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# Board Paper of Class 10 2020 Maths (Standard) Delhi(Set 1) - Solutions

General Instructions :
(i) This question paper comprises four sections – A, B, C and D. This question paper carries 40 questions. All questions are compulsory:
(ii) Section A : Q. No. 1 to 20 comprises of 20 questions of one mark each.
(iii) Section B : Q. No. 21 to 26 comprises of 6 questions of two marks each.
(iv) Section C: Q. No. 27 to 34 comprises of 8 questions of three marks each.
(v) Section D : Q. No. 35 to 40 comprises of 6 questions of four marks each.
(vi) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions 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.
(vii) In addition to this, separate instructions are given with each section and question, wherever necessary.
(viii) Use of calculators is not permitted.

• Question 1
If one of the zeroes of the quadratic polynomial x2 + 3x + k is 2, then the value of k is
(a) 10
(b) –10
(c) –7
(d) –2 VIEW SOLUTION

• Question 2
The total number of factors of a prime number is
(a) 1
(b) 0
(c) 2
(d) 3 VIEW SOLUTION

• Question 3
The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is
(a) x2 + 5x + 6
(b) x2 – 5x + 6
(c) x2 – 5x – 6
(d) –x2 + 5x + 6 VIEW SOLUTION

• Question 4
The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is
(a) $-2$
(b) $\ne$2
(c) 3
(d) 2 VIEW SOLUTION

• Question 5
The HCF and the LCM of 12, 21, 15 respectively are
(a) 3, 140
(b) 12, 420
(c) 3, 420
(d) 420, 3 VIEW SOLUTION

• Question 6
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is
(a) 6
(b) $-$6
(c) 18
(d) $-$18 VIEW SOLUTION

• Question 7
The first term of an AP is p and the common difference is q, then its 10th term is
(a) q + 9p
(b) p – 9p
(c) p + 9q
(d) 2p + 9q VIEW SOLUTION

• Question 8
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is
(a) ${a}^{2}+{b}^{2}$
(b) ${a}^{2}-{b}^{2}$
(c) $\sqrt{{a}^{2}+{b}^{2}}$
(d) $\sqrt{{a}^{2}-{b}^{2}}$ VIEW SOLUTION

• Question 9
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
(a) 1
(b) 2
(c) –2
(d) –1 VIEW SOLUTION

• Question 10
The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is
(a) –2
(b) 2
(c) –1
(d) 1 VIEW SOLUTION

• Question 11
Fill in the blank.
In the given figure ∆ABC is circumscribing a circle, the length of BC is _____ cm. VIEW SOLUTION

• Question 12
Fill in the blank.
Given ΔABC ~ ΔPQR, if VIEW SOLUTION

• Question 13
Fill in the blanks.
ABC is an equilateral triangle of side 2a, then length of one of its altitude is ____________. VIEW SOLUTION

• Question 15
Fill in the blank.
The value of = ____________.

OR

Fill in the blank.
The value of (1 + tan2 θ) (1 – sin θ) (1 + sin θ) = _____________. VIEW SOLUTION

• Question 16
The ratio of the length of a vertical rod and the length of its shadow is $1:\sqrt{3}.$ Find the angle of elevation of the sun at that moment? VIEW SOLUTION

• Question 17
Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes? VIEW SOLUTION

• Question 18
A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant. VIEW SOLUTION

• Question 19
A die is thrown once. What is the probability of getting a number less than 3?

OR

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

• Question 20
If the mean of the first n natural number is 15, then find n. VIEW SOLUTION

• Question 21
Show that (ab)2, (a2 + b2) and (a + b)2 are in AP. VIEW SOLUTION

• Question 22
In the given Figure, DE || AC and DC || AP. Prove that $\frac{\mathrm{BE}}{\mathrm{EC}}=\frac{\mathrm{BC}}{\mathrm{CP}}$ OR

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

• Question 23
The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in the given figure. If AC = 1.5 m long and CD = 3 m, find (i) tanθ (ii) secθ + cosecθ VIEW SOLUTION

• Question 24
A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle. VIEW SOLUTION

• Question 25
If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3. What is probability that x2 ≤ 4? VIEW SOLUTION

• Question 26
Find the mean of the following distribution:
 Class: 3 – 5 5 – 7 7 – 9 9 – 11 11 – 13 Frequency: 5 10 10 7 8

OR

Find the mode of the following data :
 Class: 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 120 – 140 Frequency: 6 8 10 12 6 5 3
VIEW SOLUTION

• Question 27
Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax2 + bx + c, a ≠ 0, c ≠ 0.

OR

Divide the polynomial f(x) = 3x2x3 – 3x + 5 by the polynomial g(x) = x – 1 – x2 and verify the division algorithm. VIEW SOLUTION

• Question 28
Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by 2y – x = 8, 5yx = 14 and y – 2x = 1.

OR

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

• Question 29
In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight. VIEW SOLUTION

• Question 30
Find the area of triangle PQR formed by the points P(–5, 7), Q(–4, –5) and R (4, 5).

OR

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. VIEW SOLUTION

• Question 31
In the given Figure 5, ∠D = ∠E and $\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}$, prove that BAC is an isosceles triangle. VIEW SOLUTION

• Question 32
In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to the first side is a right angle. VIEW SOLUTION

• Question 33
If , then prove that tan θ + cot θ = 1. VIEW SOLUTION

• Question 34
A cone of base radius 4 cm is divided into two parts by drawing a plane through the mid-points of its height and parallel to its base. Compare the volume of the two parts. VIEW SOLUTION

• Question 35
Show that the square of any positive integer cannot be of the form (5q + 2) or (5q + 3) for any integer q.

OR

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

• Question 36
The sum of four consecutive numbers in AP is 32 and the ratio of the product of  the first and last terms to the product of two middle terms is 7 : 15. Find the numbers.

OR

Solve : 1 + 4 + 7 + 10 + ... + x = 287 VIEW SOLUTION

• Question 37
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. VIEW SOLUTION

• Question 38
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. VIEW SOLUTION

• Question 39
A bucket in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm, respectively. Find the capacity of the bucket. Also find the cost of milk which can completely fill the bucket at the rate of Rs. 40 per litre. VIEW SOLUTION

• Question 40
The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village :
 Production yield/hect. 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70 No. of farms 4 6 16 20 30 24

Change the distribution to 'a more than' type distribution and draw its ogive.

OR

The median of the following data is 525. Find the values of x and y, if total frequency is 100:
 Class : Frequency: 0 – 100 2 100 – 200 5 200 – 300 x 300 – 400 12 400 – 500 17 500 – 600 20 600 – 700 y 700 – 800 9 800 – 900 7 900 – 1000 4
VIEW SOLUTION
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