Q 1 – If the sum of the zeroes of the quadratic polynomial kx2 + 2x + 3k is equal to their product, then k equals
(a) 1/3
(b) -1/3
(c) 2/3
(d) – 2/3
(d) -2/3
Q 2 – If the angle of depression of an object from a 75 m high tower is 30 , then the distance of the object from the tower is
(a) 25√3 m
(b) 50 √3 m
(c) 75√3 m
(d) 150 m
(c) 75√3 m
Q 3 – The value of the expression
Cosec (75º + θ ) – sec (15º – θ ) – tan (55º + θ ) + cot (35º – θ ) is
(a) – 1
(b) 0
(c) 1
(d) 3/2
(b) 0
Q 4 – For which value(s) of p, will the lines represented by the following pair of linear equations be parallel
3x – y – 5 = 0
6x – 2y – p = 0
(a) all real values except 10
(b) 10
(c) 5/2
(d) 1/2
(a) all real values except 10
Q 5 – The nth term of the AP a, 3a, 5a, … is
(a) na
(b) (2a – 1 ) a
(c) (2n + 1 ) a
(d) 2na
(b) (2a – 1 ) a
Q 6 – In the given figure, DE II BC . The value of EC is
(a) 1.5 cm
(b) 3 cm
(c) 2 cm
(d) 1 cm
(c) 2 cm
Q 7 – A sphere is melted and half of the melted liquid is used to form 11 identical cubes, whereas the remaining half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is
(a) (4/3)1/3
(b) (8/3)1/3
(c) (3)1/3
(d) 2
(b) (8/3)1/3
Q 8 – If the distance between the points A (4, p) and B (1, 0) is 5 units then the value(s) of p is (are)
(a) 4 only
(b) – 4 only
(c) ± 4
(d) 0
(c) ± 4
Q 9 – If α and β are the zeroes of the polynomial x2 + 2x + 1 then 1/α + 1/β is equal to
(a) – 2
(b) 2
(c) 0
(d) 1
(a) – 2
Q 10 – If ½ is a root of the equation x2 + kx – 5/4 = 0 then the value of k is
(a) 2
(b) – 2
(c)1/4
(d) 1/2
(d) 1/2
Q 11 – In the given figure, x is
(a) ab/a+b
(b) ac/b+c
(c) bc/b+c
(d) ac / a+c
(b) ac/b+c
Q 12 – If sin θ = a/b , then cos θ is equal to
(a) b/√ b2 – a2
(b) b/a
(c) √b2 – a2/ b
(d) a/√ b2 – a2
(c) √b2 – a2/ b
Q 13 – If cos (α + β) = 0 , then sin( α – β) can be reduced to
(a) cos β
(b) cos 2β
(c) sin α
(d) sin 2 α
(b) cos 2β
Q 14 – The pair of equations 3x + y = 81, 81x – y = 3 has
(a) no solution
(b) unique solution
(c) infinitely many solutions
(d) x = 2 1/8, y = 1 7/8
(d) x = 2 1/8, y = 1 7/8
Q 15 – The pair of linear equations 2kx + 5y = 7, 6x – 5y = 11 has a unique solution, if
(a) k ≠ – 3
(b) k ≠ – 2/3
(c) k ≠ 5
(d) k ≠ 2/9
(a) k ≠ – 3
Q 16 – In figure, AP, AQ and BC are tangents of the circle with centre O. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is
(a) 15
(b) 10
(c) 9
(d) 7.5
(d) 7.5
Q 17 – Assertion : The equation x2 + 3x +1 = ( x – 2)2 is a quadratic equation.
Reason : Any equation of the form ax2 + bx + c = 0 where a 0, is called a quadratic equation.
(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 but 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.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Q 18 – Assertion : When a positive integer a is divided by 3, the values of remainder can be 0, 1 or 2.
Reason : According to Euclid’s Division Lemma a = bq+ r, where 0 r b 1 and r is an integer.
(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 but 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.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Q 19 – C is the mid-point of PQ, if P is (4, x) C is (y, – 1) and Q is (– 2, 4) then x and y respectively are
(a) – 6 and 1
(b) – 6 and 2
(c) 6 and – 1
(d) 6 and – 2
(a) – 6 and 1
Q 20 – Ratio of lateral surface areas of two cylinders with equal height is
(a) 1:2
(b) H:h
(c) R : r
(d) None of these
(c) R : r
Q 21 – In Δ ABC AD ⊥ BC such that AD2 = BD × CD. Prove that Δ ABC is right angled at A.
Q 22 – In the given figure, from a point P, two tangents PT and PS are drawn to a circle with centre O such that ∠ SPT = 120 , Prove that OP = 2PS.
Q 23 – In given figure, AB is the diameter of a circle with centre O and AT is a tangent.
If ∠ AOQ = 58 , find ∠ ATQ.
Q 24 – Find the mode of the following frequency distribution.
Q 25 – Prove that 3 + √5 is an irrational number.
Q 26 – The mean and median of 100 observation are 50 and 52 respectively. The value of the largest observation is 100.It was later found that it is 110. Find the true mean and median.
Q 27 – The sum of four consecutive number in AP is 32 and the ratio of the product of the first and last term to the product of two middle terms is 7 : 15. Find the numbers.
Q 28 – Three horses are tied each with 7 m long rope at three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses.
Q 29 – The vertices of ABC are A (6, –2) B (0, – 6) and C (4, 8) Find the co-ordinates of mid-points of AB, BC and AC
Q 30 – Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together?
Q 31 – In the given figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠ AOC = 40º . Use π = 22/7
Q 32 – The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4kg of apples and 2kg of grapes is Rs. 300. Represent the situations algebraically and geometrically.
Q 33 – Solve for x and y :
2x – y + 3 = 0, 3x – 5y + 1 = 0
Q 34 – Draw the graphs of the equations x – y + 1= 0 and 3 x + 2y – 12 = 0. Determine the co-ordinates of the vertices of the triangle formed by these lines and the X- axis and shade the triangular region.
Q 35 – Solve the following pair of linear equations graphically:
x – 3y = 1 , 2 x + y = 9
Also shade the region bounded by the line 2x – 3y = 2 and both the co-ordinate axes.
or
From the top of tower, 100 m high, a man observes two cars on the opposite sides of the tower with the angles of depression 30 and 45 respectively. Find the distance between the cars. (Use = 1.73)
Q 36 – Model Rocketry: A model rocket is a small rocket designed to reach low altitudes and be recovered by a variety of means. Flying model rockets is a relatively safe and inexpensive way for person to learn the basics of forces and the response of a vehicle to external forces. Like an airplane, a model rocket is subjected to the forces of weight, thrust, and aerodynamics during its flight.
Shalvi is a member of first rocket club of India named STAR Club. She launches her latest rocket from a large field. At the moment its fuel is exhausted, the rocket has a velocity of 240 ft/sec and an altitude of 544 ft. After t sec, its height h (t) above the ground is
given by the function h (t) = – 16t 2 + 240t + 544
(i) How high is the rocket 5 sec after the fuel is exhausted?
(ii) How high is the rocket 10 sec after the fuel is exhausted?
(iii) What is the maximum height attained by the rocket?
Or
How many seconds was the rocket airborne after its fuel was exhausted?
Q 37 – The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.
Ramesh places a mirror on level ground to determine the height of a pole (with traffic light fired on it). He stands at a certain distance so that he can see the top of the pole reflected from the mirror. Ramesh’s eye level is 1.5 m above the ground. The distance of Ramesh and the pole from the mirror are 1.8 m and 6 m respectively
(i) Which criterion of similarity is applicable to similar triangles?
(ii) What is the height of the pole?
(iii) If angle of incidence is i , find tan i
or
Now Ramesh move behind such that distance between pole and Ramesh is 13 meters. He place mirror between him and pole to see the reflection of light in right position. What is the distance between mirror and Ramesh ?
Q 38 – Rani wants to make the curtains for her window as shown in the figure. The window is in the shape of a rectangle, whose width and height are in the ratio 2 : 3. The area of the window is 9600 square cm
(i) What is the shape of the window that is uncovered?
(ii) What will be the ratio of two sides of each curtain (other than hypotenuse) ?
(iii) What are the dimensions of the window ?
OR
How much window area is covered by the curtains?