Class 10 Mathematics - Chapters 1 to 5
Paper 1
SECTION A – MCQs (1 mark each)
1. If for any event E, P(E) + P(E') = q, then the value of q^2 - 3 is :
5. If one zero of the polynomial q(x) = (p^2 +
4)x^2 + 65x + 4p is reciprocal of the other, then p is:
7. The sum of the exponents of prime factors in the prime factorisation of 4004 is:
12. The 10th term of the AP 5, ___, ___, ___, 10 is:
16. The least number which is a perfect square and divisible by each of 16, 20 and
50 is:
18. The quadratic equation whose roots are 7 and 1/7 is:
SECTION A – Assertion–Reason (1 mark each)
19. Assertion (A): Common difference of the AP: 5, 1, -3, ...
Reason (R): Common difference of the AP a1, a2, a3, ... an is obtained by d = an -
an-1.
20. Assertion (A): The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118
= 0 will have infinitely many so
Reason (R): If the pair px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique
solution, then p ≠ 1.
SECTION B – Very Short Answer (2 marks each)
23. If p and q are zeroes of p(y) = 21y^2 - y - 2, then find the value of (1 - p)(1
- q).
SECTION C – Short Answer (3 marks each)
27. Find the sum of all 3-digit natural numbers which are divisible by 11.
SECTION D – Long Answer (5 marks each)
31. Prove that √3 is an irrational number.
Paper 2
Chapter 1 – Real Numbers
Q1 If the HCF of two positive integers a and b is 1, then their LCM is:
Q2 The number 3 + \sqrt{2} is:
Q19 (Assertion–Reason) – Relation between HCF and LCM of two natural numbers.
Q26(a) Prove that \sqrt{3} is an irrational number.
Q26(b) Factor tree question on prime factorisation.
Chapter 2 – Polynomials
Q3 Discriminant of x^2 - 3x - 2 = 0.
Q27 Find a quadratic polynomial whose sum and product of zeroes are 0 and –9, also
find zeroes.
Chapter 3 – Pair of Linear Equations in Two Variables
Q20 (Assertion–Reason) – Consistency of linear equations.
Q21 Solve \frac{x}{3} + \frac{y}{2} = 1 and x - y = 3.
Q28(a) Solve system graphically: x + 3y = 6, 2x - 3y = 12.
Q28(b) Complementary angles x : y = 1 : 2 – form equations and solve.
Q32(a) Word problem on difference of squares of two numbers.
Q32(b) Find k for real and equal roots in 2x^2 + kx + 3 = 0.
Chapter 4 – Quadratic Equations
Q4 Convert given equation to quadratic form and find a - b + c.
Q32 (Both parts) – Application and root condition problems.
Chapter 5 – Arithmetic Progressions
Q37 (Case study) – Spiral garden planting, find radius of nth spiral, total
saplings, etc.
Paper 3
Chapter 1 – Real Numbers
• Q1. The ratio of HCF to LCM of the least composite number and the least
prime number is … (MCQ)
• Q27. Prove that \sqrt{5} is an irrational number. (3 marks)
Chapter 2 – Polynomials
• Q2. The roots of the equation x^2 + 3x - 10 = 0 are … (MCQ)
• Q8. If \alpha, \beta are zeroes of the polynomial x^2 - 1, then value
of (\alpha + \beta) is … (MCQ)
• Q17. If \alpha, \beta are the zeroes of the polynomial 4x^2 - 3x - 7,
then 1/\alpha + 1/\beta is equal to … (MCQ)
• Q22. If one zero of p(x) = 6x^2 + 37x - (k - 2) is reciprocal of the
other, find k. (2 marks)
• Q23(A). Find the sum and product of roots of 2x^2 - 9x + 4 = 0. (2
marks)
• Q23(B). Find the discriminant of 4x^2 - 5 = 0 and comment on the nature
of roots. (2 marks)
• Q31. Find the value of p for which px(x - 2) + 6 = 0 has two equal real
roots. (3 marks)
Chapter 3 – Pair of Linear Equations in Two Variables
• Q7. The pair of equations 2x = 5y + 6 and 15y = 6x - 18 represents …
(MCQ)
• Q36. (Case Study) Two schools ‘P’ and ‘Q’ decided to award prizes —
form equations and solve questions. (4 marks)
Chapter 4 – Quadratic Equations
• Q9. If a pole 6 m high casts a shadow 2\sqrt{3} m long, sun’s elevation
is … (MCQ)
• Q10. \sec\theta in terms of \cot\theta is equal to … (MCQ)
⸻
Chapter 5 – Arithmetic Progressions
• Q3. The next term of the A.P.: 6, 24, 54 is … (MCQ)
• Q20. Assertion–Reason: a, b, c in A.P. if and only if 2b = a + c. (MCQ)
• Q26(A). How many terms are there in an A.P. with first term -14, fifth
term 2, and last term 62? (3 marks)
• Q26(B). Which term of the A.P. 65, 61, 57, 53, … is the first negative
term? (3 marks)
Paper 4
Chapter 1 – Real Numbers
• Q1
• Q3
• Q4
Chapter 2 – Polynomials
• Q7
• Q9
• Q12
Chapter 3 – Pair of Linear Equations in Two Variables
• Q13
• Q16
• Q19
• Q20
• Q21
Chapter 4 – Quadratic Equations
• Q23
• Q25
Chapter 5 – Arithmetic Progressions
• Q27
• Q29
• Q31
• Q35
• Q37
