The set $\{x \in R: \cos 2x + 2 \cos^2 x = 2\}$ is equal to

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is:

For a gas,$\frac{R}{C_{v}}=0.4$,where $R$ is the universal gas constant and $C_{v}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

$A$ tower,of $x$ metres high,has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then,the length of the flagstaff (in metres) is:

The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$. The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?

Among the following,the $CORRECT$ combinations are :
$A.$ $IF_3$ $\rightarrow$ $T$-shaped $(sp^3d)$
$B.$ $IF_5$ $\rightarrow$ Square pyramidal $(sp^3d^2)$
$C.$ $IF_7$ $\rightarrow$ Pentagonal bipyramidal $(sp^3d^3)$
$D.$ $ClO_4^-$ $\rightarrow$ Square planar $(sp^3d)$
Choose the correct answer from the options given below :