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# Board Paper of Class 10 Maths (Basic) Term-I 2021 Delhi(Set 4) - Solutions

General Instructions :
Read the following instructions very carefully and strictly follow them:
(i) This question paper contains 50 questions out of which 40 questions are to be attempted. All questions carry equal marks.
(ii) The question paper consists of three Sections : A, B and C.
(iii) Section A has 20 questions. Attempt any 16 questions from Q. No. 1 to 20.
(iv) Section B has 20 questions. Attempt any 16 questions from Q. No. 21 to 40.
(v) Section C contains of two Case Studies containing 5 questions in each case. Attempt any 4 questions from Q. No. 41 to 45 and another 4 from Q. No. 46 to 50.
(vi) There is only one correct option for every multiple choice question (MCQ). Marks will not be awarded for answering more than one option.
(vii) There is no negative marking.

• Question 1
HCF of 92 and 152 is
(a) 4
(b) 19
(c) 23
(d) 57 VIEW SOLUTION

• Question 2
In $∆$ABC, DE || BC, AD = 4 cm, DB = 6 cm and AE = 5 cm. The length of EC is (a) 7 cm
(b) 6.5 cm
(c) 7.5 cm
(d) 8 cm VIEW SOLUTION

• Question 3
The value of k, for which the pair of linear equations x + y – 4 = 0, 2x + ky – 3 = 0 have no solution, is
(a) 0
(b) 2
(c) 6
(d) 8 VIEW SOLUTION

• Question 4
The value of (tan2 45° – cos2 60°) is

(a) $\frac{1}{2}$

(b) $\frac{1}{4}$

(c)  $\frac{3}{2}$

(d)  $\frac{3}{4}$ VIEW SOLUTION

• Question 5
A point (x, 1) is equidistant from (0, 0) and (2, 0). The value of x is

(a) 1

(b)  0

(c)  2

(d) $\frac{1}{2}$ VIEW SOLUTION

• Question 6
Two coins are tossed together. The probability of getting exactly one head is
(a) $\frac{1}{4}$

(b) $\frac{1}{2}$

(c) $\frac{3}{4}$

(d) 1 VIEW SOLUTION

• Question 7
A circular arc of length 22 cm subtends an angle $\mathrm{\theta }$ at the centre of the circle of radius 21 cm. The value of 8 is (a) 90°
(b) 50°
(c) 60°
(d) 30° VIEW SOLUTION

• Question 8
A quadratic polynomial having sum and product of its zeroes as 5 and 0 respectively, is
(a) ${x}^{2}+5x$
(b) $2x\left(x-5\right)$
(c) $5{x}^{2}-1$
(d) ${x}^{2}-5x+5$ VIEW SOLUTION

• Question 9
If P(E) = 0.65, then the value of P(not E) is
(a) 1.65
(b) 0.25
(c) 0.65
(d) 0.35 VIEW SOLUTION

• Question 10
It is given that ∆DEF ~ ∆PQR. EF : QR = 3 : 2, then value of ar(DEF) : ar(PQR) is
(a) 4 : 9
(b) 4 : 3
(c) 9 : 2
(d) 9 : 4 VIEW SOLUTION

• Question 11
Zeroes of a quadratic polynomial x2 – 5x + 6 are
(a) −5, 1
(b) 5, 1
(c) 2, 3
(d) −2, −3 VIEW SOLUTION

• Question 12
$\frac{57}{300}$ is a
(a) non-terminating and non-repeating decimal expansion.
(b) terminating decimal expansion after 2 places of decimals.
(c) terminating decimal expansion after 3 places of decimals.
(d) non-terminating but repeated decimal expansion.  VIEW SOLUTION

• Question 13
Perimeter of a rectangle whose length (l) is 4 cm more than twice its breadth (b) is 14 cm. The pair of linear equations representing the above information is

(a)

(b)

(c)

(d)
VIEW SOLUTION

• Question 14
$5.\overline{213}$ can also be written as

(a) 5.213213213...

(b) 5.2131313...

(c) 5.213

(d) $\frac{5213}{1000}$
VIEW SOLUTION

• Question 15
The ratio in which the point (4, 0) divides the line segment joining the points (4, 6) and (4, –8) is
(a) 1 : 2
(b) 3 : 4
(c) 4 : 3
(d) 1 : 1 VIEW SOLUTION

• Question 16
Which of the following is not defined?
(a) sec 0°
(b) cosec 90°
(c) tan 90°
(d) cot 90°  VIEW SOLUTION

• Question 17
In the given figure, a circle is touching a semi-circle at C and its diameter AB at O. If AB = 28 cm, what is the radius of the inner circle? (a) 14 cm
(b) 28 cm
(c) 7 cm
(d) $\frac{7}{2}$ cm VIEW SOLUTION

• Question 18
The vertices of a triangle OAB are O(0, 0), A(4, 0) and B(0, 6). The median AD is drawn on OB. The length AD is (a) $\sqrt{52}$ units
(b) 5 units
(c) 25 units
(d) 10 units  VIEW SOLUTION

• Question 19
In a right-angled triangle PQR, ∠Q = 90°. If ∠P = 45°, then value of tanP – cos2R is
(a) 0
(b) 1
(c) $\frac{1}{2}$
(d) $\frac{3}{2}$ VIEW SOLUTION

• Question 20
If tanθ = $\frac{2}{3}$, then the value of secθ is

(a) $\frac{\sqrt{13}}{3}$

(b) $\frac{\sqrt{5}}{3}$

(c) $\sqrt{\frac{13}{3}}$

(d) $\frac{3}{\sqrt{13}}$ VIEW SOLUTION

• Question 21
The perimeter of the sector of a circle of radius 14 cm and central angle 45° is (a) 11 cm
(b) 22 cm
(c) 28 cm
(d) 39 cm VIEW SOLUTION

• Question 22
A bag contains 16 red balls, 8 green balls and 6 blue balls. One ball is drawn at random. The probability that it is blue ball is
(a) $\frac{1}{6}$
(b) $\frac{1}{5}$
(c) $\frac{1}{30}$
(d) $\frac{5}{6}$ VIEW SOLUTION

• Question 23
If $\mathrm{sin\theta }-\mathrm{cos\theta }=0,$ then the value of $\mathrm{\theta }$ is
(a) 30°
(b) 45º
(c) 90°
(d) 0º VIEW SOLUTION

• Question 24
The probability of happening of an event is 0.02. The probability of not happening of the event is
(a) 0.02
(b) 0.80
(c) 0.98
(d) $\frac{49}{100}$ VIEW SOLUTION

• Question 25
Two concentric circles are centred at O. The area of shaded region, if outer and inner radii are 14 cm and 7 cm respectively, is (a) 462 cm2
(b) 154 cm2
(c) 231 cm2
(d) 308 cm2 VIEW SOLUTION

• Question 26
can be simplified to get

(a) 2 cos2 θ

(b)

(c)

(d) 2 sec2 θ VIEW SOLUTION

• Question 27
The origin divides the line segment AB joining the points A(1, –3) and B(–3, 9) in the ratio :
(a) 3 : 1
(b) 1 : 3
(c) 2 : 3
(d) 1 : 1 VIEW SOLUTION

• Question 28
The perpendicular bisector of a line segment A(–8, 0) and B(8, 0) passes through a point (0, k). The value of k is
(a) 0 only
(b) 0 or 8 only
(c) any real number
(d) any non-zero real number VIEW SOLUTION

• Question 29
Which of the following is a correct statement?
(a) Two congruent figures are always similar.
(b) Two similar figures are always congruent.
(c) All rectangles are similar.
(d) The polygons having same number of sides are similar. VIEW SOLUTION

• Question 30
The solution of the pair of linear equations x = –5 and y = 6 is
(a) (–5, 6)
(b) (–5, 0)
(c) (0, 6)
(d) (0, 0) VIEW SOLUTION

• Question 31
A circle of radius 3 units is centered at (0, 0). Which of the following points lie outside the circle?
(a) (–1, –1)
(b) (0, 3)
(c) (1, 2)
(d) (3, 1) VIEW SOLUTION

• Question 32
The value of k for which the pair of linear equations 3x + 5y = 8 and kx + 15y = 24 has infinitely many solutions, is
(a) 3
(b) 9
(c) 5
(d) 15 VIEW SOLUTION

• Question 33
HCF of two consecutive even numbers is
(a) 0
(b) 1
(c) 2
(d) 4 VIEW SOLUTION

• Question 34
The zeroes of quadratic polynomial x2 + 99x + 127 are
(a) both negative
(b) both positive
(c) one positive and one negative
(d) reciprocal of each other VIEW SOLUTION

• Question 35
The mid-point of line segment joining the points (–3, 9) and (–6, –4) is

(a)

(b)

(c)

(d) VIEW SOLUTION

• Question 36
The decimal expansion of $\frac{13}{2×{5}^{2}×7}$ is

(a) terminating after 1 decimal place
(b) non-terminating and non-repeating
(c) terminating after 2 decimal places
(d) non-terminating but repeating
VIEW SOLUTION

• Question 37
In ∆ABC, DE || BC, AD = 2 cm, DB = 3 cm, DE : BC is equal to (a) 2 : 3
(b) 2 : 5
(c) 1 : 2
(d) 3 : 5 VIEW SOLUTION

• Question 38
The (HCF × LCM) for the numbers 50 and 20 is
(a) 1000
(b) 50
(c) 100
(d) 500 VIEW SOLUTION

• Question 39
For which natural number n, 6ends with digit zero?
(a) 6
(b) 5
(c) 0
(d) None VIEW SOLUTION

• Question 40
(1 + tan2 A) (1 + sin A) (1 – sin A) is equal to

(a)

(b) 1

(c) 0

(d) 2 VIEW SOLUTION

• Question 41
Sukriti throws a ball upwards, from a rooftop which is 8 m high from ground level. The ball reaches to some maximum height and then  returns and hit the ground.
It height of the ball at time t (in sec) is represented by h(m), then equation of its path is given as h = –t+ 2t + 8
Based on above information, answer the following: The maximum height achieved by ball is
(a) 7 m
(b) 8 m
(c) 9 m
​(d) 10 m
VIEW SOLUTION

• Question 42

Sukriti throws a ball upwards, from a rooftop which is 8 m high from ground level. The ball reaches to some maximum height and then  returns and hit the ground.
It height of the ball at time (in sec) is represented by h(m), then equation of its path is given as = – t+ 2+ 8
Based on above information, answer the following: The polynomial represented by above graph is
(a) linear polynomial
(c) constant polynomial
(d) cubic polynomial

VIEW SOLUTION

• Question 43
Sukriti throws a ball upwards, from a rooftop which is 8 m high from ground level. The ball reaches to some maximum height and then  returns and hit the ground.
It height of the ball at time (in sec) is represented by h(m), then equation of its path is given as = – t+ 2+ 8
Based on above information, answer the following: Time taken by ball to reach maximum height is
(a) 2 sec.
(b) 4 sec.
(c) 1 sec.
(d) 2 min. VIEW SOLUTION

• Question 44
Sukriti throws a ball upwards, from a rooftop which is 8 m high from ground level. The ball reaches to some maximum height and then  returns and hit the ground.
It height of the ball at time (in sec) is represented by h(m), then equation of its path is given as = – t+ 2+ 8
Based on above information, answer the following: Number of zeroes of the polynomial whose graph is given, is
(a) 1
(b) 2
(c) 0
(d) 3
VIEW SOLUTION

• Question 45
Sukriti throws a ball upwards, from a rooftop which is 8 m high from ground level. The ball reaches to some maximum height and then  returns and hit the ground.
It height of the ball at time (in sec) is represented by h(m), then equation of its path is given as = – t+ 2+ 8
Based on above information, answer the following: Zeroes of the polynomial are
(a) 4
(b) –2, 4
(c) 2, 4
(d) 0, 4 VIEW SOLUTION

• Question 46
Case study-II Quilts are available in various colours and design. Geometric design includes shapes like squares, triangles, rectangles, hexagons etc.
One such design is shown above. Two triangles are highlighted, ∆ABC and ∆PQR.
Based on above information, answer the following questions:
Which of the following criteria is not suitable for ∆ABC to be similar to
∆QRP ?
(a) SAS
(b) AAA
(c) SSS
(d) RHS VIEW SOLUTION

• Question 47
Case study-II Quilts are available in various colours and design. Geometric design includes shapes like squares, triangles, rectangles, hexagons etc.
One such design is shown above. Two triangles are highlighted, ∆ABC and ∆PQR.
Based on above information, answer the following questions:
If each square is of length x unit, then length BC is equal to
(a)
(b) 2x unit
(c)
(d)  VIEW SOLUTION

• Question 48
Case study-II
​​ Quilts are available in various colours and design. Geometric design includes shapes like squares, triangles, rectangles, hexagons etc.
One such design is shown above. Two triangles are highlighted, ∆ABC and ∆PQR.
Based on above information, answer the following questions:
Ratio BC : PR is equal to
(a) 2 : 1
(b) 1 : 4
(c) 1 : 2
(d) 4 : 1 VIEW SOLUTION

• Question 49
Case study-II Quilts are available in various colours and design. Geometric design includes shapes like squares, triangles, rectangles, hexagons etc.
One such design is shown above. Two triangles are highlighted, ∆ABC and ∆PQR.
Based on above information, answer the following questions:
ar(PQR) : ar(ABC) is equal to
(a) 2 : 1
(b) 1 : 4
(c) 4 : 1
(d) 1 : 8  VIEW SOLUTION

• Question 50
Case study-II
​​ Quilts are available in various colours and design. Geometric design includes shapes like squares, triangles, rectangles, hexagons etc.
One such design is shown above. Two triangles are highlighted, ∆ABC and ∆PQR.
Based on above information, answer the following questions:
Which of the following is not true?
(a) ∆TQS ∼ ∆PQR
(b) ∆CBA ∼ ∆STQ
(c) ∆BAC ∼ ∆PQR
(d) ∆PQR ∼ ∆ABC VIEW SOLUTION
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