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CBSE(NCERT) · Grade 10 · Maths

CBSE(NCERT) GRADE 10 MATHS 2026 SET2

70 questions from this Grade 10 Maths paper. Log in as a Grade 10 student to view solutions.

Grade 10 / Maths
Q1 mcq 1 mark
If the quadratic equation 9x^2 + 8kx + 16 = 0 has real and equal roots, then the value of k is
  • A. 3
  • B. –3
  • C. –4
  • D. 2/3

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Q2 mcq 1 mark
It is given that ΔABC ~ ΔEDF. Which of the following is not true ?
  • A. Perimeter of ΔABC / Perimeter of ΔEDF = AB/ED
  • B. AB/ED = AC/EF
  • C. ∠A = ∠D, ∠C = ∠F
  • D. AB + BC / AC = DE + DF / EF

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Q3 mcq 1 mark
The nth term of an A.P. is 2n + 1. Its common difference is
  • A. 2
  • B. 2n
  • C. 1
  • D. 2 + 1

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Q4 mcq 1 mark
If PQ and PR are tangents to the circle with centre O and radius 4 cm such that ∠QPR = 90º, then the length OP is
  • A. 4 cm
  • B. 4√2 cm
  • C. 8 cm
  • D. 2√2 cm

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Q5 mcq 1 mark
Observe the graph of polynomial p(x). Number of zeroes of p(x) is
  • A. 5
  • B. 4
  • C. 6
  • D. 3

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Q6 mcq 1 mark
In the given figure, DE || BC. If AD/DB = 1/3 and AC = 6 cm, then length AE is
  • A. 1.5 cm
  • B. 1 cm
  • C. 2 cm
  • D. 3 cm

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Q7 mcq 1 mark
In the given figure, a circle is centred at (1, 2). The diameter of the circle is
  • A. 4
  • B. 2√2
  • C. 5
  • D. 2√5

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Q8 mcq 1 mark
The value of k for which the system of linear equations 3/y + x/2 = 5 and 2x + ky = 7 is inconsistent, is
  • A. 4/3
  • B. 3/4
  • C. 1/3
  • D. 3

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Q9 mcq 1 mark
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
  • A. 77/4 cm2
  • B. 77 cm2
  • C. 154 cm2
  • D. 77/8 cm2

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Q10 mcq 1 mark
Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is
  • A. 2/9
  • B. 7/36
  • C. 1/4
  • D. 2/3

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Q11 mcq 1 mark
When sin A = 1/3, the value of cot A is
  • A. 2√2 / 3
  • B. 2√2
  • C. 1 / 2√2
  • D. 3

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Q12 mcq 1 mark
(1 + cot2 A) / (1 + tan2 A) equals to :
  • A. tan2 A
  • B. –1
  • C. – tan2 A
  • D. cot2 A

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Q13 mcq 1 mark
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is
  • A. 2πr3
  • B. 3πr3
  • C. 5πr3
  • D. 4πr3

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Q14 mcq 1 mark
PQ is tangent to a circle with centre O. If ∠POR = 65º, then m∠PTR is
  • A. 65º
  • B. 58.5º
  • C. 57.5º
  • D. 45º

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Q15 mcq 1 mark
Distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ) is
  • A. √(2a2 + b2)
  • B. a2 – b2
  • C. √(2a2 – b2)
  • D. a2 + b2

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Q15 mcq
The distance between the points (a cos  + b sin , 0) and (0, a sin – b cos ) is
  • A. 2 2 a  b
  • B. a2 – b2
  • C. 2 2 a – b
  • D. a2 + b2

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Q16 mcq 1 mark
Volume of cone of radius r and height h can be completely filled by two spheres. If radius of each sphere is r/2, then h:2r is equal to
  • A. 1 : 8
  • B. 1 : 2
  • C. 1 : 1
  • D. 2 : 1

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Q16 mcq
An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is r/2, then h : 2r equals
  • A. 1 : 8
  • B. 1 : 2
  • C. 1 : 1
  • D. 2 : 1

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Q17 mcq 1 mark
Arc PQ of a circle of radius 6.3 cm subtends an angle θ at the centre. If PQ = 11 cm, then the value of θ is
  • A. 10º
  • B. 60º
  • C. 45º
  • D. 100º

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Q17 mcq
Arc PQ subtends an angle  at the centre of the circle with radius 6.3 cm. If PQ = 11 cm, then the value of  is
  • A. 10º
  • B. 60º
  • C. 45º
  • D. 100º

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Q18 mcq 1 mark
The mean and median of a frequency distribution are 43 and 40 respectively. The value of its mode is
  • A. 34
  • B. 43
  • C. 38.5
  • D. 41.5

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Q19 mcq
Assertion (A) : If probability of happening of an event is 0.2p, p > 0, then p can’t be more than 5. Reason (R) : P( E ) = 1 – P(E) for an event E.
  • A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  • B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  • C. Assertion (A) is true, but Reason (R) is false.
  • D. Assertion (A) is false, but Reason (R) is true.

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Q20 mcq
Assertion (A) : ( 3 + 5 ) is an irrational number. Reason (R) : Sum of the any two irrational numbers is always irrational.
  • A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  • B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  • C. Assertion (A) is true, but Reason (R) is false.
  • D. Assertion (A) is false, but Reason (R) is true.

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Q21 short answer 2 marks
Verify that roots of the quadratic equation (p – q)x^2 + (q – r)x + (r – p) = 0 are equal when q + r = 2p.

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Q22 short answer 2 marks
D is a point on the side BC of ABC such that CAB = CDA. Show that CA^2 = CB  CD.

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Q25 short answer 2 marks
 and  are the zeroes of the polynomial 5x^2 – 16x – 10. Find the value of / + /.

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Q25 short answer 2 marks
α and β are the zeroes of the polynomial 5x^2 – 16x – 10. Find the value of α/β + β/α.

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Q26 short answer 2 marks
(a) Prove that : (1 – sin A) / (1  sin A) = sec A + tan A

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Q27 short answer 2 marks
(b) Evaluate : tan 60º / (3 cos 30º – 6 cosec 30º^2)

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Q27 short answer 3 marks
Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120º at the centre. Find the perimeters of the shaded region. (Use √3 = 1.73)

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Q28 short answer 2 marks
(a) Prove that 2 + 3 5 is an irrational number given that 5 is irrational number.

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Q28 short answer 3 marks
Prove that: (sec θ – tan θ) / (sin θ – cos θ + 1) = 1 / (sin θ + cos θ + 1)

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Q29 short answer 2 marks
(b) If the HCF of 210 and 55 is expressed as 210  5 + 55m, then find the value of m.

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Q30 short answer
A bag contains 30 balls out of which ‘m’ number of balls are blue in colour.

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Q31 short answer 3 marks
Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.

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Q32 short answer 3 marks
In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.

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Q33 short answer 3 marks
Solve the linear equations 3x + y = 14 and y = 2 graphically.

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Reading Passage

In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.

Q33 long answer 5 marks
In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.

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Q34 long answer 5 marks
A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30º. From the bottom of the same building, the angle of elevation of kite is 45º. Find the length of the string and height of roof from the ground. (Use 3 = 1.73)

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Q36 short answer 3 marks
To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14 m × 25 m × 16 m

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Reading Passage

Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR = x, ∠PRQ = α and ∠CRB = θ.

Q36 long answer 4 marks
Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR = x, ∠PRQ = α and ∠CRB = θ.

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Q37 short answer 3 marks
The internal and external radii of a hollow hemisphere are 5√2 cm and 10 cm respectively. A cone of height 5√7 cm and radius 5√2 cm is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of π. (Use √2 = 1.4)

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Reading Passage

A bag contains 30 balls out of which ‘m’ number of balls are blue in colour. (i) Find the probability that a ball drawn at random from the bag is not blue. (ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 4/5 times the probability of drawing a blue ball in the first case. Find the value of m.

Q38 short answer 3 marks
A bag contains 30 balls out of which ‘m’ number of balls are blue in colour. Find the probability that a ball drawn at random from the bag is not blue.

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Q39 short answer 3 marks
If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 4/5 times the probability of drawing a blue ball in the first case. Find the value of m.

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Reading Passage

Given diagram: TP and TQ are tangents to circle with centre M, they touch another circle with centre N at A and B. MQ=13cm, NB=8cm, BQ=35cm, TP=80cm. (i) Name the quadrilateral MQBN. (ii) Is MN parallel to PA? Give reason. (iii) Find length of TB. (iv) Find length of MN.

Q41 short answer 1 mark
Given diagram: TP and TQ are tangents to circle with centre M, they touch another circle with centre N at A and B. MQ=13cm, NB=8cm, BQ=35cm, TP=80cm. Name the quadrilateral MQBN.

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Q42 short answer 1 mark
Is MN parallel to PA? Give reason.

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Q43 short answer 1 mark
Find length of TB.

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Reading Passage

A bag contains 30 balls out of which ‘m’ number of balls are blue in colour.

Q45 short answer
Find the probability that a ball drawn at random from the bag is not blue.

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Q46 long answer 5 marks
A person on tour has 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by 180. Find the original duration of the tour and daily expense.

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Q47 long answer 5 marks
The total cost of certain piece of cloth was 2,100. During special sale time, the shopkeeper offered 2 m extra cloth for free thus reducing the price of cloth per metre by 120. What was the original per metre price of cloth and its length ?

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Reading Passage

In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.

Q49 short answer 1 mark
Name the quadrilateral MQBN.

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Q50 short answer 1 mark
Is MN parallel to PA ? Justify your answer.

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Q51 short answer 2 marks
Find length MN.

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Q53 long answer 5 marks
The median of the following data is 50 and sum of all frequencies is 90 : Class : 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 Frequency : p 15 25 20 q 8 10 Find the values of p and q.

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Q54 long answer 5 marks
Find mean and mode of the following distribution : Class : 0 – 15 15 – 30 30 – 45 45 – 60 60 – 75 75 – 90 90 – 105 Frequency : 4 8 11 14 10 7 6

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Reading Passage

Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR = x, ∠PRQ = α and ∠CRB = θ.

Q56 short answer 1 mark
Using law of reflection (i.e. ∠PRT = ∠CRT) prove that θ = α.

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Q57 short answer 1 mark
Prove that ΔPQR ~ ΔCBR where PQ is perpendicular to side AB.

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Q58 short answer 2 marks
Using similarity of triangles, find the value of x.

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Reading Passage

Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR = x, PRQ =  and CRB = .

Q59 short answer 1 mark
(i) Using law of reflection i.e. PRT = CRT, prove that  = .

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Q60 short answer 1 mark
(ii) Prove that PQR ~ CBR given that PQ is perpendicular to AB.

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Q61 short answer 2 marks
(iii) (a) Find the value of x using similarity of triangles.

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Q62 short answer 2 marks
(b) If Area PQR / Area CBR = (CB/PQ)^2, then find the value of x.

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Reading Passage

‘Kolam’ is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below. Observe the given figure carefully. There are 4 dots in first square, 8 dots in second square, 12 dots in third square and so on.

Q63 short answer 1 mark
(i) Show that number of dots given above form an A.P. Write the first term and common difference.

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Q64 short answer 1 mark
(ii) Write nth term of the A.P. formed.

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Q65 short answer 2 marks
(iii) (a) The pattern is expanded on a large ground. If total 220 dots are used, then find the number of squares formed.

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Q66 short answer 2 marks
(b) Is it possible to complete n number of squares using 100 dots ? If yes, then find the value of n.

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Reading Passage

Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below: Point A : (–4, 2) Rajasthan High Court, Point B : (4, –4) Birla Mandir, Point C : (4, 3) Heera Bagh, Point D : (–5, –2) Amar Jawan Jyoti.

Q67 short answer 1 mark
(i) Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ?

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Q68 short answer 1 mark
(ii) There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio.

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Q69 short answer 2 marks
(iii) (a) Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer.

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Q70 short answer 2 marks
(b) Using section formula, show that points A, O and B are not collinear.

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