Mathematics Standard - Delhi set 3 2019-2020 English Medium Class 10 Question Paper Solution

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is ______.

10

–10

–7

–2

The total number of factors of prime number is ______.

1

0

2

3

The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is ______.

x² + 5x + 6

x² – 5x + 6

x² – 5x – 6

–x² + 5x + 6

The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is ______.

– 2

≠ 2

3

2

The HCF and the LCM of 12, 21, 15 respectively are ______.

3, 140

12, 420

3, 420

420, 3

The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P., is ______.

6

– 6

18

–18

The first term of A.P. is p and the common difference is q, then its 10th term is ______.

q + 9p

p – 9q

p + 9q

2p + 9q

The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is ______.

a² + b²

a² – b²

`sqrt(a^2 + b^2)`

`sqrt(a^2 - b^2)`

If the point P(k, 0) divides the line segment joining the points A(2, –2) and B(–7, 4) in the ratio 1 : 2, then the value of k is ______.

1

2

–2

–1

The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is ______.

–2

2

–1

1

In Figure, ΔABC is circumscribing a circle, the length of BC is ______ cm.

Given ΔABC ∼ ΔPQR, if `"AB"/"PQ" = 1/3`, then `(ar(ΔABC))/(ar(ΔPQR))` = ______.

ΔABC is an equilateral triangle of side 2a, then length of one of its altitude is ______.

A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is ______ m.

`(2  cos 67^circ)/(sin 23^circ) - (tan 40^circ)/(cot 50^circ) - cos 0^circ` = ______.

The ratio of the length of a vertical rod and the length its shadow is `1 : sqrt(3)`. Find the angle of elevation of the sunat that moment?

Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?

A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant.

A die is thrown once. What is the probability of getting a number less than 3?

If the probability of winning a game is 0.07, what is the probability of losing it?

A pair of dice is thrown once. What is the probability of getting a doublet?

Show that (a – b)², (a² + b²) and (a + b)² are in A.P.

In the following figure, DE || AC and DC || AP. Prove that `"BE"/"EC" = "BC"/"CP"`

In the following figure, two tangents TP and TQ are drawn to circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.

The rod AC of TV disc antenna is fixed at right angles to wall AB and a rod CD is supporting the disc as shown in the figure. If AC = 1.5 m long and CD = 3 m, find (i) tan θ (ii) sec θ + cosec θ.

A piece of wire 22 cm long is bent into the form an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle. `["Use"  π = 22/7]`

The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

The sum of the first 7 terms of an A.P. is 63 and that of its next 7 terms is 161. Find the A.P.

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax² + bx + c, a ≠ 0, c ≠ 0.

Divide the polynomial f(x) = 3x² – x³ – 3x + 5 by the polynomial g(x) = x – 1 – x² and verify the division algorithm.

Determine graphically the coordinates of the vertices of triangle, the equations of whose sides are given by 2y – x = 8, 5y – x = 14 and y – 2x = 1.

If 4 is zero of the cubic polynomial x³ – 3x² – 10x + 24, find its other two zeroes.

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.

Find the area of triangle PQR formed by the points P(–5, 7), Q(–4, –5) and R(4, 5).

If the point C(–1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B.

In the following figure, ∠D = ∠E and `"AD"/"DB" = "AE"/"EC"`, Prove that ΔBAC is an isosceles triangle.

A man can row a boat downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find his speed of rowing in still water. Also find the speed of the stream.

In the given figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.

Prove that: `(cot θ + "cosec"  θ - 1)/(cot θ - "cosec"  θ + 1) = (1 + cos θ)/(sin θ)`

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.

Prove that one of every three consecutive positive integers is divisible by 3.

The sum of four consecutive numbers in an A.P. is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

Solve for x: 1 + 4 + 7 + 10 + ... + x = 287.

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.

A vertical tower stands on horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take `sqrt(3)` = 1.73)

Draw a ΔABC with BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct another triangle whose sides are `3/4` times the corresponding sides of ΔABC.

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.