Maths

If the sum of an infinite GP a, ar, ar², ar³,……. is 15 and the sum of the squares of its each term is 150, then the sum of ar², ar⁴, ar⁶,…… is:

Let $\overrightarrow{a}=\widehat{i}+\widehat{j}+\widehat{k}and\overrightarrow{b}=\widehat{j}-\widehat{k}.If\overrightarrow{c}$  is a vector such that $\overrightarrow{a}*\overrightarrow{c}=\overrightarrow{b}and\overrightarrow{a}.\overrightarrow{c}=3,$  then $\overrightarrow{a}.\left(\overrightarrow{b}*\overrightarrow{c}\right)is$ equal to

Let y = y(x) be a solution curve of the differential equation $\left(y+1\right)ta{n}^{2}xdx+tanxdy+ydx=0,$ $x\in \left(0,\frac{\pi }{2}\right).$  If $\underset{x\to 0^{+}}{lim}xy\left(x\right)=1,$  then the value of y   $\left(\frac{\pi }{4}\right)is:$

Let ABC be a triangle with A (-3, 1) and $\angle ACB=\theta ,$ $0<\theta <\frac{\pi }{2}.$    If the equation of the median through B is 2x + y – 3 = 0 and the equation of angle bisector of C is 7x – 4y – 1 = 0, then tanq is equal to:

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively.

It was found that by mistake one data value was taken as 25 instead of 35. If α and $\sqrt[]{\beta }$  are the mean and standard deviation respectively for correct data, then $\left(\alpha ,\beta \right)$ is:

If the truth value of the Boolean expression $\left(\left(p\vee q\right)\wedge \left(q\to r\right)\wedge \left(\sim r\right)\right)\to \left(p\wedge q\right)$  is false, then the truth values of the statements p, q, r respectively can be:

If a ling along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through of the point (-30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is:

Let A and B be independent events such that P (A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = $\frac{5}{9},is:$  

On the ellipse $\frac{x^2}{8}+\frac{y^2}{4}=1$  let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS' then, the value of (5 – e²). A is:

The value of ${\displaystyle \underset{\frac{-1}{\sqrt[]{2}}}{\overset{\frac{1}{\sqrt[]{2}}}{\int }}{\left({\left(\frac{x+1}{x-1}\right)}^2+{\left(\frac{x-1}{x+1}\right)}^2-2\right)}^{1/2}}$  dx is: