CBSE Class 10 Mathematics Basics Question Paper 2020 Set 430-3-2

SET – 2
Series : JBB/3
 .
Code No. 430/3/2
 .
   -  - 
Roll No.   
Candidates must write the Code on
the title page of the answer-book.

 NOTE
(I)       -   (I) Please check that this question
 15   paper contains 15 printed pages.
(II) -         (II) Code number given on the right
   -  -  hand side of the question paper
should be written on the title page of
 
the answer-book by the candidate.
(III)      -  40  (III) Please check that this question
  paper contains 40 questions.
(IV)         (IV) Please write down the Serial
,       Number of the question in the
answer-book before attempting it.
(V)  -     15   (V) 15 minute time has been allotted to
     -    read this question paper. The
question paper will be distributed at
 10.15     10.15  
10.15 a.m. From 10.15 a.m. to 10.30
10.30     -   a.m., the students will read the
      -  question paper only and will not
     write any answer on the answer-
book during this period.

 ()
MATHEMATICS (BASIC)
{ZYm©[aV g‘¶ : 3 KÊQ>o A{YH$V‘ A§H$ : 80
Time allowed : 3 hours Maximum Marks : 80

.430/3/2. 103B 1 P.T.O.

  :

           
(i) -        – , ,    
 -   40        
(ii) -    1  20  20          
(iii) -    21  26  6          
(iv) -    27  34  8          
(v) -    35  40  6          
(vi) -          -     , - 
   , -     , -      
               
(vii)  , ,            
(viii)        

 – 
  1  10  -  ,    1        

1095
1.
1168
    
17 25 13 15
(a) (b) (c) (d) 1
26 26 16 16

2.      52               
      ?
3 1 1 3
(a) (b) (c) (d) 1
26 52 13 52

.430/3/2. 2

General Instructions :

Read the following instructions very carefully and strictly follow them :
(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 – Question no. 1 to 20 comprises of 20 questions of one mark
each.
(iii) Section B – Question no. 21 to 26 comprises of 6 questions of two
marks each.
(iv) Section C – Question no. 27 to 34 comprises of 8 questions of three
marks each.
(v) Section D – Question 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, 2 questions of two
marks, 3 questions of three marks and 3 questions of four marks. 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.

Section – A

Question numbers 1 to 10 are multiple choice questions of 1 mark each.
Select the correct option in each.

1095
1. The simplest form of is
1168
17 25 13 15
(a) (b) (c) (d) 1
26 26 16 16

2. One card is drawn at random from a well – shuffled deck of 52 cards.
What is the probability of getting a Jack ?
3 1 1 3
(a) (b) (c) (d) 1
26 52 13 52

.430/3/2. 3 P.T.O.

3.                   ?
124 131 2027 1625
(a) (b) (c) (d) 1
165 30 625 462

4.     (k – 1) x2 + kx + 1    – 4   k    :
5 5 4 4
(a) – (b) (c) – (d) 1
4 4 3 3

5.  
  A(–3, b)  B(1, b + 4)       P(–1, 1) ,  b
  
(a) 1 (b) –1 (c) 2 (d) 0 1

6.      :
 0-5 5-10 10-15 15-20 20-25

 10 15 12 20 9

           
(a) 15 (b) 25 (c) 30 (d) 35 1

7.     ,  245  1029      5    
(a) 15 (b) 16 (c) 9 (d) 5 1

8. 
  A(2, –3)  B(2, 2)      
(a) 2  (b) 3  (c) 4  (d) 5  1

9.  3x2 – 7x – 27       :
7
(a) 27 (b) 9 (c) –9 (d) 1
3
.430/3/2. 4

3. Which of the following rational numbers is expressible as a terminating
decimal ?
124 131 2027 1625
(a) (b) (c) (d) 1
165 30 625 462

4. If one zero of the quadratic polynomial, (k – 1) x2 + kx + 1 is –4 then the
value of k is
5 5 4 4
(a) – (b) (c) – (d) 1
4 4 3 3

5. If P(–1, 1) is the midpoint of the line segment joining A(–3, b) and
B(1, b + 4), then b is equal to
(a) 1 (b) –1 (c) 2 (d) 0 1

6. Consider the following distribution :

Class 0-5 5-10 10-15 15-20 20-25

Frequency 10 15 12 20 9

The sum of lower limits of the median class and the modal class is
(a) 15 (b) 25 (c) 30 (d) 35 1

7. What is the largest number that divides 245 and 1029, leaving remainder
5 in each ?
(a) 15 (b) 16 (c) 9 (d) 5 1

8. The distance between the points A(2, –3) and B(2, 2) is
(a) 2 units (b) 3 units (c) 4 units (d) 5 units 1

9. The product of the two zeroes of the polynomial 3x2 – 7x – 27 is :
7
(a) 27 (b) 9 (c) –9 (d) 1
3

.430/3/2. 5 P.T.O.

10.     P   O        PA  PB     
 80°     ,  POA   :
(a) 50° (b) 60° (c) 70° (d) 80° 1

  11  15     

11. k        x + 2y = 3  5x + ky = 7     ,
 ________. 1

12. (tan 27º – cot 63º)    ________  1

13.         2 : 3   ,     
 ________  1

14. (a, –b)  (a, b)      ________  1

15. (sin 20° – cos 70°)    ________  1

  16-20,      
16. 14          68        
  1

    39.6         1

17.  3y – 1, 3y + 5  5y + 1       ,  y      1

25
18.  sec  = 7 ,  cot      1


 3 sin  + 2 cos  
 3 tan  = 4 ,   3 sin  – 2 cos       1

.430/3/2. 6

10. If the tangents PA and PB from an external point P to a circle with centre
O are inclined to each other at an angle of 80°, then POA equals :
(a) 50° (b) 60° (c) 70° (d) 80° 1

In Question numbers 11 to 15, fill in the blanks :

11. The value of k for which system of equations x + 2y = 3 and 5x + ky = 7
has no solution is ________. 1

12. The value of (tan 27º – cot 63º) is ________. 1

13. If ratio of the corresponding sides of two similar triangles is 2:3, then ratio
of their perimeters is _________. 1

14. Distance between (a, –b) and (a, b) is ________. 1

15. The value of (sin 20° – cos 70°) is _______. 1

Answer the following questions from Question numbers 16 to 20.
16. The perimeter of a sector of a circle of radius 14 cm is 68 cm. Find the
area of the sector. 1
OR
The circumference of a circle is 39.6 cm. Find its area. 1

17. If 3y – 1, 3y + 5 and 5y + 1 are three consecutive terms of an A.P., then
find the value of y. 1

25
18. If sec  = , then find the value of cot . 1
7
OR
 3 sin  + 2 cos  
If 3 tan  = 4, then find the value of   1
 3 sin  – 2 cos 
.430/3/2. 7 P.T.O.

19.    5 , 4   3              
            1

20.  1 , DE || BC, AD = 2.4 , AE = 3.2   CE = 4.8    BD 
  1

 1

 – 
  21  26     2   

21.    sec2 + cosec2 = tan  + cot  2

   
sin 
   1 – cos  = (cosec  + cot ) 2

22. p          x2 – 2px + 1 = 0        2

23.            –         2


               9    
    2

.430/3/2. 8

19. A bag contains 5 red, 4 blue and 3 green balls. A ball is drawn at random
from the bag. Find the probability of getting a ball not of blue colour. 1

20. In Fig. 1, DE || BC, AD = 2.4 cm, AE = 3.2 cm and CE = 4.8 cm. Find BD 1

Fig. 1

Section – B

Question numbers 21 to 26 carry 2 marks each.

21. Prove that : sec2 + cosec2 = tan  + cot  2

OR

sin 
Prove that : = (cosec  + cot ) 2
1 – cos 

22. Find the values of p for which the quadratic equation x2 – 2px + 1 = 0 has no
real roots. 2

23. Two dice are thrown at the same time. Find the probability of getting
different numbers on the two dice. 2

OR

Two dice are thrown at the same time. Find the probability that the sum
of the two numbers appearing on the top of the dice is more than 9. 2
.430/3/2. 9 P.T.O.

24.    5 , 8   7             
      
(i)       
(ii)      2

25.      5        A          
4  ,        2

26.         44    2

 – 
  27  34     3   

27.  2       (desks)       ,  
  
  A, B  C          :
(i)             
(ii)  A, B  C        B,  AC    
    3

-2

28.          10       18      
         3
.430/3/2. 10

24. A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random
from the bag. Find the probability that the drawn ball is
(i) red or white
(ii) not a white ball 2

25. The length of a tangent from a point A at a distance of 5 cm from the
centre of the circle is 4 cm. Find the diameter of the circle. 2

26. Find the area of a circle whose circumference is 44 cm. 2

Section – C
Question numbers 27 to 34 carry 3 marks each.

27. In Fig. 2, arrangement of desks in a classroom is shown. Ashima, Bharti
and Asha are seated at A, B and C respectively. Answer the following :
(i) Find whether the girls are sitting in a line.
(ii) If A, B and C are collinear, find the ratio in which point B divides the
line segment joining A and C. 3

Fig.-2

28. A number consists of two digits whose sum is 10. If 18 is subtracted from
the number, its digit are reversed. Find the number. 3

.430/3/2. 11 P.T.O.

29.     2    ,     (7 – 2 2)      3

    44, 96  404  .. (HCF)      ..
(LCM)    3

30.  1  –2,  (x3 – 4x2 – 7x + 10)   ,        3

31. 3            7            
     3

8         3 : 4       3

cos  sin 
32.    (1 – tan ) + (1 – cot ) = (cos  + sin ) 3


   (sin  + cosec )2 + (cos  + sec )2 = 7 + tan2 + cot2. 3

33.  3  XP  XQ,  O     X        AB  
 R     
  : XA + AR = XB + BR 3

 3

34.     8   6             
        3

.430/3/2. 12

29. If 2 is given as an irrational number, then prove that (7 – 2 2) is an
irrational number. 3
OR
Find HCF of 44, 96 and 404 by prime factorization method. Hence find
their LCM. 3

30. If 1 and –2 are the zeroes of the polynomial (x3 – 4x2 – 7x + 10), find its
third zero. 3

31. Draw a circle of radius 3 cm. From a point 7 cm away from its centre,
construct a pair of tangents to the circle. 3
OR
Draw a line segment of 8 cm and divide it in the ratio 3 : 4. 3

cos  sin 
32. Prove that + = (cos  + sin ) 3
(1 – tan ) (1 – cot )
OR
Prove that (sin  + cosec )2 + (cos  + sec )2 = 7 + tan2 + cot2. 3

33. In Fig. 3, XP and XQ are tangents from X to the circle with centre O. R is a
point on the circle and AB is tangent at R. Prove that : 3
XA + AR = XB + BR

Fig. 3
34. The radii of two circles are 8 cm and 6 cm. Find the radius of the circle
having its area equal to the sum of the areas of the two circles. 3
.430/3/2. 13 P.T.O.

 – 
  35  40     4   

35.                       4

                   4

36.        21 .. ,         
                    
        4

12 ..   15 ..            
      12           
                  4

37.      6    42    10   30     1 : 3 
         13     4

100  300            4

38. 7 .              60°     
  45°         (   3 = 1.732 ) 4

39.       
 : 100-150 150-200 200-250 250-300 300-350
 : 4 5 12 2 2 4

1
40.      3      5         3  
      4
____________

.430/3/2. 14

Section – D
Question Nos. 35 to 40 carry 4 marks each.

35. In a right triangle, prove that the square of the hypotenuse is equal to sum
of squares of the other two sides. 4
OR
Prove that the tangents drawn from an external point to a circle are equal
in length. 4

36. A hemispherical depression is cut out from one face of a cubical wooden
block of edge 21 cm, such that the diameter of the hemisphere is equal to
edge of the cube. Determine the volume of the remaining block. 4
OR
A solid metallic cylinder of diameter 12 cm and height 15 cm is melted and
recast into 12 toys in the shape of a right circular cone mounted on a
hemisphere of same radius. Find the radius of the hemisphere and total
height of the toy, if the height of the cone is 3 times the radius. 4

37. The sum of first 6 terms of an A.P. is 42. The ratio of its 10th term to 30th
term is 1:3. Find the first and the 13th term of the A.P. 4
OR
Find the sum of all odd numbers between 100 and 300. 4

38. 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°. Find the
height of the tower. Given that 3 = 1.732. 4

39. Find the mean of the following distribution :
Class : 100-150 150-200 200-250 250-300 300-350
Frequency : 4 5 12 2 2 4

40. The sum of the reciprocals of the ages of a child 3 years ago and 5 years
1
hence from now is . Find his present age. 4
3
____________

.430/3/2. 15 P.T.O.

.430/3/2. 16