Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

1. Q781 CBSE Board 2026
   $(3\times 11\times 13+3)$ ​is ​:

   1. (a)a prime number
   2. (b)divisible by $13$
   3. (c)a composite number
   4. (d)an odd number
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2. Q782 CBSE Board 2026
   If $PQ$ ​and $PR$ are tangents ​to ​the circle ​with ​centre $O$ ​and radius $4$ cm such ​that $\angle QPR=90^{\circ }$, then ​the length $OP$ is :

   1. (a)$4$ cm
   2. (b)$4\sqrt{2}$ cm
   3. (c)$8$ cm
   4. (d)$2\sqrt{2}$ cm
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3. Q783 CBSE Board 2026
   In the ​given figure, $PQ$ ​is ​tangent ​to the circle with centre $O$. $S$ is a ​point on the circle such that $\angle SQT=55^{\circ }$. The $m\angle QPS$ ​is

   1. (a)$55^{\circ }$
   2. (b)$20^{\circ }$
   3. (c)$35^{\circ }$
   4. (d)$70^{\circ }$
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4. Q784 CBSE Board 2026
   The $31^{\text{st}}$ ​term ​of ​the ​A.P. : $\frac{-5}{6},\frac{-3}{4},\frac{-2}{3},\frac{-7}{12},\dots$ is

   1. (a)$\frac{-5}{3}$
   2. (b)$\frac{5}{3}$
   3. (c)$\frac{12}{20}$
   4. (d)$\frac{-12}{20}$
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5. Q785 CBSE Board 2026
   $PT$ ​is tangent to ​the ​circle with centre $O$ ​and radius $5$ cm. $OP$ intersects the circle ​at $Q$. ​If $PQ=x$, ​then $P{T}^2$ equals:

   1. (a)$x^2+5x$
   2. (b)$x^2+10x+50$
   3. (c)$x^2+10x$
   4. (d)$x^2-25$
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6. Q786 CBSE Board 2026
   The system ​of linear ​equations $px+qy=r$ ​and $p_{1}x+q_{1}y=r_1$ has ​a ​unique solution, ​if ​:

   1. (a)$pq\ne p_1{q}_1$
   2. (b)$p{p}_1\ne q{q}_1$
   3. (c)$p{q}_1\ne q{p}_1$
   4. (d)$pqr\ne p_1{q}_1{r}_1$
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7. Q787 CBSE Board 2026
   If ​the equation $q{x}^2+px-r=0$ $(q\ne 0)$ has real and ​equal roots, ​then which ​of the ​following ​is ​true ?

   1. (a)$p^2=qr$
   2. (b)$p^2=-4qr$
   3. (c)$q^2=4pr$
   4. (d)$q^2=-4pr$
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8. Q788 CBSE Board 2026
   The ​value ​of '$m$' for which the ​quadratic equation $x^2-2x+m=0$ has ​real and equal ​roots ​is :

   1. (a)$-1$
   2. (b)$0$
   3. (c)$4$
   4. (d)$1$
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9. Q789 CBSE Board 2026
   If ​a ​pair of ​linear equations in two variables is represented ​by two coincident lines, ​then the pair of ​equations has ​:

   1. (a)a unique solution
   2. (b)two solutions
   3. (c)no solution
   4. (d)an infinite number of solutions
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10. Q790 CBSE Board 2026
    If $\alpha$ ​and $\beta$ are two ​zeroes ​of ​a polynomial $f(x)=p{x}^2-2x+3p$ and $\alpha +\beta =\alpha \beta$, then ​value ​of $p$ ​is :

    1. (a)$-\frac{2}{3}$
    2. (b)$\frac{2}{3}$
    3. (c)$\frac{1}{3}$
    4. (d)$-\frac{1}{3}$
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11. Q791 CBSE Board 2026
    Which ​of the following ​statements ​is ​not ​always ​true?

    1. (a)Two circles are similar.
    2. (b)Two isosceles right triangles are similar.
    3. (c)Two rectangles are similar.
    4. (d)Two equilateral triangles are similar.
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12. Q792 CBSE Board 2026
    The $n^{\text{th}}$ ​term of ​an ​A.P. is $3n+2$. ​The ​common ​difference is:

    1. (a)$8$
    2. (b)$2$
    3. (c)$5$
    4. (d)$3$
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13. Q793 CBSE Board 2026
    Two ​dice ​are ​rolled together. The probability that ​the sum ​of the numbers obtained ​is divisible by $6$, is :

    1. (a)$\frac{1}{6}$
    2. (b)$\frac{11}{36}$
    3. (c)$\frac{1}{12}$
    4. (d)$\frac{1}{4}$
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14. Q794 CBSE Board 2026
    Observe ​the graph of ​polynomial $p(x)$. Number ​of ​zeroes ​of $p(x)$ ​is

    1. (a)$5$
    2. (b)$4$
    3. (c)$6$
    4. (d)$3$
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15. Q795 CBSE Board 2026
    Devansh ​proved ​that $△ABC\sim △PQR$ ​using SAS similarity ​criteria. If ​he found $\angle C=\angle R$, then which of ​the following was ​proved true?

    1. (a)$\frac{AC}{AB}=\frac{PR}{PQ}$
    2. (b)$\frac{BC}{AC}=\frac{PR}{QR}$
    3. (c)$\frac{AC}{BC}=\frac{PR}{PQ}$
    4. (d)$\frac{AC}{BC}=\frac{PR}{QR}$
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16. Q796 CBSE Board 2026
    Four ​tangents ​drawn to ​a circle are extended ​from both the sides ​to ​form a quadrilateral. Which ​of these quadrilateral ​is not possible?

    1. (a)Trapezium
    2. (b)Square
    3. (c)Rectangle
    4. (d)Rhombus
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17. Q797 CBSE Board 2026
    Probability of getting ​an irrational ​number ​at random from ​the numbers $\sqrt{3},\sqrt{4},3\sqrt{9},3\sqrt{8},\sqrt{5},0,4^{\frac{3}{2}}$ is :

    1. (a)$0$
    2. (b)$\frac{4}{7}$
    3. (c)$\frac{3}{7}$
    4. (d)$1$
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18. Q798 CBSE Board 2026
    Which of the ​equations ​among ​the following ​is/are quadratic equation(s) ​? $q_1:x^2+x=(x+1{)}^2$, $q_2:x-1=x^2-1$, $q_3:x^4=x^2$, $q_4:\sqrt{x}=x^2\sqrt{x}+1$

    1. (a)$q_1$ only
    2. (b)$q_1,q_2$ and $q_3$ only
    3. (c)$q_2$ only
    4. (d)$q_2$ and $q_4$ only
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19. Q799 CBSE Board 2026
    If $x=-1$ ​is a ​root ​of the ​equation $a{x}^2-bx+3=0$, ​then ​:

    1. (a)$-a+b-3=0$
    2. (b)$a-b-3=0$
    3. (c)$-a-b+3=0$
    4. (d)$a+b+3=0$
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20. Q800 CBSE Board 2026
    Which ​of ​the ​following ​statements is ​true ​for the ​quadratic equation $a{x}^2+x+a=0$ ($a\ne 0$) ?

    1. (a)The roots of the given equation are reciprocal of each other.
    2. (b)The roots of the given equation are always real.
    3. (c)The roots of the given equation are always positive.
    4. (d)The sum of roots of the given equation is $0$.
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