STATEMENT - 1 - In given figure- If C is centre of the circle and - PQC - 25- and - PRC - 15- then - QCR is 40-STATEMENT - 2 - Angle subtended by arc at the centre is twice angled subtended by it at circumference of the circle-

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Angle Subtended by an Arc of a Circle on the Circle and at the Center

STATEMENT - 1...

Question

STATEMENT - 1 : In given figure, If C is centre of the circle and $∠ P Q C = 25^{\circ}$ and $∠ P R C = 15^{\circ}$ , then $∠ Q C R$ is $40^{\circ}$ .
STATEMENT - 2 : Angle subtended by arc at the centre is twice angled subtended by it at circumference of the circle.

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

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Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

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Statement - 1 is True, Statement - 2 is False

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Statement - 1 is False, Statement - 2 is True

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- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

a > 1

- 2 :

a > 1, {log}_{a} x

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

- 1 :

x^{{log}_{x} (3 - x)^{2}} = 25

x = - 2

- 2 :

a^{{log}_{a} x} = x

a > 0, x > 0

a \neq 1

n \geq 2,

\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + . . . + \frac{1}{\sqrt{n}} > \sqrt{n}

\sqrt{n (n + 1)} < n + 1

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