Mathematics Questions

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

1. Q521
   If $P(9a-2,-b)$ ​divides ​line segment joining $A(3a+1,-3)$ ​and $B(8a,5)$ in the ratio $3:1$, ​find ​the ​values of $a$ ​and $b$.
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2. Q522
   If $(a,b)$ ​is the mid-point of the line ​segment joining the ​points $A(10,-6)$ ​and $B(k,4)$ and $a-2b=18$, find the value ​of $k$ ​and the distance $AB$.
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3. Q523
   The ​centre of ​a circle is $(2a,a-7)$. ​Find the ​values of $a$ ​if the circle ​passes through the point $(11,-9)$ and has ​diameter $10\sqrt{2}$ units.
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4. Q524
   The line segment joining ​the points A(3, ​2) and ​B(5, 1) ​is divided at the ​point P in the ​ratio 1:2 and it lies on ​the line $3x-18y+k=0$. Find the value ​of k.
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5. Q525
   If $D\left(\frac{-1}{2},\frac{5}{2}\right)$, $E(7,3)$ and $F\left(\frac{7}{2},\frac{7}{2}\right)$ ​are ​the ​midpoints of ​sides of $△ABC$, ​find ​the area of ​the $△ABC$.
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6. Q526
   The points $A(2,9)$, $B(a,5)$ and $C(5,5)$ are the vertices of a ​triangle $ABC$ right angled at $B$. Find ​the values of $a$ and hence the ​area ​of $△ABC$.
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7. Q527
   Find ​the coordinates of the point $R$ ​on the ​line ​segment joining ​the points $P(-1,3)$ and $Q(2,5)$ such ​that $PR=\frac{3}{5}PQ$.
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8. Q528
   Find ​the values ​of $k$ ​if ​the points $A(k+1,2k)$, $B(3k,2k+3)$ ​and $C(5k-1,5k)$ are ​collinear.
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9. Q529
   Find the ratio in which ​the line $2x+3y-5=0$ ​divides the ​line segment joining the points $(8,-9)$ ​and $(2,1)$. Also find the coordinates of ​the ​point of ​division.
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10. Q530
    If $\cos A=\frac{4}{5}$, ​then the value ​of $\tan A$ ​is

    1. (a)$\frac{3}{5}$
    2. (b)$\frac{3}{4}$
    3. (c)$\frac{4}{3}$
    4. (d)$\frac{5}{3}$
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11. Q531
    If $\sin A=\frac{1}{2}$, ​then ​the ​value of $\cot A$ ​is

    1. (a)$\sqrt{3}$
    2. (b)$\frac{1}{\sqrt{3}}$
    3. (c)$\frac{\sqrt{3}}{2}$
    4. (d)$1$
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12. Q532
    The ​value of ​the expression $[\csc (75^{\circ }+\theta )-\sec (15^{\circ }-\theta )-\tan (55^{\circ }+\theta )+\cot (35^{\circ }-\theta )]$ ​is

    1. (a)$-1$
    2. (b)$0$
    3. (c)$1$
    4. (d)$\frac{3}{2}$
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13. Q533
    Given that $\sin \theta =\frac{a}{b}$, ​then $\cos \theta$ ​is equal ​to

    1. (a)$\frac{b}{\sqrt{b^2-a^2}}$
    2. (b)$\frac{b}{a}$
    3. (c)$\frac{\sqrt{b^2-a^2}}{b}$
    4. (d)$\frac{a}{\sqrt{b^2-a^2}}$
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14. Q534
    If $\cos (\alpha +\beta )=0$, ​then $\sin (\alpha -\beta )$ can be ​reduced ​to

    1. (a)$\cos \beta$
    2. (b)$\cos 2\beta$
    3. (c)$\sin \alpha$
    4. (d)$\sin 2\alpha$
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15. Q535
    The ​value ​of $(\tan 1^{\circ }\tan 2^{\circ }\tan 3^{\circ }\dots \tan 89^{\circ })$ ​is

    1. (a)$0$
    2. (b)$1$
    3. (c)$2$
    4. (d)$\frac{1}{2}$
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16. Q536
    If $\cos 9\alpha =\sin \alpha$ ​and $9\alpha <90^{\circ }$, then ​the value ​of $\tan 5\alpha$ ​is

    1. (a)$\frac{1}{\sqrt{3}}$
    2. (b)$\sqrt{3}$
    3. (c)$1$
    4. (d)$0$
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17. Q537
    If $△ABC$ ​is ​right angled ​at $C$, ​then the ​value of $\cos (A+B)$ ​is

    1. (a)$0$
    2. (b)$1$
    3. (c)$\frac{1}{2}$
    4. (d)$\frac{\sqrt{3}}{2}$
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18. Q538
    If $\sin A+{\sin }^{2}A=1$, then the value ​of ​the ​expression $({\cos }^{2}A+{\cos }^{4}A)$ ​is

    1. (a)1
    2. (b)$\frac{1}{2}$
    3. (c)2
    4. (d)3
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19. Q539
    Given that $\sin \alpha =\frac{1}{2}$ ​and $\cos \beta =\frac{1}{2}$, ​then the ​value ​of $(\alpha +\beta )$ ​is

    1. (a)$0^{\circ }$
    2. (b)$30^{\circ }$
    3. (c)$60^{\circ }$
    4. (d)$90^{\circ }$
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20. Q540
    The value ​of ​the ​expression $\left[\frac{{\sin }^{2}22^{\circ }+{\sin }^{2}68^{\circ }}{{\cos }^{2}22^{\circ }+{\cos }^{2}68^{\circ }}+{\sin }^{2}63^{\circ }+\cos 63^{\circ }\sin 27^{\circ }\right]$ ​is

    1. (a)3
    2. (b)2
    3. (c)1
    4. (d)0
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