Rajasthan Board Class 10 Question Paper 2024 Maths

RAJASTHAN BOARD

QUESTION
PAPER
2024

DOWNLOAD PDF


RBSE

 Roll No.

No. of Questions – 22 S-09-Mathematics
No. of Printed Pages – 15

 , 2024
SECONDARY EXAMINATION, 2024

MATHEMATICS
  3  15 
 : 80

     

GENERAL INSTRUCTIONS TO THE EXAMINEES :

(1)    -     

Candidate must write first his / her Roll No. on the question paper compulsorily.

(2)      

All the questions are compulsory.

(3)       -    

Write the answer to each question in the given answer-book only.

S-09-Mathematics [ Turn over

2

(4)      ,         
For questions having more than one part, the answers to those parts are to be written
together in continuity.

(5) -          //     
     
If there is any error / difference / contradiction in Hindi & English versions of the
question paper, the question of Hindi version should be treated valid.
(6)            
Write down the serial number of the question before attempting it.
(7)   16  22      
There are internal choices in Question Nos. 16 to 22.

(8)  -             ,  - 
            ‘ ’   
Write on both sides of the pages of your answer-book. If any rough work is to be
done, do it on last pages of the answer-book and cross with slant lines and write
‘Rough Work’ on them.

S-09-Mathematics

3

 – 
SECTION – A

  :
Multiple Choice Questions :

1.           -   :
Choose the correct option to answer the following objective questions and write in the
answer sheet :

(i)      27      162    
 54 ,     :

() 81 () 27

() 54 () 18

The Highest Common Factor of two numbers is 27 and their Least Common
Multiple is 162. If one number is 54, then the other number is :

(A) 81 (B) 27

(C) 54 (D) 18 1

(ii)  x2 – 2x – 8    :

() 2, 4 () 2, 5

() –2, 4 () –2, 6

The zeroes of the polynomial x2 – 2x – 8 are :

(A) 2, 4 (B) 2, 5

(C) –2, 4 (D) –2, 6 1
S-09-Mathematics [ Turn over

4
(iii)    x     y  7   5  ,      

   ?

() 2x = 7y + 5 () 5x = 7y + 2

() 7x = 2y – 5 () 2x = 7y – 5

If twice the first number x is 5 less than 7 times the second number y, then
which of the following equations is correct ?

(A) 2x = 7y + 5 (B) 5x = 7y + 2

(C) 7x = 2y – 5 (D) 2x = 7y – 5 1

(iv)       2    3 ,  n   –

() 3n + 2 () 3n – 1

() 2n – 1 () 3n – 2

If the first term of an arithmetic progression is 2 and the common difference is
3, then the nth term will be :

(A) 3n + 2 (B) 3n – 1

(C) 2n – 1 (D) 3n – 2 1

(v) 3        –

() 42 () 39

() 45 () 33

The sum of the first five multiples of 3 is :

(A) 42 (B) 39

(C) 45 (D) 33 1

S-09-Mathematics

5

(vi)    PQR  PQ2 + QR2 = PR2 ,       ?

() P () Q

() R ()    

If PQ2 + QR2 = PR2 in triangle PQR, then which angle will be a right angle ?

(A) P (B) Q

(C) R (D) None of these 1

(vii)  (0, 3)  x-    :

() 3 () 0

() 2 () 1

The distance of point (0, 3) from x-axis will be :

(A) 3 (B) 0

(C) 2 (D) 1 1

(viii) 2 sin 45º cos 45º    :

() 2 () 0

1
() () 1
2

The value of 2 sin 45º cos 45º is :

(A) 2 (B) 0

1
(C) (D) 1 1
2

S-09-Mathematics [ Turn over

6
1
(ix)          ,       :
3

() 90º () 60º

() 45º () 30º

1
If the shadow of a tree is times its height, then angle of elevation of the
3
sun is :

(A) 90º (B) 60º

(C) 45º (D) 30º 1

(x)          -    :

()  () 

()  () 

The tangents drawn at the ends of any diameter of a circle are mutually :

(A) perpendicular (B) parallel

(C) intersecting (D) secant 1

(xi)      176  ,     :

() 21  () 14 

() 28  () 7 

If the circumference of a circle is 176 cm, then its radius is :

(A) 21 cm (B) 14 cm

(C) 28 cm (D) 7 cm 1

S-09-Mathematics

7
(xii)      36   ,     :

() 3  () 6 

() 2  () 5 

If the volume of a sphere is 36 cm3, then its radius is :
(A) 3 cm (B) 6 cm
(C) 2 cm (D) 5 cm 1

(xiii)  11      :

() 4 () 5

() 5.5 () 6

The mean of first 11 whole numbers will be :
(A) 4 (B) 5
(C) 5.5 (D) 6 1

(xiv)  3, 3, 5, 3, 4, 2, 8, 4, 3, 4, 3    :

() 7 () 3

() 4 () 5

The mode of distribution 3, 3, 5, 3, 4, 2, 8, 4, 3, 4, 3 is :
(A) 7 (B) 3
(C) 4 (D) 5 1

(xv)  P(E) = 0.05 ,  ‘E ’    :

() 0.90 () 0.59

() 0.50 () 0.95

If P(E) = 0.05, then the probability of ‘Not E’ will be :
(A) 0.90 (B) 0.59
(C) 0.50 (D) 0.95 1

S-09-Mathematics [ Turn over

8

2.          -   
Fill in the blanks in the following questions and write them in the answer book.

–1 5
(i)   –3, , , ...  11  ________  
2 2

–1 5
The eleventh term of Arithmetic Progression –3, , , ... is ________. 1
2 2

(ii) cos2 60º – sin2 60º   ________  

The value of cos2 60º – sin2 60º is ________. 1

(iii)      154 2 ,    ________  

If the area of a circle is 154 cm2, then its radius is ________. 1

(iv)      6    8  ,     ________  
If the radius of a cone is 6 cm and height is 8 cm, then its slant height is
________. 1

(v) 3  = 2  + ________.

3 Median = 2 Mean + ________. 1

(vi)   60 – 75    __________  
The class mark of the class interval 60 – 75 is __________. 1

(vii)       6       __________   

The probability of getting a number greater than 6 when a die is thrown, is
__________. 1

S-09-Mathematics

9

3.   :
Very Short Answer Type Questions :
(i)  x = 23  32  y = 22  32 ,  x  y    (...) 
 
If x = 23  32 and y = 22  32, then find the Least Common Multiple (L.C.M.)
of x and y. 1
(ii)  x2 – 3     
Find the zeroes of the polynomial x2 – 3. 1
(iii)    x + y = 14  x – y = 4    
Solve the pair of linear equations x + y = 14 and x – y = 4. 1
(iv)     DE || BC ,  EC     

In the following figure, if DE || BC, then find the value of EC. 1

(v)  (–a, a)  (–a, –a)       
Find the distance between the points (–a, a) and (–a, –a). 1
(vi)           ,      
 
The shadow of a vertical pole is equal to the height of the pole, then find the
angle of elevation of the sun. 1

S-09-Mathematics [ Turn over

10
(vii)        100            
 60º ,       
If the angle of elevation of the top of a tower from a point at a distance of 100
metre from its foot is 60º, then find the height of the tower. 1

(viii)     7        60º      
 
The radius of circle is 7 cm and the angle subtended at the centre is 60º. Find
the length of arc. 1

(ix)       1014          
The total surface area of a cube is 1014 meter2. Find the side of the cube. 1

(x) 7          

Find the surface area of a sphere of radius 7 cm. 1

 – 
SECTION – B

  :
Short Answer Type Questions :

4.    5     

Prove that 5 is an irrational number. 2

5.  2x2 – x – 6     
Find the zeroes of the polynomial 2x2 – x – 6. 2

S-09-Mathematics

11

6.     26          ,     
The difference of two numbers is 26 and one number is three times the other number,
then find the numbers. 2

7.     DE || BC, AD = x, DB = x – 2, AE = x + 2  EC = x – 1 ,  x 
   
In the following figure, if DE || BC, AD = x, DB = x – 2, AE = x + 2 and EC = x – 1,
then find the value of x. 2

8.   (x, 3)  (5, 7)     5  ,  x     
If the distance between the points (x, 3) and (5, 7) is 5 units, then find the value of x. 2

9.  tan A = 1 ,  2 sin A cos A     
If tan A = 1, then find the value of 2 sin A cos A. 2

10.    ,   20   14  ,           
  30º    ,        (       )
The tops of two pillars, whose heights are 20 m and 14 m, are connected by a wire. If
the wire makes an angle of 30º with the horizontal line, then find the length of the
wire. (Wire is connected in straight line form) 2

11.      5   3             
      
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the
larger circle which touches the smaller circle. 2

S-09-Mathematics [ Turn over

12

12.  21         60º          
     
An arc of a circle of radius 21 cm subtends an angle of 60º at the centre. Find the area
of the sector formed by the arc. 2

13.         154 2     15  ,  
    
The area of the base of a right circular cylinder is 154 cm2 and its height is 15 cm, find
its curved surface area. 2

14.        :
x 5 6 7 8 9 10

f 8 6 12 7 5 6

Find the mean of the following frequency distribution : 2

x 5 6 7 8 9 10

f 8 6 12 7 5 6

15.                :

A B C D E A

              (i) A   (ii) D   ?
A child has a die whose six faces show the letters as given below : 2

A B C D E A

The die is thrown once. What is the probability of getting (i) A (ii) D ?

S-09-Mathematics

13
 – 
SECTION – C

-  :
Long Answer Type Questions :

16. 10  250    4     ?
How many multiples of 4 lie between 10 and 250 ? 3
/OR
0  50          
Find the sum of the odd numbers between 0 and 50. 3

17.   A(6, 1), B(8, 2), C(9, 4)  D(p, 3)  -      ,  p
    
If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram,
taken in order, find the value of p. 3
/OR
        (–1, 7)  (4, –3)      2 : 3
      
Find the coordinates of the point which divides the line segment joining the points (–1, 7)
and (4, –3) in the ratio 2 : 3. 3

18.        -    
Prove that the parallelogram circumscribing a circle is a rhombus. 3
/OR
         -        
   
Prove that opposite sides of quadrilateral circumscribing a circle subtend
supplementary angles at the centre of the circle. 3

S-09-Mathematics [ Turn over

14

19.        :
 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50

 4 28 42 20 6

Find the median of the following frequency distribution : 3
Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Frequency 4 28 42 20 6

/OR
      21.5 ,  k     
x 5 15 25 35 45
f 6 4 3 k 2
If the mean of the following frequency distribution is 21.5, then find the value of k. 3
x 5 15 25 35 45
f 6 4 3 k 2

 – 
SECTION – D
  :
Essay Type Questions :
20.         7       13   ,   
   
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is
13 cm, find the other two sides. 4
/OR
          365  
Find two consecutive positive integers, sum of whose squares is 365. 4

S-09-Mathematics

15
1 – cos 
21.    (cosec  – cot )2 = .
1  cos 
1 – cos 
Prove that (cosec  – cot )2 = . 4
1  cos 
/OR
   (cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1.
Prove that (cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1. 4

22.    17.5       :
 0–5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30

 3 7 15 24 16 5

Find the mean of the following distribution by considering assumed mean as 17.5 : 4
Class 0–5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30
Frequency 3 7 15 24 16 5
/OR
       :
 1–3 3–5 5–7 7–9 9 – 11

 7 8 2 2 1

Find the mode of the following frequency distribution : 4
Class 1–3 3–5 5–7 7–9 9 – 11
Frequency 7 8 2 2 1

___________

S-09-Mathematics [ Turn over

16

S-09-Mathematics

QUESTION PAPERS
GET PREVIOUS YEAR QUESTION PAPERS FOR ALL CLASSES FOR CBSE, ISCSE, ISC AND ALL ALL
STATE BOARDS HERE AT

Andhra Pradesh Board Question Papers
BOARD
WISE Assam Board Question Papers
Bihar Board Question Papers
Chhattisgarh Board Question Papers
Goa Board Question Papers
Gujarat Board Question Papers
Haryana Board Question Papers
Himachal Pradesh Board Question Papers
J&K State Board Question Papers
Jharkhand Board Question Papers
Karnataka Board Question Papers
Kerala Board Question Papers
Madhya Pradesh Board Question Papers
Maharashtra State Board Question Papers
Manipur Board Question Papers
Meghalaya Board Question Papers
Mizoram Board Question Papers
Nagaland Board Question Papers
Orissa Board Question Papers
Punjab Board Question Papers
Rajasthan Board Question Papers
Tamil Nadu Board Question Papers
Telangana State Board Question Papers
Tripura Board Question Papers
Uttarakhand Board Question Papers
Uttar Pradesh (UP) Board Question Papers
West Bengal (WB) Board Question Papers