If $y_k$ is the $k$-th derivative of $y$ with respect to $x$, and $y = \cos(\sin x)$, then $y_1 \sin x + y_2 \cos x$ is equal to

$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1\%$. The tension produced is $1000 \ N$. The Young's modulus of the wire is:

Which of the following oxides will produce hydrogen peroxide upon reaction with dilute acid?

Water flows in a streamlined manner through a capillary tube of radius $a$,the pressure difference being $P$ and the rate of flow $Q$. If the radius is reduced to $a/2$ and the pressure is increased to $2P$,the rate of flow becomes:

$A$ random variable $X$ has the following probability distribution:

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.15$	$0.23$	$K$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the event $E = \{X \mid X \text{ is a prime number}\}$ and the event $F = \{X \mid X < 4\}$, the probability $P(E \cup F) = $

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycles/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is