BOARD OF SECONDARY EDUCATION IN ANDHRA PRADESH Class 10 Mathematics MCQs: Real Numbers, Pair of Linear Equations in Two Variables, Polynomials +1 more

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Real Numbers

   1.

   If $x$ and $y$ are two positive integers such that $x = 2^3 \times 3^2$ and $y = 2^2 \times 3^3$, what is the Least Common Multiple (LCM) of $x$ and $y$?

   1. (A)

      $2^2 \times 3^2$

   2. (B)

      $2^1 \times 3^1$

   3. (C)

      $2^5 \times 3^5$

   4. (D)

      $2^3 \times 3^3$

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   Answer: (D)

   $2^3 \times 3^3$

   Real Numbers · Medium

2. 2.

   Which of the following numbers is an irrational number?

   1. (A)

      $\frac{2}{7}$

   2. (B)

      $\sqrt{7}$

   3. (C)

      $0.333...$

   4. (D)

      $\sqrt{49}$

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   Answer: (B)

   $\sqrt{7}$

   Real Numbers · Easy

3. Pair of Linear Equations in Two Variables

   3.

   Which of the following represents a linear equation in two variables?

   1. (A)

      $5x + \frac{3}{y} = 6$

   2. (B)

      $4x - 7y = 0$

   3. (C)

      $3x^2 + 2y = 5$

   4. (D)

      $xy + 2x = 1$

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   Answer: (B)

   $4x - 7y = 0$

   Pair of Linear Equations in Two Variables · Easy

4. 4.

   For what value of $k$ does the pair of equations $2x + 3y = 7$ and $4x + ky = 14$ have infinitely many solutions?

   1. (A)

      12

   2. (B)

      3

   3. (C)

      6

   4. (D)

      9

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   Answer: (C)

   6

   Pair of Linear Equations in Two Variables · Medium

5. 5.

   If $x = 2$ and $y = 3$ is a solution to the equation $ax - by = -4$ and $ax + by = 10$, what are the values of $a$ and $b$?

   1. (A)

      $a=1, b=2$

   2. (B)

      $a=2, b=1$

   3. (C)

      $a=2, b=3$

   4. (D)

      $a=3, b=2$

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   Answer: (A)

   $a=1, b=2$

   Pair of Linear Equations in Two Variables · Hard

6. 6.

   The lines representing the equations $3x + 2y = 5$ and $6x + 4y = 10$ are:

   1. (A)

      parallel lines

   2. (B)

      perpendicular lines

   3. (C)

      coincident lines

   4. (D)

      intersecting lines

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   Answer: (C)

   coincident lines

   Pair of Linear Equations in Two Variables · Medium

7. 7.

   What is the condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have a unique solution?

   1. (A)

      $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

   2. (B)

      $\frac{a_1}{a_2} = \frac{c_1}{c_2} \neq \frac{b_1}{b_2}$

   3. (C)

      $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

   4. (D)

      $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

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   Answer: (C)

   $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

   Pair of Linear Equations in Two Variables · Easy

8. 8.

   The sum of the digits of a two-digit number is 9. If 27 is added to the number, its digits are reversed. Find the number.

   1. (A)

      45

   2. (B)

      27

   3. (C)

      36

   4. (D)

      63

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   Answer: (C)

   36

   Pair of Linear Equations in Two Variables · Hard

9. 9.

   If the pair of linear equations $x - y = 1$ and $3x + 2y = 12$ is solved, what is the value of $y$?

   1. (A)

      4

   2. (B)

      3

   3. (C)

      1

   4. (D)

      2

   Show answerHide answer

   Answer: (B)

   3

   Pair of Linear Equations in Two Variables · Medium

10. Polynomials

    10.

    What is the degree of the polynomial $p(x) = 5x^3 - 2x^2 + 7x - 1$?

    1. (A)

       2

    2. (B)

       1

    3. (C)

       4

    4. (D)

       3

    Show answerHide answer

    Answer: (D)

    3

    Polynomials · Easy

11. 11.

    If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $x^2 - 5x + 6$, then what is the value of $\alpha + \beta$?

    1. (A)

       -5

    2. (B)

       -6

    3. (C)

       6

    4. (D)

       5

    Show answerHide answer

    Answer: (D)

    5

    Polynomials · Medium

12. 12.

    Which of the following is a polynomial?

    1. (A)

       $\sqrt{x} + 2$

    2. (B)

       $x^2 + 3x - 4$

    3. (C)

       $x + \frac{1}{x}$

    4. (D)

       $\frac{1}{x^2 + 1}$

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    Answer: (B)

    $x^2 + 3x - 4$

    Polynomials · Easy

13. 13.

    Find the zeroes of the quadratic polynomial $x^2 - 9$.

    1. (A)

       9, -9

    2. (B)

       3, -3

    3. (C)

       0, -9

    4. (D)

       3, 0

    Show answerHide answer

    Answer: (B)

    3, -3

    Polynomials · Medium

14. 14.

    If one zero of the polynomial $p(x) = x^2 - 4x + k$ is 2, then what is the value of $k$?

    1. (A)

       4

    2. (B)

       2

    3. (C)

       0

    4. (D)

       -2

    Show answerHide answer

    Answer: (A)

    4

    Polynomials · Hard

15. 15.

    If the sum of the zeroes of a quadratic polynomial is $-3$ and the product is $2$, what is the polynomial?

    1. (A)

       $x^2 - 3x + 2$

    2. (B)

       $x^2 - 3x - 2$

    3. (C)

       $x^2 + 3x - 2$

    4. (D)

       $x^2 + 3x + 2$

    Show answerHide answer

    Answer: (D)

    $x^2 + 3x + 2$

    Polynomials · Medium

16. 16.

    For a cubic polynomial $ax^3 + bx^2 + cx + d$, what is the product of its zeroes?

    1. (A)

       $c/a$

    2. (B)

       $-b/a$

    3. (C)

       $-d/a$

    4. (D)

       $d/a$

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    Answer: (C)

    $-d/a$

    Polynomials · Hard

17. Quadratic Equations

    17.

    What is the nature of the roots of the quadratic equation $2x^2 - 4x + 3 = 0$?

    1. (A)

       Rational and equal

    2. (B)

       No real roots

    3. (C)

       Real and distinct

    4. (D)

       Real and equal

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    Answer: (B)

    No real roots

    Quadratic Equations · Medium

18. 18.

    If one root of the quadratic equation $x^2 - 3x + k = 0$ is 2, what is the value of $k$?

    1. (A)

       $10$

    2. (B)

       $-10$

    3. (C)

       $2$

    4. (D)

       $-2$

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    Answer: (C)

    $2$

    Quadratic Equations · Easy

19. 19.

    For what value of $p$ does the quadratic equation $px(x-3) + 9 = 0$ have real and equal roots?

    1. (A)

       $-1$

    2. (B)

       $-4$

    3. (C)

       $1$

    4. (D)

       $4$

    Show answerHide answer

    Answer: (D)

    $4$

    Quadratic Equations · Hard

20. 20.

    What is the sum of the roots of the quadratic equation $3x^2 - 5x + 2 = 0$?

    1. (A)

       $\frac{5}{3}$

    2. (B)

       $\frac{-2}{3}$

    3. (C)

       $\frac{-5}{3}$

    4. (D)

       $\frac{2}{3}$

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    Answer: (A)

    $\frac{5}{3}$

    Quadratic Equations · Easy

21. Progressions

    21.

    What is the 10th term of an arithmetic progression whose first term is 5 and common difference is 3?

    1. (A)

       32

    2. (B)

       38

    3. (C)

       41

    4. (D)

       35

    Show answerHide answer

    Answer: (D)

    35

    Progressions · Easy

22. 22.

    If the sum of the first $n$ terms of an arithmetic progression is given by $S_n = 3n^2 - n$, what is the common difference of the progression?

    1. (A)

       2

    2. (B)

       6

    3. (C)

       4

    4. (D)

       8

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    Answer: (B)

    6

    Progressions · Medium

23. 23.

    Find the sum of the first 20 terms of an arithmetic progression if the first term is 2 and the last term is 59.

    1. (A)

       610

    2. (B)

       590

    3. (C)

       650

    4. (D)

       630

    Show answerHide answer

    Answer: (A)

    610

    Progressions · Medium

24. 24.

    Which term of the arithmetic progression $7, 13, 19, \dots$ is 205?

    1. (A)

       33rd

    2. (B)

       30th

    3. (C)

       34th

    4. (D)

       35th

    Show answerHide answer

    Answer: (A)

    33rd

    Progressions · Medium

25. 25.

    If $a, b, c$ are in arithmetic progression, then which of the following is true?

    1. (A)

       $b = ac$

    2. (B)

       $2b = a + c$

    3. (C)

       $b = a + c$

    4. (D)

       $b^2 = ac$

    Show answerHide answer

    Answer: (B)

    $2b = a + c$

    Progressions · Easy

— End of the paper · updated 1 November 2026 —