SECTION : A
1. If the
equation x2 + 8x + k = 0 has real and distinct roots, then the value of 'k' is
(a) K > 16
(b) k ≥ 16
(c) k ≤ 16
(d) none of
these
2. The
probability of an impossible event is
(a) 0
(b) 1
(c) 2
(d) none of
these
3. If the
sector of a circle of diameter 10 cm subtends an angle of 1440 at the centre
then the length of the arc of the sector is
(a) 2π
(b) 8π
(c) 4π
(d) none of
these
4. If the
volume of a cube is 216 cubic m its edge is
(a) 4 cm
(b) 6 cm
(c) 9 cm
(d) none of
these
5. If the
perimeter and the area of a circle are numerically equal, then the radius of
the circle is
(a) π units
(b) 12 units
(c) 8 units
(d) none of
these
6. A card is
drawn from a well shuffled deck of 52 playing cards. The probability that it is
not a face card is
(a) 14/52
(b) 16/13
(c) 12/52
(d) none of
these
7. The distance
between the points (2,3), (4,1) is
(a) 14√2
(b) 12√4
(c) 3√2
(d) none of
these
8. Volume of
two spheres are in the ratio 125 : 27, the ratio of their radii are
(a) 5: 3
(b) 3: 5
(c) 1: 11
(d) none of
these
SECTION : B
9. Find the roots of the quadratic equation x2 – 3x – 10 = 0
10. Find the value of 'k' for the equation 2x2 + k x + 3 = 0,
so that it has two equal roots.
11. The angle of elevation of the top of a tower, at a
distance of 150 m from its foot on a horizontal plane, is found to be 600. Find
the height of the tower.
12. Find the centroid of triangle PQR, whose vertices are P (-3,
0), Q (5, -2), R (-8, 5).
OR
Find the coordinates of point which divides the line segment
joining the points (-1, 7) and (4, -3) in the ratio 2: 3.
13. A drinking glass is in the shape of a frustum of height 14
cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity
of the glass.
14. Prove that, the lengths drawn from an external point to
a circle are equal.
SECTION : C
15. A solid toy is in the form of a right circular cylinder
with a hemispherical shape at one end and a cone at the other end. The common
diameter is 4.2 cm and height of the cylinder and conical portion are 12 cm and
7 cm respectively. Find the volume of the solid toy.
OR
A toy is in the form of a cone mounted on a hemisphere of
radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface
area of toy.
16. The sum of the reciprocals of Mohan’s age (in years) 3
years ago and 5 years from now is 1/3. Find his present age.
17. The first and the last term of an AP are 17 and 350
respectively. If the common difference is 9, how many terms are there and what
is their sum.
18. Draw a pair of tangents to a circle of radius 5 cm,
which are inclined to each other at an angle of 600.
19. A box contains 5 red marbles, 8 white marbles and 4
green marbles. One marble is taken out of the box at random. What is the
probability that the ball taken out will be
Red
Not White
20. coin is tossed thrice. Find the probability of
Three tails
At least two tails
21. From a point on the ground, the angles of elevation of
the bottom and top of a transmission tower fix at the top of a 20 m high
building are 450 and 600 respectively. Find the height of the tower.
OR
Two poles of equal heights are standing opposite to each
other on the either side of the road, which is 80 m wide. From a point between
them on the road, the angles of elevation of the top of the poles are 60o and 30o
respectively. Find the height of the poles and the distances of the point from
the poles.
22. From the top of a 7 m high building, the angle of
elevation of the top of a cable tower is 60o and the angle of depression of its
foot is 450. Determine the height of the tower.
23. Three cows are tethered with 10 m long rope at the three
corners of a triangular field having sides 42 m, 20 m and 34 m. Find the area
of the plot which can be grazed by the cows, also, find the area of the
remaining field ungrazed.
OR
The wheels of a car are of diameter 80 cm each. How many
complete revolutions does each wheel make in 10 minutes when the car is
travelling at the speed of 66 km/h.
A chord of a circle of radius 12 cm subtends an angle of 120o
at the centre. Find the area of the corresponding segments of the circle. (Use π = 3.14
and √3 = 1.73)
25. A plane left 30 minutes later than the schedule time and
in order to reach its destination 1500 km away in time, it has to increase its
speed by 250 km/h from its usual speed. Find its usual speed.
OR
Solve the equation for 'x' by using factorization method: 4x2
– 4a2x + (a4 – b4)
26. How many multiples of 4 lie between 10 and 250.
OR
Find the 31st term of an AP whose 11th term is 38 and 16th
term is 73.
27. Find the sum -5) + (-8) + (-11) + ………… + (-230)
28. Prove that the parallelogram circumscribing a circle is
a rhombus.
29. Ram, a juice seller has set up his juice shop. He has
three types of glasses of inner diameter 5 cm to serve the customers. The
height of the glasses is 10 cm. (Use π = 3.14)
He decided to serve the customer in "A" type of
glasses.
Find the volume of glass of type A.
Which glass has the minimum capacity?
Which mathematical concept is used in above problem?
By choosing the glass of type A, which value is depicted by
juice seller Ram?
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thanks