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:
x-axis divides the line segment joining A(2, –3) and B(5, 6) in the ratio:
2 : 3
3 : 5
1 : 2
2 : 1
Chapter:
If the sum of the zeroes of the quadratic polynomial kx2 + 2x + 3k is equal to their product, then k equals
`1/3`
`- 1/3`
`2/3`
`- 2/3`
Chapter:
A chord of a circle of radius 10 cm subtends a right angle at the centre. The length of the chord (in cm) is ______.
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 θ/(cos(90^circ - θ)) + cos 43^circ/sin 47^circ` 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:
A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting a red king,
Chapter:
Two similar triangles ABC and PQR have their areas 25 cm2 and 49 cm2 respectively. If QR = 9.8 cm, find BC.
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:
An isosceles triangle ABC, with AB = AC, circumscribes a circle, touching BC at P, AC at Q and AB at R. Prove that the contact point P bisects BC.
Chapter:
The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.
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 horse is tethered to one corner of a rectangular field of dimensions 70 m × 52 m, by a rope of length 21 m. How much area of the field can it graze?
Chapter:
Find the quadratic polynomial, the sum and product of whose zeroes are –3 and 2 respectively. Hence find the zeroes.
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:
Three consecutive positive integers are such that the sum of the square of the first and product of the other two is 46. Find the integers.
Chapter:
Find the mean of the following distribution:
| Class | 10 - 25 | 25 - 40 | 40 - 55 | 55 - 70 | 70 - 85 | 85 - 100 |
| Frequency | 2 | 3 | 7 | 6 | 6 | 6 |
Chapter:
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