$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$

Two waves represented by $y_1 = 10 \sin(200\pi t)$ and $y_2 = 20 \sin(200\pi t + \pi/2)$ are superimposed at a point. The amplitude of the resultant wave is

Let $A$ and $B$ be two sets. Then $(A \cup B)' \cup (A' \cap B)$ is equal to:

If $z = \sec(y - ax) + \tan(y + ax)$,then $\frac{\partial^2 z}{\partial x^2} - a^2 \frac{\partial^2 z}{\partial y^2}$ is equal to

The instantaneous values of alternating current and voltage in a circuit are given as $i = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ A}$ and $e = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ V}$. The average power in Watts consumed in the circuit is:

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \,\, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to: