If \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=5,|\vec{b}|=3,|\vec{c}|=7\), then the acute angle between \(\vec{a}\) and \(\vec{b}\) is

If z = 5x + 8y is the objective function of a LPP and (0,0), (3, 1), (2, 4), (0, 3), (5,0) are corner points of the bounded feasible region, then the maximum value of the objective function is

If \(A\) and \(B\) are skew-symmetric matrices, then which one of the following is NOT true?

\(\int \frac{\sin 2 x d x}{\sqrt{9-\cos ^4 x}}\) equals

Let \(f(x)=x|x|\). Then \(f(x)\) is:

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

A coin is tossed 6 times. The probability that tail appears odd number of times is:

During the p-n junction formation, when an electron diffuses from n \( \rightarrow \) p, it leaves behind an :

The reaction for the conversion of phenol into salicylic acid is known as

Three charges Q, +2q and +2q are placed at the vertices of an equilateral triangle. If the net electrostatic potential energy of the system is zero, then Q is equal to

Match List I with List II

LIST I	LIST II
A. Gatterman-Koch reaction	I. Diphenyl
B. Stephens reaction	II. Ethyl amine
C. Hoffmann Bromamide degradation	III. Benzaldehyde
D. Fittig reaction	IV. Acetaldehyde

Choose the correct answer from the options given below:

The probability distribution function of a normal variate with mean \(\mu\) and variance \(\sigma^2\) is given by :
\(f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2},-\infty< x< \infty,-\infty < \mu < \infty, \sigma>0\)
If \(y=f(x)\) be the normal probability curve, then which of the following is correct?
(A) The normal curve is symmetrical about the line \(x=\mu\).
(B) Mean, median and mode of the distribution coincide.
(C) \(Y\)-axis is an asymptote to the normal curve.
(D) If \(x\) increases numerically, \(f(x)\) decreases rapidly.
Choose the correct answer from the options given below :

Down's syndrome is a genetic disorder. It is due to: