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The given linear polynomial y = f(x) has
(a) 2 zeros
(b) 1 zero and the zero is ‘3’
(c) 1 zero and the zero is ‘4’
(d) No zero
3. The given pair of linear equations is non-intersecting. Which of the following statements is true?
4. Write the nature of roots of the quadratic equation 9x² – 6x – 2 = 0.
(a) No real roots (b) 2 equal real roots
(c) 2 distinct real roots (d) More than 2 real roots
5. Two APs have the same common difference. The first term of one of these is –1 and that of
the other is – 8. Then the difference between their 4th terms is
(a) 1 (b) -7 (c) 7 (d) 9
6. Find the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis.
(a) 1:2 (b) 2:1 (c) 2:5 (d) 5:2
7. (x,y) is 5 unit from the origin. How many such points lie in the third quadrant?
(a) 0 (b) 1 (c) 2 (d) infinitely many
8. In ? ABC, DE ‖ AB. If AB = a, DE = x, BE = b and EC = c.
Express x in terms of a, b and c.
(a) ??/b
(b) ??/ ?+?
(c) ??/?
(d)??/?+c
9. If O is the center of a circle and Chord PQ makes an angle of 50° with the tangent PR at the point of contact P, find the angle made by the chord at the center.
(a) 130° (b) 100°
(c) 50° (d) 30°
10. A Quadrilateral PQRS is drawn to circumscribe a circle.
If PQ = 12 cm, QR = 15 cm, and RS = 14 cm, find the length of SP.
(a) 15 cm (b) 14 cm (c) 12 cm (d) 11 cm
11.Given that sin θ = ?/?’ , find cos θ .
12. (sec A + tan A) (1 – sin A) =
(a) sec A (b) sin A (c) cosec A (d) cos A
13. A pole 6 m high casts a shadow 2 √3m long on the ground, then the Sun’s elevation is
(a) 60° (b) 45° (c) 30° (d) 90°
14. If the perimeter and the area of a circle are numerically equal, then the radius of the circle
is
(a) 2 units (b) π units (c) 4 units (d) 7 units
15. It is proposed to build a single circular park equal in area to the sum of areas of two circular
parks of diameters 16 m and 12 m in a locality. The radius of the new park is
(a) 10m (b) 15m (c) 20m (d) 24m
16. There is a green square board of side ‘2a’ unit circumscribing a red circle. Jayadev is asked
to keep a dot on the abovesaid board. Find the probability that he keeps the dot on the green
region.
(a) ?/4
(b) 4−?/4
(c) ?−4/4
(d)4/?
17. 2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. What is the probability of getting a black card from the remaining pack?
(a) 22/ 52
(b) 22/ 46
(c)24 /52
(d) 24 /46
18. Find the upper limit of the modal class from the given distribution.
(a) 165 (b) 160 (c) 155 (d) 150
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by fixing the plane surfaces of the hemisphere and cone together.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
20. Statement A (Assertion): -5,−5/2, 0,5/ 2 , …. is in Arithmetic Progression.
Statement R (Reason) : The terms of an Arithmetic Progression cannot have both positive
and negative rational numbers.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
23. From an external point P, two tangents, PA and PB are drawn to a circle with centre O.
At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D,respectively. If PA = 10 cm, find the perimeter of ∆PCD.
24. If tan (A + B) = √3 and tan (A – B) = 1/√3; 0° < A + B < 90°; A > B, find A and B.
[or]
Find the value of x
2 cosec²30 + x sin²60 – 3/4 tan²30 = 10
25. With vertices A, B and C of ΔABC as centres, arcs are drawn with radii 14 cm and the three
portions of the triangle so obtained are removed. Find the total area removed from the
triangle.
[or]
Find the area of the unshaded region shown in the given figure.
[or]
29. PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB
makes an angle of 30° with the radius at the point of contact.
If length of the chord is 6 cm, find the length of the tangent PA and the length of the radius OA.
[or]
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove
that ∠ PTQ = 2 ∠ OPQ.
30. If 1 + sin2θ = 3sinθ cosθ , then prove that tanθ = 1 or 1/ 2
31. The length of 40 leaves of a plant are measured correct to nearest millimetre, and the data
obtained is represented in the following table.
(i) 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. 1
38.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°.
(i) 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?
