Q 1 – Each root of x2 bx + = 0 is decreased by 2. The resulting equation is x2 – 2x + 1 = 0, then
(a) b = 6 , c = 9
(b) b = 3 , c = 3
(c) b = 2, c = – 1
(d) b = – 4, c = 3
Q 2 – (x2 + 1)2 – x2 = 0 has
(a) four real roots
(b) two real roots
(c) no real roots
(d) one real root
Q 3 – The real roots of the equation x2/3 + x1/3 – 2 = 0 are
(a) 1 , 8
(b) – 1, – 8
(c) – 1, 8
(d) 1, – 8
Q 4 – The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6, is
(a) x2 + 5x + 6
(b) x2 – 5x + 6
(c) x2 – 5x – 6
(d) – x2 + 5x + 6
Q 5 – The roots of the quadratic equation x2 – 0.0 4 = 0 are
(a) ± 0.2
(b) ± 0.02
(c) 0.4
(d) 2
Q 6 – Consider the following frequency distribution of the heights of 60 students of a class
The upper limit of the median class in the given data is
(a) 165
(b) 155
(c) 160
(d) 170
Q 7 – The ratio of the length of a rod and its shadow is 1 : 3 then the angle of elevation of the sun is
(a) 90º
(b) 45º
(c) 30º
(d) 75º
Q 8 – The zeroes of the polynomial x2 – 3x – m (m+3) are
(a) m, m+3
(b) –m ,m + 3
(c) m, – (m + 3)
(d) –m , – (m + 3)
Q 9 – If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other, then
(a) b = c
(b) a = b
(c) ac = 1
(d) a = c
Q 10 – If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3: 1 then the value of y is
(a) 4
(b) 3
(c) 2
(d) 1
Q 11 – 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
Q 12 – The cumulative frequency table is useful in determining
(a) Mean
(b) Median
(c) Mode
(d) All of these
Q 13 – If the height and length of the shadow of a man are equal, then the angle of elevation of the sun is,
(a) 45º
(b) 60º
(c) 90º
(d) 120º
Q 14 – In figure, O is the centre of circle. PQ is a chord and PT is tangent at P which makes an angle of 50 with PQ∠ POQ is
(a) 130º
(b) 90º
(c) 100º
(d) 75º
Q 15 – If a card is selected from a deck of 52 cards, then the probability of its being a red face card is
(a) 3/26
(b) 3/13
(c) 2/3
(d) 1/2
Q 16 – The first term of AP is p and the common difference is q, then its 10th term is
(a) q+ 9q
(b) p – 9q
(c) p + 9q
(d) 2p + 9q
Q 17 – In a right angled TABC right angled at B, if P and Q are points on the sides AB and BC respectively, then
Q 18 – 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
Q 19 – Assertion : Common difference of the AP –5, –1, 3, 7, ………. is 4.
Reason : Common difference of the AP a, a + d, a + 2d……………… is given by d = a2 – a1.
(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.
Q 20 – A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is
(a) 2
(b) 3
(c) 5
(d) 15
Q 20 – A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is
(a) 2
(b) 3
(c) 5
(d) 15
Q 21 – In figure, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD.
Q 22 – In an equilateral triangle of side 24 cm, find the length of the altitude.
Q 23 – Check whether 4n can end with the digit 0 for any natural number n.
Q 24 – Find the value of cos 2θ, if 2 sin 2θ = √3
Q 25 – Show that 571 is a prime number.
Q 26 – Show that the sum of all terms of an AP whose first term is a, the second term is b and last term is c, is equal to 
Q 27 – Prove that (sinθ + cosecθ)2 + (cosθ + secθ )2 = 7 + tan2 θ + cot2θ
Q 28 – 144 cartons of Coke cans and 90 cartons of Pepsi cans are to be stacked in a canteen. If each stack is of the same height and if it equal contain cartons of the same drink, what would be the greatest number of cartons each stack would have?
Q 29 – In the given figure, a chord AB of the circle with centre O and radius 10 cm, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence find the area of major segment ALBQA (Use π = 3.14)
Q 30 – Prove that the diagonals of a rectangle ABCD, with vertices A (2, –1), B (5, –1), C (5,6) and D (2,6) are equal and bisect each other.
Q 31 – Given that √5 is irrational, prove that 2√5 – 3 is irrational, prove that
Q 32 – Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Q 33 – The angle of elevation of an aeroplane from a point on the ground is 60º. After a flight of 30 seconds the angle of elevation becomes 30º. If the aeroplane is flying at a constant height of 3000 m, find the speed of the aeroplane.
Q 33 – The angle of elevation of an aeroplane from a point on the ground is 60º. After a flight of 30 seconds the angle of elevation becomes 30º. If the aeroplane is flying at a constant height of 3000 √3 m, find the speed of the aeroplane.
Q 34 – As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30c and 45c. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships [Use √3 = 1.732]
Q 35 – Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.
(i) If the length of the flowerbed is x m then what is the total length of the lawn ?
(ii) What is the value of x if the area of total lawn is 1260 m2 ?
(iii) What is the area of grassland ?
Q 36 – Family Structures : For a recent year, 51% of the families in the United States had no children under the age of 18; 20% had one child; 19% had two children; 7% had three children; and 3% had four or more children.
If a family is selected at random, find the following probability.
(i) Find the probability that the family has two or three children.
(ii) Find the probability that the family has more than one child.
(iii) Find the probability that the family has less than three children.
Q 37 – Political survey questions are questions asked to gather the opinions and attitudes of potential voters. Political survey questions help you identify supporters and understand what the public needs. Using such questions, a political candidate or an organization can formulate policies to gain support from these people
A survey of 100 voters was taken to gather information on critical issues and the demographic information collected is shown in the table. One out of the 100 voters is to be drawn at random to be interviewed on the India Today News on prime time.
(i) What is the probability the person is a woman or a Republican ?
or
What is the probability the person is a Democrat ?
(ii) What is the probability the person is a Independent men ?
(iii) What is the probability the person is a Independent men or green party men ?