If a matrix P is both symmetric and skew-symmetric, then

If \(y=\sin ^{-1} \sqrt{\frac{x}{x+1}}+\sec ^{-1} \sqrt{\frac{x+1}{x}}\), then \(\frac{d y}{d x}\) is

Distance of the point \((2,4,-1)\) from the line \(\frac{10+2 x}{2}=\frac{y+3}{4}=\frac{6-z}{9}\) is

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 :

Mr. Jain wishes to purchase a shop for ₹25,00,000 with down payment of ₹2, 00, 000. If he can amortize the balance at 9% per annum compounded monthly for 25 years, what will be his monthly installment if it is given that \(\left(a_{\frac{300}{0.0075}}=119.1616\right)\)?

If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is:

If \(x\) is in the 1 st Quadrant, then the value of \(\tan ^{-1}\left(\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}\right)\) is :

The resistance of a cylindrical conductor is :

Match List-I with List-II

Llst-I	Llst-(II)
(A) \(f(x)=[x]\)	(I) Continuous everywhere but not differentiable at \(x=-1\)
(B) \(f(x)=|x-1|\)	(II) Continuous everywhere except at all integral values
(C) \(f(x)=e^{|x|}\)	(III) Continuous everywhere but not differentiable at \(x=1\)
(D) \(f(x)=|x+1|\)	(IV) Continuous everywhere but not differentiable at \(x=0\)

Choose the correct answer from the options given below:

Assume that an electric field \( (20\hat{i}) \text{ V m}^{-1} \) exists in the region of space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 1 \text{ m} \), then the potential difference \( V_A - V_0 \) is :

A bubble in glass slab (\( \mu = 1.5 \)) when viewed from one side appears at 5 cm and 2 cm from otherside, then the thickness of the glass slab is:

If A and B are symmetric matrices of the same order, then which one of the following is true?

Entamoeba histolytica is a protozoan parasite found in which part of human body?