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.
HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 54, then the other number is ______.
36
35
9
81
Chapter:
The cumulative frequency table is useful in determining ______.
Mean
Median
Mode
All of these
Chapter:
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
130°
90°
100°
75°
Chapter:
`2sqrt(3)` is ______.
an integer
a rational number
an irrational number
a whole number
Chapter:
Two coins are tossed simultaneously. The probability of getting at most one head is ______.
`1/4`
`1/2`
`2/3`
`3/4`
Chapter:
If one zero of the polynomial (3x2 + 8x + k) is the reciprocal of the other, then value of k is ______.
3
–3
`1/3`
`-1/3`
Chapter:
The decimal expansion of `23/(2^5 xx 5^2)` will terminate after how many places of decimal?
2
4
5
1
Chapter:
The maximum number of zeroes a cubic polynomial can have, is ______.
1
4
2
3
Chapter:
The distance of the point (–12, 5) from the origin is ______.
12
5
13
169
Chapter:
If the centre of a circle is (3, 5) and end points of a diameter are (4, 7) and (2, y), then the value of y is ______.
3
–3
7
4
Chapter:
The area of triangle formed with the origin and the points (4, 0) and (0, 6) is ______.
Chapter:
The co-ordinate of the point dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 is ______.
Chapter:
Value of the roots of the quadratic equation, x2 – x – 6 = 0 are ______.
Chapter:
If `sin θ = 5/13`, then the value of tan θ is ______.
Chapter:
The value of the (tan2 60° + sin2 45°) is ______.
Chapter:
The corresponding sides of two similar triangles are in the ratio 3 : 4, then the ratios of the areas of triangles is ______.
Chapter:
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In the following figure, `hat(PQ)` and `hat(AB)` are two arcs of concentric circles of radii 7 cm and 3·5 cm respectively, with centre O. If ∠POQ = 30°, then find the areas of shaded region.
Chapter:
A card is drawn at random from a well shuffled deck of 52 playing cards. What is the probability of getting a black king?
Chapter:
A ladder 25 m long just reaches the top of a building 24 m high from the ground. What is the distance of the foot of ladder from the base of the building?
Chapter:
If 3k – 2, 4k – 6 and k + 2 are three consecutive terms of A.P., then find the value of k.
Chapter:
In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?
Chapter:
In a family of three children, find the probability of having at least two boys.
Chapter:
Two dice are tossed simultaneously. Find the probability of getting an even number on both the dice.
Chapter:
Two dice are tossed simultaneously. Find the probability of getting the sum of two numbers more than 9.
Chapter:
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Chapter:
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
Chapter: [9] Introduction to Trigonometry
Prove that: `(1 - tan^2 θ)/(1 + tan^2 θ) = cos^2 θ - sin^2 θ`
Chapter:
The wheel of a motorcycle is of radius 35 cm. How many revolutions are required to travel a distance of 11 m?
Chapter:
Divide (2x2 – x + 3) by (2 – x) and write the quotient and the remainder.
Chapter:
If α and β are the zeroes of the polynomial f(x) = 5x2 – 7x + 1 then find the value of `(α/β + β/α)`.
Chapter:
Draw a line segment of length 7 cm and divide it in the ratio 2 : 3.
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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The minute hand of a clock is 21 cm long. Calculate the area swept by it and the distance travelled by tip in 20 minutes.
Chapter:
If x = 3 sin θ + 4 cos θ and y = 3 cos θ – 4 sin θ then prove that x2 + y2 = 25.
Chapter:
If sin θ + sin2 θ = 1; then prove that cos2 θ + cos4 θ = 1.
Chapter:
Using Euclid’s algorithm, find the HCF of 272 and 1032.
Chapter:
In a rectangle ABCD, P is any interior point. Then prove that PA2 + PC2 = PB2 + PD2.
Chapter:
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.
Chapter: [6] Coordinate Geometry
Solve the system of equations graphically:
2x – 3y + 13 = 0,
3x – 2y + 12 = 0
Chapter:
The product of two consecutive positive integers is 306. Find the integers.
Chapter:
The 17th term of an A.P. is 5 more than twice its 8th term. If 11th term of A.P. is 43; then find its nth term.
Chapter:
How many terms of A.P. 3, 5, 7, 9, ..... must be taken to get the sum 120?
Chapter:
A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on opposite bank is 60°. When he moves 30 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. [Take `sqrt(3)` = 1.732]
Chapter:
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Chapter:
Prove that the length of tangents drawn from an external point to a circle are equal.
Chapter:
From a solid cylinder whose height is 15 cm and the diameter is 16 cm, a conical cavity of the same height and same diameter is hollowed out, Find the total surface area of remaining solid. (Give your answer in terms of π).
Chapter:
The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.
Chapter:
The mode of the following frequency distribution is 36. Find the missing frequency (f).
| Class | Frequency |
| 0 - 10 | 8 |
| 10 - 20 | 10 |
| 20 - 30 | f |
| 30 - 40 | 16 |
| 40 - 50 | 12 |
| 50 - 60 | 6 |
| 60 - 70 | 7 |
Chapter:
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