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Board Paper of Class 10 2020 Maths (Standard) Delhi(Set 3) - 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
    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) 2
    (c) 3
    (d) 2 VIEW SOLUTION


  • Question 2
    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 3
    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 4
    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 5
    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 6
    The total number of factors of a prime number is
    (a) 1
    (b) 0
    (c) 2
    (d) 3 VIEW SOLUTION


  • Question 7
    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 8
    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 9
    The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is
    (a) a2+b2
    (b) a2-b2
    (c) a2+b2
    (d) a2-b2 VIEW SOLUTION


  • Question 10
    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 11
    Fill in the blank.
    Given ΔABC ~ ΔPQR, if ABPQ=13, then arΔABCarΔPQR=_________. VIEW SOLUTION


  • Question 12
    Fill in the blank.
    In the given figure ∆ABC is circumscribing a circle, the length of BC is _____ cm.
    VIEW SOLUTION


  • Question 13
    Fill in the blank.
    The value of sin2θ+11+tan2 θ = ____________.

    OR

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


  • Question 14
    Fill in the blank.
    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. VIEW SOLUTION


  • Question 15
    Fill in the blank.
    2cos 67°sin 23°-tan 40°cot 50°-cos 0°=_________. VIEW SOLUTION


  • Question 16
    If the mean of the first n natural number is 15, then find n. VIEW SOLUTION


  • Question 17
    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 18
    The ratio of the length of a vertical rod and the length of its shadow is 1:3. Find the angle of elevation of the sun at that moment? VIEW SOLUTION


  • Question 19
    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 20
    A pair of dice is thrown once. What is the probability of getting a doublet? VIEW SOLUTION


  • Question 21
    In the given Figure, DE || AC and DC || AP. Prove that BEEC=BCCP

    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 22
    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 23
    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 24
    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 25
    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. VIEW SOLUTION


  • Question 26
    The sum of the first 7 terms of an AP is 63 and that of its next 7 terms is 161. Find the AP. VIEW SOLUTION


  • Question 27
    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 28
    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 29
    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 30
    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 31
    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 32
    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. VIEW SOLUTION


  • Question 33
    In the given figure 5, 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.
    VIEW SOLUTION


  • Question 34
    Prove that : cot θ+cosec θ-1cot θ-cosec θ+1=1+cos θsin θ VIEW SOLUTION


  • Question 35
    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


  • Question 36
    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. Use π=227 VIEW SOLUTION


  • Question 37
    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 38
    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 39
    Draw a ΔABC with BC = 7  cm, ∠B = 45° and ∠A = 105°. Then construct another triangle whose sides are 34 times the corresponding sides of ΔABC. VIEW SOLUTION


  • Question 40
    From the top of a 7 m high building the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. VIEW SOLUTION
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