Mathematics Questions

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

1. Q441
   If $△ABC\sim △EDF$ and $△ABC$ is ​not ​similar to $△DEF$, then ​which of ​the following ​is ​not ​true?

   1. (a)$BC\cdot EF=AC\cdot FD$
   2. (b)$AB\cdot EF=AC\cdot DE$
   3. (c)$BC\cdot DE=AB\cdot EF$
   4. (d)$BC\cdot DE=AB\cdot FD$
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2. Q442
   If ​in two ​triangles ​ABC ​and ​PQR, $\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$, then

   1. (a)$△PQR\sim △CAB$
   2. (b)$△PQR\sim △ABC$
   3. (c)$△CBA\sim △PQR$
   4. (d)$△BCA\sim △PQR$
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3. Q443
   In Fig. 6.3, two ​line ​segments $AC$ and $BD$ ​intersect each other at ​the point $P$ such that $PA=6$ ​cm, $PB=3$ cm, $PC=2.5$ ​cm, $PD=5$ ​cm, $\angle APB=50^{\circ }$ and $\angle CDP=30^{\circ }$. ​Then, $\angle PBA$ is equal to

   1. (a)$50^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$100^{\circ }$
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4. Q444
   If in two triangles DEF ​and PQR, $\angle D=\angle Q$ and $\angle R=\angle E$, ​then which ​of ​the following is ​not true?

   1. (a)$\frac{EF}{PR}=\frac{DF}{PQ}$
   2. (b)$\frac{DE}{PQ}=\frac{EF}{RP}$
   3. (c)$\frac{DE}{QR}=\frac{DF}{PQ}$
   4. (d)$\frac{EF}{RP}=\frac{DE}{QR}$
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5. Q445
   In ​triangles $ABC$ and $DEF$, $\angle B=\angle E$, $\angle F=\angle C$ ​and $AB=3DE$. ​Then, ​the two ​triangles are

   1. (a)congruent but not similar
   2. (b)similar but not congruent
   3. (c)neither congruent nor similar
   4. (d)congruent as well as similar
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6. Q446
   It is ​given that $△ABC\sim △PQR$, with $\frac{BC}{QR}=\frac{1}{3}$. ​Then, $\frac{\mathrm{ar}(PRQ)}{\mathrm{ar}(BCA)}$ ​is equal ​to

   1. (a)$9$
   2. (b)$3$
   3. (c)$\frac{1}{3}$
   4. (d)$\frac{1}{9}$
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7. Q447
   It ​is given ​that $△ABC\sim △DFE$, $\angle A=30^{\circ }$, $\angle C=50^{\circ }$, $AB=5$ ​cm, $AC=8$ cm ​and $DF=7.5$ cm. Then, the ​following ​is true:

   1. (a)$DE=12$ cm, $\angle F=50^{\circ }$
   2. (b)$DE=12$ cm, $\angle F=100^{\circ }$
   3. (c)$EF=12$ cm, $\angle D=100^{\circ }$
   4. (d)$EF=12$ cm, $\angle D=30^{\circ }$
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8. Q448
   If ​in ​triangles $ABC$ and $DEF$, $\frac{AB}{DE}=\frac{BC}{FD}$, ​then ​they will ​be similar, when

   1. (a)$\angle B=\angle E$
   2. (b)$\angle A=\angle D$
   3. (c)$\angle B=\angle D$
   4. (d)$\angle A=\angle F$
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9. Q449
   If $△ABC\sim △QRP$, $\frac{\text{ar}(ABC)}{\text{ar}(PQR)}=\frac{9}{4}$, $AB=18$ cm ​and $BC=15$ ​cm, then ​PR ​is ​equal ​to

   1. (a)$10$ cm
   2. (b)$12$ cm
   3. (c)$\frac{20}{3}$ cm
   4. (d)$8$ cm
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10. Q450
    If ​S ​is a ​point on side PQ of ​a $△PQR$ such ​that $PS=QS=RS$, ​then

    1. (a)$PR\cdot QR=R{S}^2$
    2. (b)$Q{S}^2+R{S}^2=Q{R}^2$
    3. (c)$P{R}^2+Q{R}^2=P{Q}^2$
    4. (d)$P{S}^2+R{S}^2=P{R}^2$
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11. Q451
    Is ​the triangle ​with sides 25 cm, 5 ​cm and 24 ​cm a right ​triangle? Give reasons ​for ​your answer.
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12. Q452
    It is given ​that triangle DEF ~ ​triangle RPQ. Is it ​true to ​say ​that angle D = angle R ​and angle F = angle ​P? Why?
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13. Q453
    A and B are ​respectively the points on the ​sides PQ and PR of a triangle PQR ​such that $PQ=12.5$ ​cm, $PA=5$ ​cm, $BR=6$ cm ​and $PB=4$ cm. Is $AB\parallel QR$? Give ​reasons for your answer.
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14. Q454
    In ​Fig. ​6.4, ​BD and CE ​intersect ​each other ​at the point P. ​Is $△PBC\sim △PDE$? Why?

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15. Q455
    In triangles $PQR$ ​and $MST$, $\angle P=55^{\circ }$, $\angle Q=25^{\circ }$, $\angle M=100^{\circ }$ ​and $\angle S=25^{\circ }$. ​Is $△QPR\sim △TSM$? Why?
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16. Q456
    Is the following statement true? ​Why? ​"Two ​quadrilaterals ​are similar, ​if ​their corresponding ​angles ​are equal".
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17. Q457
    Two sides and ​the ​perimeter ​of one triangle are respectively ​three times the corresponding ​sides ​and ​the perimeter of the other triangle. Are the two triangles similar? Why?
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18. Q458
    If in two right triangles, one ​of the acute angles of one ​triangle is equal to ​an ​acute angle of the other ​triangle, can you ​say that the two triangles will be similar? Why?
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19. Q459
    The ratio of the ​corresponding altitudes of ​two similar triangles ​is $\frac{3}{5}$. Is it correct to ​say that ratio ​of their ​areas is $\frac{6}{5}$? ​Why?
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20. Q460
    D is a ​point on ​side ​QR of $△PQR$ such that $PD\perp QR$. Will ​it be correct ​to say ​that $△PQD\sim △RPD$? Why?
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