Mathematics Standard - Outside Delhi set 2 2019-2020 English Medium Class 10 Question Paper Solution

The sum of exponents of prime factors in the prime-factorisation of 196 is ______.

3

4

5

2

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

The zeroes of the polynomial x² – 3x – m (m + 3) are ______.

m, m + 3

– m, m + 3

m, – (m + 3)

– m, – (m + 3)

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

The roots of the quadratic equation x² – 0.04 = 0 are ______.

± 0.2

± 0.02

0.4

2

The common difference of the A.P. `1/p, (1 - p)/p, (1 - 2p)/p`, ... is ______.

1

`1/p`

–1

`- 1/p`

The n^th term of the A.P. a, 3a, 5a, ... is ______.

na

(2n – 1)a

(2n + 1)a

2na

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)

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)

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

In figure, MN || BC and AM : MB = 1 : 2, then `(ar(ΔAMN))/(ar(ΔABC))` = ______.

In given figure, the length PB = ______ cm.

In ΔABC, AB = `6sqrt(3)` cm, AC = 12 cm and BC = 6 cm, then B = ______.

Two triangles are similar if their corresponding sides are ______.

The value of (tan 1° tan 2° ...... tan 89°) is equal to ______.

The value of sin 23° cos 67° + cos 23° sin 67° is ______.

If sin A + sin² A = 1, then find the value of the expression (cos² A + cos⁴ A).

In the following figure is a sector of circle of radius 10.5 cm. Find the perimeter of the sector. `("Take"  π = 22/7)`

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.

What is the probability that a randomly taken leap year has 52 Sundays?

If tan A = cot B, then find the value of (A + B).

Find the class marks of the classes 15 – 35 and 45 – 60.

Answer the following question:

1. How many of the above ten, are not polynomials?   [1]
2. How man of the above ten, are quadratic polynomials?   [1]

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)`

In the following figure, if AD ⊥ BC, then prove that AB² + CD² = BD² + AC².

Prove that `1 + (cot^2 α)/(1 + "cosec"  α) = "cosec"  α`

Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ

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.

A child has a die whose six faces show the letters as shown below:

\[\boxed{\text{A}}\] \[\boxed{\text{A}}\] \[\boxed{\text{B}}\] \[\boxed{\text{C}}\] \[\boxed{\text{C}}\] \[\boxed{\text{C}}\]

The die is thrown once. What is the probability of getting (i) A, (ii) C?

A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then find the ratio of the radius and the height of the conical part.

If 2x + y = 23 and 4x – y = 19, find the values of (5y – 2x) and `(y/x - 2)`.

Solve for x: `1/(x + 4) - 1/(x + 7) = 11/30, x ≠ - 4, 7`.

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))`.

Solve the equation: 1 + 4 + 7 + 10 + ... + x = 287.

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.

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.

Find the area of triangle ABC with A(1, –4) and the mid-points of sides through A being (2, –1) and (0, –1).

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.

If in an A.P., the sum of first m terms is n and the sum of its first n terms is m, then prove that the sum of its first (m + n) terms is –(m + n).

Find the sum of all the 11 terms of an A.P. whose middle most term is 30.

A fast train takes 3 hours less than a slow train for a journey of 600 kms. If the speed of the slow train is 10 km/hr less than the fast train, find the speed of the fast train.

If 1 + sin²θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.

Prove that `sqrt(5)` is an irrational number. 

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?

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.

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.

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.

Draw two tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.

Construct a triangle ABC with sides 3 cm, 4 cm and 5 cm. Now, construct another triangle whose sides are `4/5` times the corresponding sides of ΔABC. 

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.