English Medium
Academic Year: 2019-2020
Date & Time: 12th March 2020, 10:30 am
Duration: 3h
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General Instructions:
Read the following instructions very carefully and strictly follow them:
- This question paper comprises four sections – A, B, C and D.
This question paper carries 40 questions. All questions are compulsory. - Section A – Question no. 1 to 20 comprises of 20 questions of one mark each.
- Section B – Question no. 21 to 26 comprises of 6 question of two marks each.
- Section C – Question no. 27 to 34 comprises of 8 questions of three marks each.
- Section D – Question no. 35 to 40 comprises of 6 questions to four marks each.
- There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of one mark, 2 questions of two marks, 3 question of three marks and 3 questions of four marks. You have to attempt only one of the choices in such questions.
- In addition to this, separate instructions are given with each section and question, wherever necessary.
- Use of calculators is not permitted.
The median and mode respectively of a frequency distribution are 26 and 29. Then its mean is ______.
27.5
24.5
28.4
25.8
Chapter:
In the figure, on a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the centre of the circle, then the length of PR is
30 cm
28 cm
32 cm
25 cm
Chapter:
225 can be expressed as ______.
5 × 32
52 × 3
52 × 32
53 × 3
Chapter:
The probability that a number selected at random from the numbers 1, 2, 3, ....., 15 is a multiple of 4 is ______.
`4/15`
`2/15`
`1/15`
`1/5`
Chapter:
If one zero of a quadratic polynomial (kx2 + 3x + k) is 2, then the value of k is ______.
`5/6`
`- 5/6`
`6/5`
`- 6/5`
Chapter:
`2.bar(35)` is ______.
an integer
a rational number
an irrational number
a natural number
Chapter:
If α and β are the zeroes of the polynomial 2x2 – 13x + 6, then α + β is equal to ______.
– 3
3
`13/2`
`- 13/2`
Chapter:
The mid-point of the line-segment AB is P(0, 4). If the coordinates of B are (–2, 3) then the coordinates of A are ______.
(2, 5)
(–2, –5)
(2, 9)
(–2, 11)
Chapter:
In the following 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
15
10
9
7.5
Chapter:
If the point C(k, 4) divides the line segment joining two points A(2, 6) and B(5, 1) in ratio 2 : 3, the value of k is ______.
Chapter:
If points A(–3, 12), B(7, 6) and C(x, 9) are collinear, then the value of x is ______.
Chapter:
If the equations kx – 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is ______.
Chapter:
If quadratic equation 3x2 – 4x + k = 0 has equal roots, then the value of k is ______.
Chapter:
The value of (sin 20° cos 70° + sin 70° cos 20°) is ______.
Chapter:
If `tan (A + B) = sqrt(3)` and `tan (A - B) = 1/sqrt(3)`, A > B, then the value of A is ______.
Chapter:
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The value of (sin 43° · cos 47° + sin 47° cos 43°) is ______.
Chapter:
If 5 tan θ = 3, then what is the value of `((5 sin θ - 3 cos θ)/(4 sin θ + 3 cos θ))`?
Chapter:
The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences?
Chapter:
If a pair of dice is thrown once, then what is the probability of getting a sum of 8?
Chapter:
In a ΔPQR, S and T are points on the sides PQ and PR respectively, such that ST || QR. If PT = 2 cm and TR = 4 cm, find the ratio of the areas of ΔPST and ΔPQR.
Chapter:
Two different coins are tossed simultaneously, What is the probability of getting at least one head?
Chapter:
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball at random from the bag is three times that of a red ball, find the number of blue balls in the bag.
Chapter:
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Chapter: [9] Introduction to Trigonometry
Prove that `(tan^2 θ)/(1 + tan^2 θ) + (cot^2 θ)/(1 + cot^2 θ) = 1`
Chapter:
Two different dice are thrown together, find the probability that the sum of the numbers appeared is less than 5.
Chapter:
Find the probability that 5 Sundays occur in the month of November of a randomly selected year.
Chapter:
In the following 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.
Chapter:
A circle is inscribed in a ΔABC touching AB, BC and AC at P, Q and R respectively. If AB = 10 cm, AR = 7 cm and CR = 5 cm, find the length of BC.
Chapter:
The length of the minute hand of clock is 14 cm. Find the area swept by the minute hand in 15 minutes.
Chapter:
If α and β are the zeroes of the polynomial f(x) = x2 – 4x – 5 then find the value of α2 + β2.
Chapter:
Draw a circle of radius 4 cm. From a point 7 cm away from the centre of circle. Construct a pair of tangents to the circle.
Chapter:
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Draw a line segment of 6 cm and divide it in the ratio 3 : 2.
Chapter:
A solid metallic cuboid of dimension 24 cm × 11 cm × 7 cm is melted and recast into solid cones of base radius 3.5 cm and height 6 cm. Find the number of cones so formed.
Chapter:
Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A
Chapter:
Prove that `("cosec" θ)/("cosec" θ - 1) + ("cosec" θ)/("cosec" θ + 1) = 2 sec^2 θ`
Chapter:
Given that `sqrt(3)` is an irrational number, show that `(5 + 2sqrt(3))` is an irrational number.
Chapter:
An army contingent of 612 members is to march behind an army band of 48 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Chapter:
Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Chapter:
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Chapter:
In the following figure, two circles touch each other at a point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.
Chapter:
A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digit interchange their places. Find the number.
Chapter:
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
Chapter: [5] Arithmetic Progressions
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
Chapter: [5] Arithmetic Progressions
The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
Chapter:
In the following figure, DEFG is a square in a triangle ABC right angled at A.
Prove that
- ΔAGF ∼ ΔDBG
- ΔAGF ∼ ΔEFC
Chapter:
In an obtuse ΔABC (∠B is obtuse), AD is perpendicular to CB produced. Then prove that AC2 = AB2 + BC2 + 2BC × BD.
Chapter:
Find the median for the given frequency distribution:
| Class | Frequency |
| 40 – 50 | 2 |
| 45 – 50 | 3 |
| 50 – 55 | 8 |
| 55 – 60 | 6 |
| 60 – 65 | 6 |
| 65 – 70 | 3 |
| 70 – 75 | 2 |
Chapter:
If the price of a book is reduced by ₹ 5, a person can buy 4 more books for ₹ 600. Find the original price of the book.
Chapter:
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