If the function
\(f(x)=\left\{\begin{array}{ll}a x+2, & x \leq 1 \\x^2+3 x+b, & x>1\end{array}\right.\)
is differentiable at \(x=1\), then the value of \((2 a+b)\) is

The probability distribution of a random variable X is given below:

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
P(X)	p	2p	3p	4p	5p	7p	8p	9p	10p	11p	12p

\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)

The values of x and y in \(\left[\begin{array}{l}2 x+y \\ x+2 y\end{array}\right]=\left[\begin{array}{l}4 \\ 5\end{array}\right]\) are :

Let \(A\) be a non-singular square matrix of order \(n\) with \(|\operatorname{adj} A|=64\) and \(|A|=4\), then ' \(n\) ' is :

The present value of a perpetuity of ₹2,500 payable at the end of each year, if money is worth 10% compounded annually, is:

If \(A\) and \(B\) are square matrices of the same order, then \((A+B)(A-B)\) is equal to

A plane electromagnetic wave of frequency 50 MHz travels in free space along the z-direction. If at a particular point in space and time, \( \vec{E} = (9.3\hat{j}) \text{ V m}^{-1} \), what is \( \vec{B} \) at this point?

500 g of jaggery syrup has 30% jaggery in it.
The quantity of jaggery that should be added to make it 50% of syrup is:

Answer the question on the basis of passage given below :
There are some deposits of nitrates and phosphates in the earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under laboratory conditions, but microbes do it easily. Ammonia forms a large number of complexes with transition metals. Hybridisation easily explains the ease of sigma donation capability of NH₃ and PH₃. Phosphine is an inflammable gas, prepared from white phosphorus.
Which of the following is the correct statement?
A. Between NH₃ and PH₃, NH₃ is a better electron donor because the lone pair of electrons occupy spherical 's' orbital and is less directional.
B. Between NH₃ and PH₃, NH₃ is a better electron donor because the lone pair of electrons occupies sp³ orbital and is more directional.
C. Between NH₃ & PH₃, PH₃ is a better electron donor because the lone pair of electrons occupies sp² orbital and is more directional.
D. Between NH₃ & PH₃, PH₃ is a better electron donor because the lone pair of electrons occupies 's' orbital and is less directional.
Choose the most appropriate answer from the options given below:

The calculated magnetic moment using the 'spin only' formula \(\mu=\sqrt{n(n+2)}\) for \(\mathrm{Cr}^{2+}\) and \(\mathrm{Fe}^{2+}\) respectively is

A tank is filled with water to a height of 15 cm. If the refractive index of water is 1.33, the apparent depth of a needle lying at the bottom of the tank will be

The repetitive use of which of the following logic gate/s separately can be used to prepare an AND gate ?
(A) OR gate
(B) NOT gate
(C) NOR gate
(D) NAND gate
Choose the correct answer from the options given below :