(a) 17

(b) 137

(c) 143

(d) -143

Which of the following triangles have the same side lengths?

(a) Scalene

(b) Isosceles

(c) Equilateral

(d) None of these

Which of the following are not similar figures?

(a) Circles

(b) Squares

(c) Equilateral triangles

(d) Isosceles triangles

The points (-1, –2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:

(a) Square

(b) Rectangle

(c) Parallelogram

(d) Rhombus

If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the
value of x is:

(a) 2

(b) -2

(c) 1

(d) -1

The midpoint of a line segment joining two points A(2, 4) and B(-2, -4) is

(a) (-2, 4)

(b) (2, -4)

(c) (0, 0)

(d) (-2, -4)

—-------------------------------------------------------------------------------------------------------------

2 marks
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5,
where q is some integer.

p(x) =x4–5x+6, g(x) = 2–x2

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied
from the top of a vertical pole to the ground. Find the height of the pole, if the
angle made by the rope with the ground level is 30°.

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles
triangle.

Which term of the A.P. 3, 8, 13, 18, … is 78?

3 marks

Prove that 3 + 2√5 + is irrational.

On dividing x3-3x2+x+2 by a polynomial g(x), the quotient and remainder were

x–2 and –2x+4, respectively. Find g(x).

Find the roots of the following equations:

(i) x-1/x = 3, x ≠ 0
(ii) 1/x+4 – 1/x-7 = 11/30, x = -4, 7
The diagonals of a quadrilateral ABCD intersect each other at the point O
such that AO/BO = CO/DO. Show that ABCD is a trapezium.

The angle of elevation of the top of a building from the foot of the tower is 30°
and the angle of elevation of the top of the tower from the foot of the building
is 60°. If the tower is 50 m high, find the height of the building.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of
getting

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

5 mark
As observed from the top of a 75 m high lighthouse from the sea-level, the
angles of depression of two ships are 30° and 45°. If one ship is exactly behind
the other on the same side of the lighthouse, find the distance between the two
ships.

Two APs have the same common difference. The difference between their 100th
term is 100, what is the difference between their 1000th terms?

Find the values of k for each of the following quadratic equations so that they
have two equal roots.

(i) 2x2 + kx + 3 = 0

(ii) kx (x – 2) + 6 = 0

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the
coordinates of the other two vertices.
The following frequency distribution gives the monthly consumption of an
electricity of 68 consumers in a locality. Find the median, mean and mode of
the data and compare them.

4 mark
Manpreet Kaur is the national record holder for women in the shot-put discipline. Her
throw of 18.86m at the Asian Grand Prix in 2017 is the maximum distance for an
Indian female athlete. Keeping her as a role model, Sanjitha is determined to earn gold
in Olympics one day. Initially her throw reached 7.56m only. Being an athlete in
school, she regularly practiced both in the mornings and in the evenings and was
able to improve the distance by 9cm every week. During the special camp for 15 days,
she started with 40 throws and every day kept increasing the number of throws by 12
to achieve this remarkable progress
(i)How many throws Sanjitha practiced on 11th day of the camp?
(ii) What would be Sanjitha’s throw distance at the end of 6 weeks?
(or)
When will she be able to achieve a throw of 11.16 m?
(iii) How many throws did she do during the entire camp of 15 days ?

Tharunya was thrilled to know that the football tournament is fixed with a
monthly timeframe from 20th July to 20th August 2023 and for the first time in
the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her
father felt that the game can be better understood if the position of players is
represented as points on a coordinate plane.

At an instance, the midfielders and forward formed a parallelogram. Find the

position of the central midfielder (D) if the position of other players who
formed the parallelogram are :- A(1,2), B(4,3) and C(6,6) 1 (ii) Check if the Goal
keeper G(-3,5), Sweeper H(3,1) and Wing-back K(0,3) fall on a same straight
line. [or] Check if the Full-back J(5,-3) and centre-back I(-4,6) are equidistant
from forward C(0,1) and if C is the mid-point of IJ. 2 (iii) If Defensive midfielder
A(1,4), Attacking midfielder B(2,-3) and Striker E(a,b) lie on the same straight
line and B is equidistant from A and E, find the position of E.

One evening, Kaushik was in a park. Children were playing cricket. Birds were
singing on a nearby tree of height 80m. He observed a bird on the tree at an
angle of elevation of 45°. When a sixer was hit, a ball flew through the tree
frightening the bird to fly away. In 2 seconds, he observed the bird flying at the
same height at an angle of elevation of 30° and the ball flying towards him at
the same height at an angle of elevation of 60°

At what distance from the foot of the tree was he observing the bird sitting on
the tree? 1 (ii) How far did the bird fly in the mentioned time? (or) After hitting
the tree, how far did the ball travel in the sky when Kaushik saw the ball? 2 (iii)
What is the speed of the bird in m/min if it had flown 20(√3 + 1) m?