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:
QP is a tangent to a circle with centre O at a point P on the circle. If ΔOPQ is isosceles, then ∠OQP equals.
30°
45°
60°
90°
Chapter:
If α and β are the zeroes of the polynomial x2 + 2x + 1, then `1/α + 1/β` is equal to ______.
–2
2
0
1
Chapter:
The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are ______.
(4, 0)
(0, 4)
(– 4, 0)
(0, – 4)
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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If `cot θ = 12/5`, then the value of sin θ 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 the following figure, in ΔABC, DE || BC such that AD = 2.4 cm, AB = 3.2 cm and AC = 8 cm, then what is the length of AE?
Chapter:
The areas of two similar triangles ∆ABC and ∆PQR are 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:
Find the probability that 5 Sundays occur in the month of November of a randomly selected year.
Chapter:
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Chapter:
Divide the polynomial 16x2 + 24x + 15 by (4x + 3) and write the quotient and the remainder.
Chapter:
If tangents PA and PB drawn from an external point P to a circle with centre O are inclined to each other at an angle of 80°, then find ∠POA.
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:
Draw a line segment of 6 cm and divide it in the ratio 3 : 2.
Chapter:
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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:
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Chapter: [2] Polynomials
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.
Chapter:
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
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:
An open metal bucket is in the shape of a frustum of cone of height 21 cm with radii of its lower and upper ends are 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of ₹ 40 per litre.
Chapter:
A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.
Chapter:
A person on tour has ₹ 4200 for his expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by ₹ 70. Find the original duration of the tour.
Chapter:
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