English Medium
Academic Year: 2019-2020
Date & Time: 12th March 2020, 10:30 am
Duration: 3h
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General Instructions:
- This question paper comprises four sections – A, B, C and D.
This question paper carries 40 questions. All questions are compulsory. - Section A : Q. No. 1 to 20 question of one mark each.
- Section B : Q. No. 21 to 26 comprises of 6 question of two mark each.
- Section C : Q. No. 27 to 34 comprises of 8 questions of three marks each.
- Section D : Q. No. 35 to 40 comprises of 6 questions of four marks each.
- There is no overall choice in the question paper. However, an internal choice has been provided in 2 question of one mark each. 2 questions of two marks each, 3 questions of three marks each and 3 questions of four marks each. 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 sum of exponents of prime factors in the prime-factorisation of 196 is ______.
3
4
5
2
Chapter:
Euclid’s division Lemma states that for two positive integers a and b, there exists unique integer q and r satisfying a = bq + r, and ______.
0 < r < b
0 < r ≤ b
0 ≤ r < b
0 ≤ r ≤ b
Chapter:
The zeroes of the polynomial x2 – 3x – m (m + 3) are ______.
m, m + 3
– m, m + 3
m, – (m + 3)
– m, – (m + 3)
Chapter:
The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is ______.
`- 14/3`
`2/5`
5
10
Chapter:
The roots of the quadratic equation x2 – 0.04 = 0 are ______.
± 0.2
± 0.02
0.4
2
Chapter:
The common difference of the A.P. `1/p, (1 - p)/p, (1 - 2p)/p`, ... is ______.
1
`1/p`
–1
`- 1/p`
Chapter:
The nth term of the A.P. a, 3a, 5a, ... is ______.
na
(2n – 1)a
(2n + 1)a
2na
Chapter:
The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is ______.
(2, 0)
(0, 2)
(3, 0)
(2, 2)
Chapter:
The co-ordinates of the point which is reflection of point (–3, 5) in x-axis are ______.
(3, 5)
(3, –5)
(–3, –5)
(–3, 5)
Chapter:
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 ______.
4
3
2
1
Chapter:
In figure, MN || BC and AM : MB = 1 : 2, then `(ar(ΔAMN))/(ar(ΔABC))` = ______.
Chapter:
In ΔABC, AB = `6sqrt(3)` cm, AC = 12 cm and BC = 6 cm, then B = ______.
Chapter:
Two triangles are similar if their corresponding sides are ______.
Chapter:
The value of (tan 1° tan 2° ...... tan 89°) is equal to ______.
Chapter:
The value of sin 32° cos 58° + cos 32° sin 58° is ______.
Chapter:
The value of `(tan 35^circ)/(cot 55^circ) + (cot 78^circ)/(tan 12^circ)` is ______.
Chapter:
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If sin A + sin2 A = 1, then find the value of the expression (cos2 A + cos4 A).
Chapter:
In the following figure is a sector of circle of radius 10.5 cm. Find the perimeter of the sector. `("Take" π = 22/7)`
Chapter:
If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3, then find the probability of x2 < 4.
Chapter:
What is the probability that a randomly taken leap year has 52 Sundays?
Chapter:
Find the area of the sector of a circle of radius 6 cm whose central angle is 30°. (Take π = 3.14)
Chapter:
Find the class marks of the classes 20 – 50 and 35 – 60.
Chapter:
|
A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to hand over the paper. The following were the answers given by the students: `2x + 3, 3x^2 + 7x + 2, 4x^3 + 3x^2 + 2, x^3 + sqrt(3x) + 7, 7x + sqrt(7), 5x^3 - 7x + 2, 2x^2 + 3 - 5/x, 5x - 1/2, ax^3 + bx^2 + cx + d, x + 1/x`. |
Answer the following question:
- How many of the above ten, are not polynomials? [1]
- How man of the above ten, are quadratic polynomials? [1]
Chapter:
In the following figure, ABC and DBC are two triangles on the same base BC. If AD intersects B at O, show that `(ar(ΔABC))/(ar(ΔDBC)) = (AO)/(DO)`
Chapter:
In the following figure, if AD ⊥ BC, then prove that AB2 + CD2 = BD2 + AC2.
Chapter:
Prove that `1 + (cot^2 α)/(1 + "cosec" α) = "cosec" α`
Chapter:
The volume of a right circular cylinder with its height equal to the radius is `25 1/7` cm3. Find the height of the cylinder.
Chapter:
Find the mode of the following frequency distribution:
| Class | Frequency |
| 15 – 20 | 3 |
| 20 – 25 | 8 |
| 25 – 30 | 9 |
| 30 – 35 | 10 |
| 35 – 40 | 3 |
| 40 – 45 | 2 |
Chapter:
From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same height and same base removed. Find the volume of the remaining solid.
Chapter:
If 2x + y = 23 and 4x – y = 19, find the values of (5y – 2x) and `(y/x - 2)`.
Chapter:
Solve for x: `1/(x + 4) - 1/(x + 7) = 11/30, x ≠ - 4, 7`.
Chapter:
Show that the sum of all terms of an A.P. whose first term is a, the second term is b and the let term is c is equal to `((a + c)(b + c - 2a))/(2(b - a))`.
Chapter:
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Solve the equation: 1 + 4 + 7 + 10 + ... + x = 287.
Chapter:
In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduce by 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight.
Chapter:
If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y – 10 = 0, find the value of k.
Chapter:
Find the area of triangle ABC with A(1, –4) and the mid-points of sides through A being (2, –1) and (0, –1).
Chapter:
In the following figure, if ΔABC ∼ ΔDEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle.
Chapter:
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative term?
Chapter: [5] Arithmetic Progressions
Find the middle term of the A.P. 7, 13, 19, ...., 247.
Chapter:
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm standing water is required?
Chapter:
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
Chapter: [9] Introduction to Trigonometry
It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?
Chapter:
Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.
Chapter:
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then construct another triangle whose sides are `3/4` times the corresponding sides of the first triangle.
Chapter:
From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Chapter:
Draw a circle of radius 3.5 cm. From a point P, 6 cm from its centre, draw two tangents to the circle.
Chapter:
Construct a ΔABC with AB = 6 cm, BC = 5 cm and ∠B = 60°. Now construct another triangle whose sides are `2/3` times the corresponding sides of ΔABC.
Chapter:
A solid is in the shape of a hemisphere surmounted by a cone. If the radius of hemisphere and base radius of cone is 7 cm and height of cone is 3.5 cm, find the volume of the solid. `("Take" π = 22/7)`
Chapter:
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