If \(A=\left[\begin{array}{ll}3 & -5 \\ 4 & -7\end{array}\right]\), then \(A^{-1}\) is:

Area lying in the first quadrant and bounded by the circle \(x^2+y^2=4\) and the lines x = 0 and x = 2 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

The mean of numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

If A speaks truth in \(75\%\) cases and B speaks truth in \(80\%\) cases, then the probability that they contradict each other in a statement, is :

A box contains 10 balls, each marked with one of the digits 0 to 9 .
If four balls are drawn successively with replacement from the box,
then the probability that none is marked with the digit \(0\) is :

The differential equation whose solution is \(A x^2+B y^2=1\) where \(A\) and \(B\) are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below :

The maximum value of the function \(f(x)=-x^2+2 x-1\) is:

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O _2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature.
Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
Sulphate of magnesium of the following is :

Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II

List - I	List - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is	(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is	(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is	(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is	(IV) \(2 \alpha\)

Choose the correct answer from the options given below:

Match List-I with List-II

List-I (AC circuit)	List-II (Features)
(A) Only resistor in a circuit	(I) Current leads or lag the voltage
(B) Only capacitor in a circuit	(II) Voltage and Current are in phase
(C) Only inductor in a circuit	(III) The current lags the voltage by \(\frac{\pi}{2}\)
(D) Series LCR circuit \(X_C \neq X_L\) and \(R \neq 0\)	(IV) The current leads the voltage by \(\frac{\pi}{2}\)

Choose the correct answer from the options given below :

Which types of bonds or interactions are found in the β-helix of protein?

The energy equivalent of 5 g of substance is