CBSE Class 10 Question Paper 2026 Mathematics Standard

FOR CBSE CLASS 10 EXAM PREPARATION

CBSE Class 10 2026
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT DETAILS

CBSE Class 10 2026 Question Paper Mathematics Standard

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Series : 4MNKL SET ~ 1

 .
- 
Q.P. Code 430/4/1
Roll No.  -   - 
-    
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Candidates must write the Q.P. Code
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/ NOTE :
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(I)
g
a      -    23  
Please check that this question paper contains 23 printed pages.
(II) -        -    -  - 
 
Q.P. Code 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)       -  38   
o m
c
Please check that this question paper .contains 38 questions.
e m-        
l a s
(IV)         ,
 
a g
Please write down the Serial Number of the question in the
answer-book at the given place before attempting it.
(V)  -     15        -     10.15
    10.15   10.30     -     
   -      
15 minute time has been allotted to read this question paper. The question
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paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the
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g la  () a
a
MATHEMATICS (BASIC)
  : 3    : 80
Time allowed : 3 hours Maximum Marks : 80

430/4/1 Page 1 of 24 P.T.O.
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  :
             :

(i)  -   38        

(ii) -      – , , ,    

(iii)  –     1  18   (MCQ)    19  20

    1     

(iv)  –     21  25   - (VSA)   2     

(v)  –     26  31  - (SA)   3     

(vi)  –     32  35  - (LA)   5     

(vii)  –     36  38     4      

     2        

(viii) -         ,  –   2  ,  –   2 

,  –   2    -  3          

(ix)            = 22 ,   
7

   

(x)      

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General Instructions :

Read the following instructions very carefully and strictly follow them :

(i) This question paper contains total 38 questions. All questions are
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compulsory.
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(ii) This question paper is divided into five Sections – A, B, C, D and E.
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(iii) In aSection–A,
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questions number 1 to 18 are Multiple Choice Questions
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a (MCQs) and questions number 19 & 20 are Assertion-Reason based
questions of 1 mark each.

(iv) In Section–B, questions number 21 to 25 are Very Short Answer (VSA)

type questions of 2 marks each.

(v) In Section–C, questions number 26 to 31 are Short Answer (SA) type
m
questions carrying 3 marks each.
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(vi) In Section–D, questions number 32 to 35 are Long Answer (LA) type
l a
ag each.
questions carrying 5 marks

(vii) In Section–E, questions number 36 to 38 are case study based

questions carrying 4 marks each. Internal choice is provided in 2 marks

questions in each case study.

(viii) There is no overall choice. However, an internal choice has been provided
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m in 2 questions in Section-B, 2 questions in Section-C, 2 questions in
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m .co Section-D and 3 questions in Section-E.
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s (ix) Draw neat diagrams wherever required. Take = gl wherever required,
g la a7
a if not stated.

(x) Use of calculator is NOT allowed.

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 –  20  1 = 20
( )
  1  20        1    
1. HCF (850, 325) = 25    LCM (850, 325) 
(A) 442 (B) 11050
(C) 8450 (D) 2210

2.   2kx2 – 6x + 3 = 0      ,  k    
3 1
(A) (B)
2 2
3
(C) – (D) 2
2

3.   r                  
      

(A) 4r2 (B) 6r2
(C) 3r2 (D) 5r2

4. PT     O   5 cm ,        OP   
Q      PQ = x ,  PT2   

(A) x2 + 5x (B) x2 + 10x + 50
(C) x2 + 10x (D) x2 – 25

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Section – A 20  1 = 20
(Multiple Choice Questions)
Q. No. 1 to 20 are multiple choice questions of 1 mark each.

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1. If HCF (850, 325) is 25, then LCM (850, 325) is :
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(A) 442
. c (B) 11050
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(C) 8450
e m (D) 2210
l as
l as a g
2. Theag 2
value of k for which the equation 2kx – 6x + 3 = 0 has real and equal
roots, is :
3 1
(A) (B)
2 2
3
(C) – (D) 2
2

3. m
Two wooden solid hemispheres of same radii r, are joined at a point, as
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shown in the figure. The total surface area of the object is :
m
s e
l a
ag
(A) 4r2 (B) 6r2
(C) 3r2 (D) 5r2

4. PT is tangent to the circle with centre O and radius 5 cm. OP intersects
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the circle at Q. If PQ = x, then PT2 equals :
m
m .co s e m
s e g la
g la a
a
(A) x2 + 5x (B) x2 + 10x + 50
(C) x2 + 10x (D) x2 – 25

430/4/1 {} Page 5 of 24 P.T.O.

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3
5.  3, 4, 3 9, 3 8, 5, 0, 4 2         
  
4
(A) 0 (B)
7
3
(C) (D) 1
7

6.   p(x) = k        p(x)      

(A) 0 (B) 1
(C) 2 (D)    

7.      n    50 2         2 
19 2 ,  n    
(A) 10 (B) 5
(C) 15 (D) 20

x a
8.               u    
 h 
–– ––
     x = 62, a = 47.5  h = 5   u    
(A) 3 (B) 14.5
(C) 2.9 (D) 3.1

9. 52                      
     
1 2
(A) (B)
13 13
1 4
(C) (D)
26 13
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5. Probability of getting an irrational number at random from the numbers
3
3, 4, 3 9, 3 8, 5, 0, 4 2 is :
4
(A) 0 (B)
7
3
m
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(C) (D) 1
7

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6.
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The graph of polynomial p(x) = k is shown here. Number of zeroes of
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l as
polynomial p(x) is :
ag
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(A) 0 (B) 1
m
(C) 2
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(D) infinitely many

e
The sum of first n terms of an A.P.s is 50 2. If the first and the last terms
7.
la the value of n is :
are 2 and 19 2 respectively,gthen
(A) 10
a (B) 5
(C) 15 (D) 20

8. While calculating mean of a grouped frequency distribution using step
 x a ––
deviation method  u   it was found that x = 62, a = 47.5, h = 5. The
 h 
––
value of u is :
m
m(A) 3 (B) 14.5
.co
m .co (C) 2.9
s em (D) 3.1

s e la probability of
A card is drawn from a well shuffled deck of 52 cards.gThe
g la 9.
getting an ace or a ten is : a
a 1 2
(A) (B)
13 13
1 4
(C) (D)
26 13
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10.   (– 4, 2)  (1, 0)      

(A) 13  (B) 3 
(C) 9  (D) 29 

11.  6 cm    10 cm  ,        
    

(A) 12 cm (B) 16 cm
(C) 14 cm (D) 10 cm

12.    , PQ  PR  O       -   
ORQ = 25 ,  PQR    

(A) 65 (B) 25
(C) 50 (D) 75

13. sin 90 cos 90 – sin2 60    
1 3
(A) (B)
4 4
3 5
(C) – (D)
4 4
–3 3 9
14.   2 , 2, 2, ...  n   
3n 9
(A) –3 (B) 3n –
2 2
3n – 9 3
(C) (D) 3n +
2 2

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.co s e m

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10. The distance between the points (– 4, 2) and (1, 0) is :
(A) 13 units (B) 3 units
(C) 9 units (D) 29 units

11. A cone with slant height 10 cm and radius 6 cm is surmounted on a
m
hemisphere of same radius. The height of the toy is :
om . co
. c e m
em l as
l as ag
ag
(A) 12 cm (B) 16 cm
(C) 14 cm (D) 10 cm

12. In the given figure, PQ and PR are two tangents drawn to a circle with
centre O. If ORQ = 25, then the measure of PQR is :

m
m .co
s e
l a
ag
(A) 65 (B) 25
(C) 50 (D) 75

13. The value of sin 90 cos 90 – sin2 60 is :
1 3
(A) (B)
4 4
m
m(C) –
3
(D)
5
.co
.co
4 4
e m
e m las
las 14. nth term of the A.P. –
3 3 9
, , , ... is :
2 2 2 ag
ag 3n 9
(A) –3 (B) 3n –
2 2
3n – 9 3
(C) (D) 3n +
2 2

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15.    , PQ || BC    AP : AB = 3 : 7 ,  AQ : QC   

(A) 3 : 7 (B) 3 : 10
(C) 7 : 3 (D) 3 : 4
1
16.  sin  = 7 ,  tan  
1 1
(A) (B)
4 3 2 3
4 3 6
(C) (D)
7 7
17. 7  29  23 + 1
(A)      (B) 23     
(C)      (D)     
18. 9 cm       AB   40        AB 
  
22 198
(A) cm (B)
cm
7 7
44 54
(C) cm (D) cm
7 7
( –   )
 :   19  20    (A)     (R),     
   :
(A) ,  (A)   (R)     (R),  (A)      
(B) ,  (A)   (R)  ,   (R),  (A)   
   
(C)  (A)  ,   (R)   
(D)  (A)  ,   (R)   
1
19.  (A) :        0.9     
 (R) :    (E)   0  P(E)  1   
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15. In the given figure, PQ || BC. If AP : AB = 3 : 7 then, AQ : QC equals :

m
om . co
. c e m
(A) 3 : 7
e m (B) 3 : 10
l as
l as
(C) 7 : 3 (D) 3 : 4
ag
g
a 1
16. If sin  = , then tan  is :
7
1 1
(A) (B)
4 3 2 3
4 3 6
(C) (D)
7 7

om divisible by 23.
17. 7  29  23 + 1 is :
(A) a prime number. c. (B)
(C) an odd number.
e m (D) a composite number.

l a s
18. Chord AB subtends an angle of
9 cm. The length of arc AB isa:
g 40 at the centre of the circle of radius

22 198
(A) cm (B) cm
7 7
44 54
(C) cm (D) cm
7 7
(Assertion – Reason based questions)
Directions : In questions number 19 and 20, a statement of Assertion (A)
is followed by a statement of Reason (R). Choose the correct option :
m
m (A) Both, Assertion (A) and Reason (R) are true and Reason (R) is correct
.co
m .co explanation of Assertion (A).
(B) Both, Assertion (A) and Reason (R) are true, but Reason (R) is not s e m
s e correct explanation for Assertion (A).
g la
g la (C) Assertion (A) is true, but Reason (R) is false. a
a (D) Assertion (A) is false, but Reason (R) is true.
1
19. Assertion (A) : The probability of an event can not be .
0.9
Reason (R) : 0  P(E)  1 for an event E.

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20.  (A) : 4n,   (0)       
 (R) : 4n      

 – 
( - ) 5  2 = 10

  21  25   -         2   
1
21.  sin (A – B) = 2   tan (A + B) = 3 ,  0  A + B < 90  A > B
,  A  B     

1 1
22. (a)      p(x) = 6x2 – 5x – 3   ,   +      

(b)  4x2 – 12x + (2k + 1)   ,        k   
 

23. A(– 2, 3)  B(4, 1)            y-   P 
     P     

24. (a)    , AP, AQ  BC  O      -   
AB = 6 cm, AC = 7 cm  BC = 5 cm ,  AP     



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20. Assertion (A) : 4n can not end with the digit zero.
Reason (R) : Prime factorisation of 4n is unique.

Section – B
(Very Short Answer Type Questions) 5  2 = 10
m
Q. Nos. 21 to 25 are Very Short Answer type questions of 2 marks each.
om . co
. c1 e m
m
e 2
21. If sin (A – B) = and tan (A + B) = 3, 0  A + B < 90, A > B then find l as
as
l of A and B. ag
g
the values
a
22. (a) If ,  are the zeroes of polynomial p(x) = 6x2 – 5x – 3, then find the
1 1
value of + .
 
OR
(b) One zero of the polynomial 4x2 – 12x + (2k + 1) is five times the
other. Find the value of k.
o m
c
23. A (– 2, 3) and B (4, 1) are end points. of the diameter of a semi-circle.
m P. Find the co-ordinates of the
The semi-circle intersects y-axis atepoint
point P. l as
ag
24. (a) In the given figure, AP, AQ and BC are tangents to the circle with
centre O. If AB = 6 cm, AC = 7 cm and BC = 5 cm, then what is the
length of AP ?

m
m .co
m .co s e m
s e g la
g la a
a
OR

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(b)    , TP  O    -    BA,   -
  T       ABP = 35 ,   PTA     

25.    , QR || CB   RP || AC    BR = 10 cm, QA = 12 cm,
BP = 12 cm  PC = 18 cm ,  AR  QC     

 – 
(- ) 6  3 = 18
  26  31  -         3   

26.             

27.  14 cm               (i)  
 (ii)       

cot A – cos A sec A – tan A
28. (a)    cot A + cos A = sec A + tan A

1
(b)    (cosec A – sin A) (sec A – cos A) = tan A + cot A

29.    5     

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(b) In the given figure, TP is tangent to a circle with centre O. Diameter
BA when produced meets the tangent at T. If  ABP = 35, then find
the measure of  PTA.

m
om . co
. c e m
e m l as
a s
lgiven figure, QR || CB and RP || AC. If BR = 10 cm, QA = 12 cm,ag
ag
25. In the
BP = 12 cm and PC = 18 cm, then find the lengths of AR and QC.

m
m .co
e
s –C
l a
Section
ag Type Questions)
(Short Answer 6  3 = 18
Q. Nos. 26 to 31 are Short Answer type questions of 3 marks each.

26. Prove that a parallelogram circumscribing a circle, is a rhombus.

27. A chord of a circle of radius 14 cm subtends a right angle at the centre.
Find the area of the corresponding (i) minor segment (ii) major segment.
m
m .co
.co
cot A – cos A sec A – tan A
28. (a) Prove that =
cot A + cos A sec A + tan A e m
e m las
las OR
g
a1
ag (b) Prove that (cosec A – sin A) (sec A – cos A) =
tan A + cot A

29. Prove that 5 is an irrational number.

430/4/1 {} Page 15 of 24 P.T.O.

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30.               :
(i)     10  
(ii)     6  

31. (a) A(–3, –4), B(5, –3), C(1, 4)  D(–7, 3)   ABCD     
          ABCD     

(b)   A(–5, 1)  B(7, 6)       P  Q  
     P,  A       P  x + y = k  
  k     

 – 
(- ) 4  5 = 20
  32  35    -        5   

32.          4  –8  
(i)  A.P.       ?
(ii)  Sn = –36 ,  n     

33. (a)               
   
                 
    

(b)

AD  PS  ABC  PQR       ABC ~ PQR
AD BC
,     (i) ADC ~ PSR   (ii) PS = QR  

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.co s e m

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30. Two dice are rolled together. Find the probability that :
(i) the sum of the numbers obtained is 10.
(ii) the product of the numbers obtained is 6.

31. (a) The vertices of a rhombus ABCD are A(– 3, – 4), B(5, – 3), C(1, 4) and
m
D(– 7, 3). Find the length of both the diagonals. Hence, find area of
the rhombus ABCD. om . co
. c e m
e m OR
l as
(b)
l as
The line segment joining the points A (– 5, 1) and B (7, 6) is trisected
at the points P and Q such that P is nearer to A. If P lies on the line ag
agx + y = k, then find the value of k.

Section – D
(Long Answer Type Questions) 4  5 = 20
Q. Nos. 32 to 35 are Long Answer type questions of 5 marks each.

32. The third and ninth term of an A.P. are 4 and – 8 respectively.
(i) Which term of the A.P. is zero ? m
(ii) Find the value of n if Sn = – 36.
m .co
s e
33. (a) If a line is drawn parallella
ag points, then prove that the other two sides
to one side of a triangle to intersect the
other two sides in distinct
are divided in the same ratio.
OR

(b)

m
m .co
m .co s em
s e g
AD and PS are respectively, the medians of ABCla and PQR. If
g la ABC ~ PQR, then prove that a
a (i) ADC ~ PSR
AD BC
(ii) =
PS QR

430/4/1 {} Page 17 of 24 P.T.O.

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34.              30        
     60     60 m  ,       
        ( 3 = 1.73 )

35. (a)     12    ,       6   
(i)        ,     
(ii)        
(iii)          

(b)         :
x + y = 7  2x – 5y = 7

 – 
(   ) 3  4 = 12
  36  38           4   

36.

                    
                 
       x   y   
         152        80 
 
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34. The angle of elevation of the top of a building from the foot of the tower is
30 and the angle of elevation of the top of the tower from the foot of the
building is 60. If the tower is 60 m high, find the height of the building
and distance between the building and the tower. (Use 3 = 1.73)

m
35. (a) The difference between two numbers is 12. The greater number is 6
om . co
less than twice the smaller one.
. c e m
em
(i) Representing the above situation, frame two linear equations in
l as
l as two variables.
ag
ag(ii) Show that the equations have unique solution.
(iii) Solve the equations and hence find the numbers.
OR
(b) Solve the following equations graphically :
x + y = 7 and 2x – 5y = 7

Section – E
(Case-study based Questions) 3  4 = 12
m
.co
Q. Nos. 36 to 38 are Case-study based Questions of 4 marks each.
36.
e m
l as
ag

m
m .co
m .co s em
s e g l a
g la a
Observe the figure given above. It shows six identical rectangular enclosures
a made by using fencing wire mesh. These enclosures are used to protect baby
animals in a zoo. Dimensions of each enclosure is x feet  y feet. The total
length of fencing required is 152 feet and area of each enclosure is
80 square feet.

430/4/1 {} Page 19 of 24 P.T.O.

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   ,      :
(i)         x  y          1
(ii)     x      1
(iii) (a)             
            2

(b)               
             2

37.

Air Quality Index (AQI)             0 
500       AQI     ,       
         
          AQI        
     
AQI   1 – 100 101 – 200 201 – 300 301 – 400 401 – 500
    3 9 12 4 2
(i)      - (continuous frequency distribution) 
  1
(ii)             ? 1
(iii) (a)  (i)          2

(b)  (i)          2

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.co s e m

s em l a
a ag
Based on the above, answer the following questions :
(i) Write an expression for length of fencing required in terms of x and y. 1
(ii) Write the area of each enclosure in terms of x. 1
(iii) (a) Write the above equation in quadratic equation form and thus
m
find the dimensions of each enclosure using factorisation method.
om
2
. co
. c OR
e m
(b) se
m
Using above equation in quadratic form, solve the equation and l a s
l a find the dimensions of each enclosure using quadratic formula. ag 2
ag
37.

m
m .co
s e
l a
ag
The Air Quality Index (AQI) is a scale from 0 to 500 that indicates air
quality, with higher numbers signifying more pollution and greater health
concerns.
Mansi collected the daily data of AQI of her city for a month and
presented it as given below :
m
m AQI Range :
c. o Number of Days :
1 – 100 101 – 200 201 – 300 301 – 400
.co
401 – 500

m
3 9
s em 12 4 2

s e (i) Convert the data to continuous frequency distribution.
g la 1

g la a month ?
(ii) What is the quality of air in most of the days of the 1
a (iii) (a) Using table formed in part (i), find mode of the data. 2
OR
(b) Using table formed in part (i), find median of the data. 2

430/4/1 {} Page 21 of 24 P.T.O.

m . c
c. o s e m
s em
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38. ‘ ’                 
      ‘’     ‘’   

 –  4 cm   42 cm      
-                
    7 cm       1.5 cm   2.8 cm
 
   ,      :
(i)                1

(ii)               1

(iii) (a) 1.5 cm   14 cm          
          2


(b) ‘’        2

_____________

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.co s e m

s em l a
a ag
38. ‘Gilli Danda’ is a very popular traditional game of India which is played
with two wooden sticks – the larger one is called ‘Danda’ and smaller one
‘Gilli’.

m
om . co
. c e m
em l as
l as ag
ag

‘Danda’ – It is cylindrical in shape with diameter 4 cm and length 42 cm.
Gilli – It is cylindrical in middle with identical conical ends of same radius
1.5 cm and length 2.8 cm. The length of cylindrical part is 7 cm.

o m
Based on the above, answer the following questions :
(i) Find the volume of wood used m
. c
in making both the conical parts of
s e
Gilli.
g a
l in making cylindrical part of Gilli.
1

a
(ii) Find the volume of wood used 1
(iii) (a) A cylindrical log of wood of radius 1.5 cm and length 14 cm is
used to make Gilli. Find the volume of the wood scrapped. 2
OR
(b) Find the total surface area of ‘Danda’. 2
_____________
m
m .co
m .co s e m
s e g la
g la a
a

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m . c
c. o s e m
s em
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