Mathematics Questions

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

1. Q761 CBSE Board 2026
   The ​value of $k$ ​for which the equation $2k{x}^2-6x+3=0$ ​has ​real and ​equal roots, ​is ​:

   1. (a)$\frac{3}{2}$
   2. (b)$\frac{1}{2}$
   3. (c)$-\frac{3}{2}$
   4. (d)$2$
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2. Q762 CBSE Board 2026
   A ​letter is selected ​from the letters ​of the word FEBRUARY. The probability that ​it ​is a ​vowel ​is ​:

   1. (a)$\frac{1}{8}$
   2. (b)$\frac{2}{8}$
   3. (c)$\frac{3}{8}$
   4. (d)$\frac{3}{7}$
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3. Q763 CBSE Board 2026
   Which of the following statements is true ​for HCF and ​LCM of two distinct natural numbers $a$ and $b$ ​?

   1. (i)HCF is always greater than ​LCM.
   2. (ii)HCF is ​a ​factor ​of LCM.
   3. (iii)LCM is a factor of HCF.

   1. (a)(i) only
   2. (b)(i) and (iii)
   3. (c)(i) and (ii)
   4. (d)(ii) only
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4. Q764 CBSE Board 2026
   The ​LCM ​of two ​consecutive ​natural ​numbers $p$ and $p+1$ is ​:

   1. (a)$p$
   2. (b)$p^2+p$
   3. (c)$1$
   4. (d)$2p+1$
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5. Q765 CBSE Board 2026
   For any ​natural ​number $n$, $6^n$ ​ends ​with ​the digit ​:

   1. (a)$0$
   2. (b)$6$
   3. (c)$3$
   4. (d)$2$
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6. Q766 CBSE Board 2026
   For any ​natural ​number $n$, $5^n$ ends with ​the ​digit :

   1. (a)$0$
   2. (b)$5$
   3. (c)$3$
   4. (d)$2$
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7. Q767 CBSE Board 2026
   The ​distance ​between ​the points $(-2,5)$ and $(5,-2)$ is

   1. (a)$7\sqrt{2}$
   2. (b)$14$
   3. (c)$2\sqrt{7}$
   4. (d)$7$
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8. Q768 CBSE Board 2026
   The value ​of $k$ ​for which ​the pair of ​linear equations $kx-3y=5$, $4x-6y=10$ has ​infinitely many ​solutions, ​is:

   1. (a)$4$
   2. (b)$3$
   3. (c)$2$
   4. (d)$1$
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9. Q769 CBSE Board 2026
   In $△DEF$, $AB\parallel EF$. ​The value ​of $x$ ​is :

   1. (a)$0,2$
   2. (b)$2$ only
   3. (c)$-2$
   4. (d)$1$
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10. Q770 CBSE Board 2026
    The $n^{\text{th}}$ term of an A.P. is $\sqrt{2}n+1$. ​Its common ​difference ​is ​:

    1. (a)$\sqrt{2}$
    2. (b)$\sqrt{2}n$
    3. (c)$1$
    4. (d)$\sqrt{2}+1$
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11. Q771 CBSE Board 2026
    If ​the ​zeroes of a ​polynomial $p(x)$ are $-3$ and $8$, then $p(x)$ ​equals

    1. (a)$x^2+5x-4$
    2. (b)$(x+3)(-x+8)$
    3. (c)$a(x^2+5x-24)$
    4. (d)$x^2-24$
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12. Q772 CBSE Board 2026
    If ​pair of linear equations ​given by $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ ​has infinitely many solutions, ​then ​which of ​the following is definitely true?

    1. (a)$\frac{a_1}{a_2}=\frac{c_2}{c_1}$
    2. (b)$a_1{a}_2\ne b_1{b}_2$
    3. (c)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
    4. (d)$a_1{b}_2=a_2{b}_1$
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13. Q773 CBSE Board 2026
    Two ​wooden ​solid hemispheres ​of ​same radii $r$, are joined at ​a point, ​as shown in the figure. The ​total surface ​area of the object is:

    1. (a)$4\pi r^2$
    2. (b)$6\pi r^2$
    3. (c)$3\pi r^2$
    4. (d)$5\pi r^2$
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14. Q774 CBSE Board 2026
    Which of ​the following ​numbers will not ​end ​with $0$ ​for any ​natural ​number $n$ ?

    1. (a)$4n$
    2. (b)$4^n$
    3. (c)$3^n+1$
    4. (d)$10^{n+1}$
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15. Q775 CBSE Board 2026
    Which of the ​following ​system ​of equations has ​a unique ​solution ​?

    1. (a)$x=0,x=1$
    2. (b)$x+y=0,2x+2y=0$
    3. (c)$x+y=2,x-y=3$
    4. (d)$x+y=5,x+y=10$
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16. Q776 CBSE Board 2026
    The system ​of ​equations $2x+ky=4$ and $3x-6y=6$ ​has ​infinitely many ​solutions, ​if ​:

    1. (a)$k\ne 4$
    2. (b)$k=4$
    3. (c)$k=-4$
    4. (d)No value of $k$
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17. Q777 CBSE Board 2026
    The ​graph of $y=f(x)$ ​is given. ​The number ​of ​zeroes of $f(x)$ is ​:

    1. (a)$0$
    2. (b)$1$
    3. (c)$2$
    4. (d)$4$
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18. Q778 CBSE Board 2026
    The graph of $y=f(x)$ ​is ​given. The ​number of ​distinct ​zeroes ​of $y=f(x)$ is :

    1. (a)$0$
    2. (b)$1$
    3. (c)$2$
    4. (d)$3$
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19. Q779 CBSE Board 2026
    A cylinder ​of radius $r$ is ​surmounted on a hemisphere ​of same ​radius. If ​total ​height ​of the object is $13$ cm, then its inner surface area is

    1. (a)$2\pi r(r+13)$
    2. (b)$13\pi r$
    3. (c)$2\pi (13+r{)}^2$
    4. (d)$26\pi r$
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20. Q780 CBSE Board 2026
    If $x=\sqrt{3}$ ​is a ​solution ​of the ​equation $a{x}^2+\sqrt{3}x-12=0$, ​then

    1. (a)$a=3$
    2. (b)$a=2$
    3. (c)$a=1$
    4. (d)$a=\sqrt{3}$
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