MHT CET 2019 on Mathematics Questions and Answers | ExamFriend.in | General questions

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31.

For a G P, if $S_{n}=\frac{4^{n}-3^{n}}{3^{n}}$ , then $t_{2}$ = .....

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{7}{9}$

$\frac{4}{9}$

Option D

We have, $S_{n}=\frac{4^{n}-3^{n}}{3^{n}}$

For $n=1,S_{1}=t_{1}=\frac{4-3}{3}=\frac{1}{3}$

For $n=2,S_{2}=t_{1}+t_{2}=\frac{4^{2}-3^{2}}{3^{2}}=\frac{7}{9}$

$\therefore$ $t_{2}=\frac{7}{9}-t_{1}=\frac{7}{9}-\frac{1}{3}=\frac{7-3}{9}=\frac{4}{9}$

32.

If $P( x_{1},y_{1})$ is a point on the hyperbola x²-y² =a² , then SP.S'P=.....

$\frac{x_{1}^{2}-y_{1}^{2}}{a^{2}}$

$\frac{x_{1}^{2}+y_{1}^{2}}{a^{2}}$

$x_{1}^{2}-y_{1}^{2}$

$x_{1}^{2}+y_{1}^{2}$

Option D

Given , equation of hyperbola

x²-y² =a²..............(i)

If P(x₁,y₁) is a point on Eq.(i) , then

$x_{1}^{2}-y_{1}^{2}$ = $a_{}^{2}$ ......(ii)

Now, SP= ex₁-a

and SP'= ex₁+a

$\therefore$ SP.SP' = (ex₁-a)(ex₁+a)

= e².x₁²-a²

= $2x_1^2-a^{2}$ (since , for x²-y²= a², e = $\sqrt{2}$ )

= $2x_1^2-(x_1^2-y_1^2)$ [using Eq. (ii)]

= $x_1^2+y_1^2$

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MHT CET 2019 :: Mathematics :: General questions