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CBSE Class 10 Answer Key 2021 Maths Basic Question Paper

Mathematics  Term - I (Basic)

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- Section A, B and C.
(iii) Section-A contains of 20 questions. Attempt any 16 questions from Q. No. 01 to 20 .
(iv) Section-B also contains of 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.

Section - A
(In this Section, there are 20 questions. Any 16 are to be attempted.)
1. HCF of 92 and 152 is
(a) 4
(b) 19
(c) 23
(d) 57
2. In $\triangle \mathrm{ABC}, \mathrm{DE} \| \mathrm{BC}, \mathrm{AD}=4 \mathrm{~cm}, \mathrm{DB}=6 \mathrm{~cm}$ and $\mathrm{AE}=5 \mathrm{~cm}$. The length of $\mathrm{EC}$ is

(a) $7 \mathrm{~cm}$
(b) $6.5 \mathrm{~cm}$
(c) $7.5 \mathrm{~cm}$
(d) $8 \mathrm{~cm}$

3. The value of $\mathrm{k}$, for which the pair of linear equations $x+\mathrm{y}-4=0$, $2 x+\mathrm{ky}-3=0$ have no solution, is
(a) 0
(b) 2
(c) 6
(d) 8
4. The value of $\left(\tan ^{2} 45^{\circ}-\cos ^{2} 60^{\circ}\right)$ is
(a) $1 / 2$
(b) $1 / 4$
(c) $3 / 2$
(d) $3 / 4$
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) $1 / 2$
6. Two coins are tossed together. The probability of getting exactly one head is
(a) $1 / 4$
(b) $1 / 2$
(c) $3 / 4$
(d) 1
7. A circular arc of length $22 \mathrm{~cm}$ subtends an angle $\theta$ at the centre of the circle of radius $21 \mathrm{~cm}$. The value of $\theta$ is

(a) $90^{\circ}$
(b) $50^{\circ}$
(c) $60^{\circ}$
(d) $30^{\circ}$

8. A quadratic polynomial having sum and product of its zeroes as 5 and 0 respectively, is
(a) $x^{2}+5 x$
(b) $2 x(x-5)$
(c) $5 x^{2}-1$
(d) $x^{2}-5 x+5$
9. If $\mathrm{P}(\mathrm{E})=0.65$, then the value of $\mathrm{P}($ not $\mathrm{E})$ is
(a) $1.65$
(b) $0.25$
(c) $0.65$
(d) $0.35$
10. It is given that $\Delta \mathrm{DEF} \sim \Delta \mathrm{PQR} . \mathrm{EF}: \mathrm{QR}=3: 2$, then value of $\operatorname{ar}(\mathrm{DEF}):$ $\operatorname{ar}(\mathrm{PQR})$ is
(a) $4: 9$
(b) $4: 3$
(c) $9: 2$
(d) $9: 4$
11. Zeroes of a quadratic polynomial $x^{2}-5 x+6$ are
(a) $-5,1$
(b) 5,1
(c) 2,3
(d) $-2,-3$
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.

13. Perimeter of a rectangle whose length $(l)$ is $4 \mathrm{~cm}$ more than twice its breadth (b) is $14 \mathrm{~cm}$. The pair of linear equations representing the above information is
(a) $l+4=2 \mathrm{~b}$
(b) $l-\mathrm{b}=4$
(a) $2(l+\mathrm{b})=14$
(b) $2(l+b)=14$
(c) $l=2 \mathrm{~b}+4$
(d) $l=2 \mathrm{~b}+4$
(c) $l+b=14$
(d) $2(l+b)=14$
14. $5 . \overline{213}$ can also be written as
(a) $5.213213213 \ldots$
(b) $5.2131313 \ldots$
(c) $5.213$
(d) $5213 / 1000$
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) $1: 1$
16. Which of the following is not defined?
(a) $\sec 0^{\circ}$
(b) $\operatorname{cosec} 90^{\circ}$
(c) $\tan 90^{\circ}$
(d) $\cot 90^{\circ}$
17. In the given figure, a circle is touching a semi-circle at $\mathrm{C}$ and its diameter $\mathrm{AB}$ at $\mathrm{O}$. If $\mathrm{AB}=28 \mathrm{~cm}$, what is the radius of the inner circle ?

(a) $14 \mathrm{~cm}$
(b) $28 \mathrm{~cm}$
(c) $7 \mathrm{~cm}$
(d) $\frac{7}{2} \mathrm{~cm}$

18. The vertices of a triangle $\mathrm{OAB}$ are $\mathrm{O}(0,0), \mathrm{A}(4,0)$ and $\mathrm{B}(0,6)$. The median $\mathrm{AD}$ is drawn on $\mathrm{OB}$. The length $\mathrm{AD}$ is

(a) $\sqrt{52}$ units
(b) 5 units
(c) 25 units
(d) 10 units
19. In a right-angled triangle $\mathrm{PQR}, \angle \mathrm{Q}=90^{\circ}$. If $\angle \mathrm{P}=45^{\circ}$, then value of tan $P-\cos ^{2} R$ is
(a) 0
(b) 1
(c) $1 / 2$
(d) $3 / 2$
20. If $\tan \theta=\frac{2}{3}$, then the value of $\sec \theta$ is
(a) $\frac{\sqrt{13}}{3}$
(b) $\frac{\sqrt{5}}{3}$
(c) $\sqrt{\frac{13}{3}}$
(d) $\frac{3}{\sqrt{13}}$

Section-B
(There are 20 questions of 1 mark each. Any 16 are to be attempted.)
21. The perimeter of the sector of a circle of radius $14 \mathrm{~cm}$ and central angle $45^{\circ}$ is

(a) $11 \mathrm{~cm}$
(b) $22 \mathrm{~cm}$
(c) $28 \mathrm{~cm}$
(d) $39 \mathrm{~cm}$
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) $\frac{5}{6}$
23. If $\sin \theta-\cos \theta=0$, then the value of $\theta$ is
(a) $30^{\circ}$
(b) $45^{\circ}$
(c) $90^{\circ}$
(d) $0^{\circ}$
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) $\frac{49}{100}$
25. Two concentric circles are centred at $\mathrm{O}$. The area of shaded region, if outer and inner radii are $14 \mathrm{~cm}$ and $7 \mathrm{~cm}$ respectively, is

(a) $462 \mathrm{~cm}^{2}$
(b) $154 \mathrm{~cm}^{2}$
(c) $231 \mathrm{~cm}^{2}$
(d) $308 \mathrm{~cm}^{2}$

26. $\frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}$ can be simplified to get
(a) $2 \cos ^{2} \theta$
(b) $\frac{1}{2} \sec ^{2} \theta$
(c) $\frac{2}{\sin ^{2} \theta}$
(d) $2 \sec ^{2} \theta$
27. The origin divides the line segment $\mathrm{AB}$ joining the points $\mathrm{A}(1,-3)$ and $\mathrm{B}(-3,9)$ in the ratio :
(a) $3: 1$
(b) $1: 3$
(c) $2: 3$
(d) $1: 1$
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
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.
30. The solution of the pair of linear equations $x=-5$ and $\mathrm{y}=6$ is
(a) $(-5,6)$
(b) $(-5,0)$
(c) $(0,6)$
(d) $(0,0)$

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) $(3,1)$
32. The value of $\mathrm{k}$ for which the pair of linear equations $3 x+5 \mathrm{y}=8$ and $k x+15 y=24$ has infinitely many solutions, is
(a) 3
(b) 9
(c) 5
(d) 15
33. HCF of two consecutive even numbers is
(a) 0
(b) 1
(c) 2
(d) 4
34. The zeroes of quadratic polynomial $x^{2}+99 x+127$ are
(a) both negative
(b) both positive
(c) one positive and one negative
(d) reciprocal of each other
35. The mid-point of line segment joining the points $(-3,9)$ and $(-6,-4)$ is
(a) $\left(\frac{-3}{2}, \frac{-13}{2}\right)$
(b) $\left(\frac{9}{2}, \frac{-5}{2}\right)$
(c) $\left(\frac{-9}{2}, \frac{5}{2}\right)$
(d) $\left(\frac{9}{2}, \frac{5}{2}\right)$

36. The decimal expansion of $\frac{13}{2 \times 5^{2} \times 7}$ is
(a) terminating after 1 decimal place.
(b) non-terminating and non-repeating.
(c) terminating after 2 decimal places.
(d) non-terminating but repeating.
37. In $\Delta \mathrm{ABC}, \mathrm{DE} \| \mathrm{BC}, \mathrm{AD}=2 \mathrm{~cm}, \mathrm{DB}=3 \mathrm{~cm}, \mathrm{DE}: \mathrm{BC}$ is equal to

(a) $2: 3$
(b) $2: 5$
(c) $1: 2$
(d) $3: 5$
38. The $(\mathrm{HCF} \times \mathrm{LCM})$ for the numbers 50 and 20 is
(a) 1000
(b) 50
(c) 100
(d) 500
39. For which natural number $\mathrm{n}, 6^{\mathrm{n}}$ ends with digit zero ?
(a) 6
(b) 5
(c) 0
(d) None
40. $\left(1+\tan ^{2} A\right)(1+\sin A)(1-\sin A)$ is equal to
(a) $\frac{\cos ^{2} \mathrm{~A}}{\sec ^{2} \mathrm{~A}}$
(b) 1
(c) 0
(d) 2

Section - C
Attempt any 4 questions from Q. No. 41 to 45 and another 4 from $Q .$ No. 46 to $50 .$
Case Study - I
Sukriti throws a ball upwards, from a rooftop which is $8 \mathrm{~m}$ 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 $\mathrm{h}=-\mathrm{t}^{2}+2 \mathrm{t}+8$
Based on above information, answer the following :

41. The maximum height achieved by ball is
(a) $7 \mathrm{~m}$
(b) $8 \mathrm{~m}$
(c) $9 \mathrm{~m}$
(d) $10 \mathrm{~m}$
42. The polynomial represented by above graph is
(a) linear polynomial
(b) quadratic polynomial
(c) constant polynomial
(d) cubic polynomial
43. Time taken by ball to reach maximum height is
(a) 2 sec.
(b) $4 \mathrm{sec}$.
(c) $1 \mathrm{sec}$.
(d) $2 \mathrm{~min}$.
44. Number of zeroes of the polynomial whose graph is given, is
(a) 1
(b) 2
(c) 0
(d) 3
45. Zeroes of the polynomial are
(a) 4
(b) $-2,4$
(c) 2,4
(d) 0,4

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, $\triangle \mathrm{ABC}$ and $\triangle \mathrm{PQR}$.
Based on above information, answer the following questions:
46. Which of the following criteria is not suitable for $\triangle \mathrm{ABC}$ to be similar to $\Delta \mathrm{QRP}$ ?
(a) SAS
(b) AAA
(c) SSS
(d) RHS
47. If each square is of length $x$ unit, then length $\mathrm{BC}$ is equal to
(a) $x \sqrt{2}$ unit
(b) $2 x$ unit
(c) $2 \sqrt{x}$ unit
(d) $x \sqrt{x}$ unit
48. Ratio BC : PR is equal to
(a) $2: 1$
(b) $1: 4$
(c) $1: 2$
(d) $4: 1$
49. $\operatorname{ar}(\mathrm{PQR}): \operatorname{ar}(\mathrm{ABC})$ is equal to
(a) $2: 1$
(b) $1: 4$
(c) $4: 1$
(d) $1: 8$
50. Which of the following is not true?
(a) $\triangle \mathrm{TQS} \sim \triangle \mathrm{PQR}$
(b) $\Delta \mathrm{CBA} \sim \Delta \mathrm{STQ}$
(c) $\Delta \mathrm{BAC} \sim \Delta \mathrm{PQR}$
(d) $\Delta \mathrm{PQR} \sim \Delta \mathrm{ABC}$

CBSE Class 10 Answer Key 2021 Maths Basic