NCERT Exemplar Class 10 Mathematics
Chapter-wise Multiple Choice Questions (MCQs) with Answers
📑 Table of Contents
- Chapter 1: Real Numbers
- Chapter 2: Polynomials
- Chapter 3: Pair of Linear Equations in Two Variables
- Chapter 4: Quadratic Equations
- Chapter 5: Arithmetic Progressions
- Chapter 6: Triangles
- Chapter 7: Coordinate Geometry
- Chapter 8: Introduction to Trigonometry
- Chapter 9: Circles
- Chapter 10: Constructions
- Chapter 11: Area Related to Circles
- Chapter 12: Surface Areas and Volumes
- Chapter 13: Statistics and Probability
Chapter 1: Real Numbers
1. For some integer \( m \), every even integer is of the form
✅ Correct Answer: (C) $2m$
2. For some integer \( q \), every odd integer is of the form
✅ Correct Answer: (D) $2q + 1$
3. \( n^2 - 1 \) is divisible by 8, if \( n \) is
✅ Correct Answer: (C) an odd integer
4. If the HCF of 65 and 117 is expressible in the form $65m - 117$, then the value of \( m \) is
✅ Correct Answer: (B) 2
5. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
✅ Correct Answer: (A) 13
6. If two positive integers \( a \) and \( b \) are written as \( a = x^3y^2 \) and \( b = xy^3 \); \( x, y \) are prime numbers, then HCF\( (a, b) \) is
✅ Correct Answer: (B) \( xy^2 \)
7. If two positive integers \( p \) and \( q \) can be expressed as \( p = ab^2 \) and \( q = a^3b \); \( a, b \) being prime numbers, then LCM\( (p, q) \) is
✅ Correct Answer: (C) \( a^3b^2 \)
8. The product of a non-zero rational and an irrational number is
✅ Correct Answer: (A) always irrational
9. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
✅ Correct Answer: (D) 2520
10. The decimal expansion of the rational number \( \frac{14587}{1250} \) will terminate after:
✅ Correct Answer: (D) four decimal places
Chapter 2: Polynomials
1. If one of the zeroes of the quadratic polynomial \( (k-1)x^2 + kx + 1 \) is \( -3 \), then the value of \( k \) is
✅ Correct Answer: (A) \( \frac{4}{3} \)
2. A quadratic polynomial, whose zeroes are \( -3 \) and $4$, is
✅ Correct Answer: (C) \( \frac{x^2 - x - 12}{2} \)
3. If the zeroes of the quadratic polynomial \( x^2 + (a + 1)x + b \) are 2 and \( -3 \), then
✅ Correct Answer: (D) \( a = 0, b = -6 \)
4. The number of polynomials having zeroes as \( -2 \) and $5$ is
✅ Correct Answer: (D) more than 3
5. Given that one of the zeroes of the cubic polynomial \( ax^3 + bx^2 + cx + d \) is zero, the product of the other two zeroes is
✅ Correct Answer: (B) \( \frac{c}{a} \)
6. If one of the zeroes of the cubic polynomial \( x^3 + ax^2 + bx + c \) is \( -1 \), then the product of the other two zeroes is
✅ Correct Answer: (A) \( b - a + 1 \)
7. The zeroes of the quadratic polynomial \( x^2 + 99x + 127 \) are
✅ Correct Answer: (B) both negative
8. The zeroes of the quadratic polynomial \( x^2 + kx + k \), \( k \ne 0 \),
✅ Correct Answer: (A) cannot both be positive
9. If the zeroes of the quadratic polynomial \( ax^2 + bx + c \), \( c \ne 0 \) are equal, then
✅ Correct Answer: (C) \( c \) and \( a \) have the same sign
10. If one of the zeroes of a quadratic polynomial of the form \( x^2 + ax + b \) is the negative of the other, then it
✅ Correct Answer: (B) has no linear term and the constant term is positive.
11. Which of the following is not the graph of a quadratic polynomial?
✅ Correct Answer: (C) Straight line
Chapter 3: Pair of Linear Equations in Two Variables
1. Graphically, the pair of equations $6x - 3y + 10 = 0$ and $2x - y + 9 = 0$ represents two lines which are
✅ Correct Answer: (D) parallel
2. The pair of equations \( x + 2y + 5 = 0 \) and \( -3x - 6y + 1 = 0 \) have
✅ Correct Answer: (D) no solution
3. If a pair of linear equations is consistent, then the lines will be
✅ Correct Answer: (C) intersecting or coincident
4. The pair of equations \( y = 0 \) and \( y = -7 \) has
✅ Correct Answer: (D) no solution
5. The pair of equations \( x = a \) and \( y = b \) graphically represents lines which are
✅ Correct Answer: (D) intersecting at \( (a, b) \)
6. For what value of \( k \), do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?
✅ Correct Answer: (C) 2
7. If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, then the value of \( k \) is
✅ Correct Answer: (C) \( \frac{15}{4} \)
8. The value of \( c \) for which the pair of equations \( cx - y = 2 \) and $6x - 2y = 3$ will have infinitely many solutions is
✅ Correct Answer: (D) no value
9. One equation of a pair of dependent linear equations is \( -5x + 7y = 2 \). The second equation can be
✅ Correct Answer: (D) $10x - 14y = -4$
10. A pair of linear equations which has a unique solution \( x = 2 \), \( y = -3 \) is
✅ Correct Answer: (D) \( x - 4y = 14 \), $5x - y = 13$
11. If \( x = a \), \( y = b \) is the solution of the equations \( x - y = 2 \) and \( x + y = 4 \), then the values of \( a \) and \( b \) are, respectively
✅ Correct Answer: (C) 3 and 1
12. Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively
✅ Correct Answer: (D) 25 and 25
13. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
✅ Correct Answer: (C) 6 and 36
Chapter 4: Quadratic Equations
1. Which of the following is a quadratic equation?
✅ Correct Answer: (D) \( x^3 - x^2 = (x - 1)^3 \)
2. Which of the following is not a quadratic equation?
✅ Correct Answer: (C) \( (\sqrt{2}x + \sqrt{3})^2 = 3x^2 + 5 \)
3. Which of the following equations has 2 as a root?
✅ Correct Answer: (C) $2x^2 - 7x + 6 = 0$
4. If \( \frac{1}{2} \) is a root of the equation \( x^2 + kx - \frac{5}{4} = 0 \), then the value of \( k \) is
✅ Correct Answer: (A) 2
5. Which of the following equations has the sum of its roots as 3?
✅ Correct Answer: (B) \( -x^2 + 3x - 3 = 0 \)
6. Values of \( k \) for which the quadratic equation $2x^2 - kx + k = 0$ has equal roots is/are
✅ Correct Answer: (D) 0, 8
7. Which constant must be added and subtracted to solve the quadratic equation $4x^2 - \sqrt{3}x - 5 = 0$ by the method of completing the square?
✅ Correct Answer: (B) \( \frac{3}{16} \)
8. The quadratic equation $2x^2 - \sqrt{5}x + 1 = 0$ has
✅ Correct Answer: (C) no real roots
9. Which of the following equations has two distinct real roots?
✅ Correct Answer: (B) \( x^2 + x - 5 = 0 \)
10. Which of the following equations has no real roots?
✅ Correct Answer: (A) \( x^2 - 4x + 3\sqrt{2} = 0 \)
11. \( (x^2 + 1)^2 - x^2 = 0 \) has
✅ Correct Answer: (C) no real roots
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