Let \(A=\left[a_{i j}\right]_{2 \times 3}\) and \(B=\left[b_{i j}\right]_{3 \times 2}\), then \(|5 A B|\) is equal to:

If \(y=5 \cos x-3 \sin x\), then \(\frac{d^2 y}{d x^2}\) is equal to :

If \(f(x)=a \log _e|x|+b x^2+x\) has critical points at \(x=-2\) and \(x=1\), then

If \(f(x)=\left\{\begin{array}{cl}\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is :

Differential equation of a parabola with vertex at origin and symmetric about \(x\)-axis is :

The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = -x + 1\) is:

The maximum value of \(4 \sin ^2 x+3 \cos ^2 x\) is:

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
Which one is the correct electronic configuration of sulphur?

A coil \(C_1\) is connected to a galvanometer G. Second coil \(C_2\) is connected to a battery through a tapping key. The steady current in the coil \(C_2\) produces a steady magnetic field. As coil \(C_2\) is moved towards the coil \(C_1\), the galvanometer shows a deflection. To obtain a large deflection, one or more of the following steps can be taken:
(A) Use a rod made of soft iron inside the coil \(C_2\)
(B) Connect the coil \(C_2\) to a more powerful battery
(C) Move the arrangement of coil \(C_2\) rapidly towards the coil \(C_1\)
(D) hold the key pressed continuously
Choose the correct answer from the options given below:

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

List-I	List-II
(A) Tollen's reagent	(I) Rochelle salt
(B) Jones reagent	(II) Conc. HCl and \(ZnCl _2\)
(C) Lucas reagent	(III) Ammoniacal silver nitrate
(D) Fehling solution	(IV) Chromium trioxide-sulfuric acid

Choose the correct match:

Identify the carbohydrate which is not a polysaccharide

A boat covers 32 km upstream and 36 km downstream in 7 hours.
Also, it covers 40 km upstream and 48 km downstream in 9 hours.
The speed of the boat in still water is :