Circles

1. A.
   $3\sqrt{3}$ cm
2. B.
   $3$ cm
3. C.
   $6$ cm
4. D.
   $\sqrt{3}$ cm

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1. A.
   $55^\circ$
2. B.
   $20^\circ$
3. C.
   $35^\circ$
4. D.
   $70^\circ$

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1. A.
   $4$ cm
2. B.
   $4\sqrt{2}$ cm
3. C.
   $8$ cm
4. D.
   $2\sqrt{2}$ cm

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1. A.
   $a^2 + (a + 2)^2 = (2b)^2$
2. B.
   $b^2 = a + 4$
3. C.
   $2a^2 + 1 = b^2$
4. D.
   $b^2 = a + 1$

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1. A.
   $8$ cm
2. B.
   $10$ cm
3. C.
   $9$ cm
4. D.
   $12$ cm

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1. A.
   $60^\circ$
2. B.
   $70^\circ$
3. C.
   $80^\circ$
4. D.
   $90^\circ$

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1. A.
   $r\sqrt{2}$
2. B.
   $\sqrt{2r}$
3. C.
   $2r$
4. D.
   $r^2$

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1. A.
   $25^\circ$
2. B.
   $65^\circ$
3. C.
   $90^\circ$
4. D.
   $35^\circ$

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1. A.
   $30^\circ$
2. B.
   $15^\circ$
3. C.
   $45^\circ$
4. D.
   $10^\circ$

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1. A.
   $65^\circ$
2. B.
   $60^\circ$
3. C.
   $50^\circ$
4. D.
   $35^\circ$

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1. A.
   $65^\circ$
2. B.
   $58.5^\circ$
3. C.
   $57.5^\circ$
4. D.
   $45^\circ$

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1. A.
   $130^\circ$
2. B.
   $50^\circ$
3. C.
   $120^\circ$
4. D.
   $90^\circ$

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false, but Reason (R) is true.

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1. A.
   $30^\circ$
2. B.
   $60^\circ$
3. C.
   $120^\circ$
4. D.
   $300^\circ$

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1. A.
   $r$
2. B.
   $\dfrac{3r}{2}$
3. C.
   $2r$
4. D.
   $4r$

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1. A.
   parallel
2. B.
   perpendicular
3. C.
   equal
4. D.
   intersecting

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1. A.
   $30^\circ$
2. B.
   $60^\circ$
3. C.
   $90^\circ$
4. D.
   $120^\circ$

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1. A.
   $40^\circ$
2. B.
   $50^\circ$
3. C.
   $60^\circ$
4. D.
   $80^\circ$

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1. A.
   $3\sqrt{2}$ cm
2. B.
   $6\sqrt{2}$ cm
3. C.
   3 cm
4. D.
   6 cm

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1. A.
   Infinite number of tangents can be drawn to a circle.
2. B.
   Infinite number of tangents can be drawn to a circle from a point outside the circle.
3. C.
   Infinite number of secants can be drawn to a circle from a point outside the circle.
4. D.
   Angle between tangent and diameter at point of contact is $90^\circ$.

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1. A.
   P
2. B.
   Q
3. C.
   R
4. D.
   S

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1. A.
   $210^\circ$
2. B.
   $150^\circ$
3. C.
   $105^\circ$
4. D.
   $30^\circ$

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1. A.
   $22.5$
2. B.
   $45$
3. C.
   $67.5$
4. D.
   $90$

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1. A.
   8 cm
2. B.
   4 cm
3. C.
   2 cm
4. D.
   3 cm

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1. A.
   $2r$
2. B.
   $4r$
3. C.
   $2\sqrt{2}\,r$
4. D.
   $\sqrt{2}\,r$

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1. A.
   $2r$
2. B.
   $3r$
3. C.
   $2\sqrt{2}\,r$
4. D.
   $\sqrt{2}\,r$

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1. A.
   20 cm
2. B.
   less than 20 cm
3. C.
   more than 20 cm but less than 40 cm
4. D.
   40 cm

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1. A.
   $25^\circ$
2. B.
   $65^\circ$
3. C.
   $90^\circ$
4. D.
   $35^\circ$

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1. A.
   Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
2. B.
   Both, Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. C.
   Assertion (A) is true but Reason (R) is false.
4. D.
   Assertion (A) is false but Reason (R) is true.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false, but Reason (R) is true.

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1. A.
   Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
2. B.
   Both, Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. C.
   Assertion (A) is true but Reason (R) is false.
4. D.
   Assertion (A) is false but Reason (R) is true.

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1. A.
   $65^\circ$
2. B.
   $57.5^\circ$
3. C.
   $67.5^\circ$
4. D.
   $32.5^\circ$

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1. A.
   $4$
2. B.
   $3$
3. C.
   $2$
4. D.
   $1$

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1. A.
   $110^\circ$
2. B.
   $115^\circ$
3. C.
   $120^\circ$
4. D.
   $125^\circ$

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1. A.
   5 cm
2. B.
   $5\sqrt{2}$ cm
3. C.
   $2\sqrt{5}$ cm
4. D.
   10 cm

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1. A.
   $96^\circ$
2. B.
   $42^\circ$
3. C.
   $106^\circ$
4. D.
   $86^\circ$

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1. A.
   $42^\circ$
2. B.
   $84^\circ$
3. C.
   $96^\circ$
4. D.
   $138^\circ$

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1. A.
   $70^\circ$
2. B.
   $50^\circ$
3. C.
   $65^\circ$
4. D.
   $40^\circ$

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1. A.
   $4{\cdot}2$ cm
2. B.
   $2{\cdot}1$ cm
3. C.
   $8{\cdot}4$ cm
4. D.
   $6{\cdot}3$ cm

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1. A.
   $120^\circ$
2. B.
   $140^\circ$
3. C.
   $70^\circ$
4. D.
   $90^\circ$

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1. A.
   Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
2. B.
   Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).
3. C.
   Assertion (A) is true but Reason (R) is false.
4. D.
   Assertion (A) is false but Reason (R) is true.

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1. A.
   $47.5^\circ$
2. B.
   $42.5^\circ$
3. C.
   $85^\circ$
4. D.
   $95^\circ$

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1. A.
   $5\sqrt{3}$ cm
2. B.
   $\dfrac{10}{\sqrt{3}}$ cm
3. C.
   $10$ cm
4. D.
   $\dfrac{5}{\sqrt{3}}$ cm

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1. A.
   $3{\cdot}5$ cm
2. B.
   $7$ cm
3. C.
   $6{\cdot}5$ cm
4. D.
   $5$ cm

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1. A.
   $3$ cm
2. B.
   $3\sqrt{3}$ cm
3. C.
   $2$ cm
4. D.
   $\sqrt{3}$ cm

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1. A.
   $40$ cm
2. B.
   $9$ cm
3. C.
   $41$ cm
4. D.
   $50$ cm

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1. A.
   $50^\circ$
2. B.
   $40^\circ$
3. C.
   $100^\circ$
4. D.
   $130^\circ$

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1. A.
   $45^\circ$
2. B.
   $90^\circ$
3. C.
   $60^\circ$
4. D.
   $180^\circ$

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1. A.
   $62\frac{1}{2}^\circ$
2. B.
   $125^\circ$
3. C.
   $55^\circ$
4. D.
   $90^\circ$

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1. A.
   $2\sqrt{3}$ cm
2. B.
   $2$ cm
3. C.
   $2\sqrt{2}$ cm
4. D.
   $\sqrt{3}$ cm

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1. A.
   QR
2. B.
   PR
3. C.
   PS
4. D.
   PQ

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1. A.
   $30^\circ$
2. B.
   $60^\circ$
3. C.
   $45^\circ$
4. D.
   $90^\circ$

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1. A.
   $25^\circ$
2. B.
   $65^\circ$
3. C.
   $90^\circ$
4. D.
   $115^\circ$

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false, but Reason (R) is true.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false, but Reason (R) is true.

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