CBSE BOARD EXAM PAPER – 2022 – Term 1

Class 10 - Mathematics Set – 4, Code – 430/2/4

Max. Marks: 40                                                                                                                                              Duration: 90 minutes

General Instructions :

(i) This question paper contains 50 questions out of which 40 questions are to be attempted. All questions carry equal marks.

(ii) This question paper contains three sections : A, B and C.

(iii) Section A has 20 questions. Attempt any 16 questions from Q. No 1 to 20.

Section B has 20 questions. Attempt any 16 questions from Q. No 21 to 40.

(iv) Sections 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.

(v) There is only one correct option for every multiple choice question (MCQ). Marks will not be awarded for answering more than one option.

(vi) There is no negative marking.

 

SECTION A

Question 1:

HCF of 92 and 152 is

(a) 4                           

(b) 19                        

(c) 23                         

(d) 57

 

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

 

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

 

Question 4:

The value of ( ° - °)

(a)                            

(b)                            

(c)                            

(d)

 

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)

 

Question 6:

Two coins are tossed together. The probability of getting exactly one head is

(a)                            

(b)                            

(c)                            

(d) 1

 

Question 7:

A circular arc of length 22 cm subtends an angle θ  at the centre of the circle of radius 21cm. The value of θ  is

(a) 90°                       

(b) 50°                      

(c) 60°                       

(d) 30°

 

Question 8:

A quadratic polynomial having sum and product of its zeroes as 5 and 0 respectively, is

(a) x² + 5x                 

(b) 2x(x - 5)              

(c) 5x² - 1                 

(d) x² – 5x+5

 

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

 

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

 

Question 11:

Zeroes of a quadratic polynomial x² – 5x + 6 are

(a) - 5, 1                                

(b) 5, 1                                  

(c) 2, 3                      

(d) -2, -3

 

Question 12:

 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.

 

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) l + 4 = 2b                                                            

 2(l + b) = 14                                                

(b) l – b = 4

2(l + b) = 14

(c) l = 2b + 4                                                

l + b = 14      

(d) l = 2b + 4

2(l + b) = 14

 

Question 14:

5.  can also be written as

(a) 5.21323213…..             

(b) 5.2131313….                

(c) 5.213                   

(d)

 

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

 

Question 16:

Which of the following is not defined ?

(a) sec 0°                  

(b) cosec 90°                       

(c) tan 90°                

(d) cot 90°

 

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) 24 cm                  

(b) 28 cm                             

(c) 7 cm                                

(d)  cm

 

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)  units                      

(b) 5 units                

(c) 25 units              

(d) 10 units

 

Question 19:

In a right-angled triangle PQR, Q = 90° If P = 45°, then value of tan P - R is

(a) 0                           

(b) 1                          

(c)                            

(d)

 

Question 20:

If tan  = , then the value of sec  is

(a)                        

(b)                          

(c)                       

(d)

 

SECTION B

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

 

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)                            

(b)                            

(c)                          

(d)

 

Question 23:

If sin  – cos  = 0, then the value of  is

(a) 30°                       

(b) 45°                      

(c) 90°                       

(d) 0°

 

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)

 

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

 

Question 26:

 +  can be simplified to get

(a) 2cos²                 

(b)               

(c)                     

(d)

 

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

 

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

 

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.

 

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)

 

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)

 

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

 

Question 33:

HCF of two consecutive even numbers is

(a) 0                           

(b) 1                          

(c) 2                            

(d) 4

 

Question 34:

The zeroes of a quadratic polynomial x² + 99x + 127 are

(a) Both negative

(b) Both positive

(c) One positive and one negative

(d) Reciprocal of each other

 

Question 35:

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

(a)                    

(b)               

(c)                

(d)

 

Question 36:

The decimal expansion of  is

(a) terminating after 1 decimal place.

(b) non-terminating and non-repeating.

(c) terminating after 2 decimal places.

(d) non-terminating but repeating.

 

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

 

Question 38:

The (HCF×LCM ) for the numbers 50 and 20 is

(a) 1000                    

(b) 50                        

(c) 100                       

(d) 500

 

Question 39:

For which natural number n,  ends with digit zero ?

(a) 6                           

(b) 5                          

(c) 0                            

(d) None

 

Question 40:

(1 + )(1 + sin A)(1 – sin A) is equal to

(a)                     

(b) 1                          

(c) 0                            

(d) 2

 

SECTION C

Case Study – I

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.

If height of the ball at time t (in sec) is represented by h(m), then equation of its path is given as h = - t² + 2t + 8.

Based on above information, answer the following :

Question 41:

The maximum height achieved by ball is

(a) 7 m                      

(b) 8 m                      

(c) 9 m                      

(d) 10 m

 

Question 42:

The polynomial represented by the graph is

(a) Linear polynomial       

(b) quadratic polynomial 

(c) constant polynomial

(d) cubic polynomial

 

Question 43:

Time taken by ball to reach maximum height is

(a) 2 sec                   

(b) 4 sec                   

(c) 1 sec                    

(d) 2 min

 

Question 44:

Number of zeroes of the polynomial whose graph is given is, is

(a) 1                           

(b) 2                          

(c) 0                           

(d) 3

 

Question 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, ∆ ABC and ∆ PQR.

Based on above information, answer the following questions :

 

Question 46:

Which of the following criteria is suitable for ∆ ABC to be similar to ∆ QRP ?

(a) SAS                      

(b) AAA                     

(c) SSS                       

(d) RHS

 

Question 47:

If each square is of length x unit, then length BC is equal to

(a) x  unit             

(b) 2x unit                

(c) 2  unit             

(d) x  unit

 

Question 48:

Ratio BC : PR is equal to

(a) 2 : 1                     

(b) 1 : 4                     

(c) 1 : 2                     

(d) 4 : 1

 

Question 49:

ar(PQR) : ar(ABC) is equal to

(a) 2 : 1                     

(b) 1 : 4                     

(c) 4 : 1                     

(d) 1 : 8

 

Question 50:

Which of the following is not true ?

(a) TQS   PQR              

(b) CBA STQ

(c) BAC PQR  

(d) PQR   ABC

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