If \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]\), then \(A^{-1}\) is equal to :

Two infinitely long parallel conductors carrying currents I 1 and I 2 are at distance d apart. The force \(F\) on length \(L\) of one conductor due to the other is :

The value of the integral \(I=\int_{-3}^3\left(x^3-x\right) d x\) is :

A runs 9 times slower than B. If B gives A a start of 80 meters, how far must be the winning post on the tracks so that A and B reach there at the same time?

If a line makes angles \(\frac{2 \pi}{3}\) and \(\frac{\pi}{3}\) with positive direction of \(x\)-axis and \(y\)-axis respectively,
then the acute angle made by the line with positive \(z\)-axis is:

The area enclosed between the graph of \(y=x^3\) and the lines \(x=0, y=1, y=8\) is

Match List - I with List - II

List - I (terms)	List - II (Definitions)
(A) POPULATION	(I) Measurable characteristics of the population such as mean, variance, standard deviation etc. of population
(B) SAMPLE	(II) Measurable characteristics of the sample such as mean, variance, standard deviation etc. of a sample
(C) PARAMETER	(III) Finite set of statistical individuals drawn from a population for investigation
(D) STATISTIC	(IV) Collection of objects having the same characteristics

Choose the correct answer from the options given below:

Which of the following is NOT a means of transmission of Sexually Transmitted Infections (STIs)?

An alkyl halide with molecular formula \(\text{C}_5\text{H}_{11}\text{Br}\) on dehydrohalogenation give two isomeric alkenes X and Y with formula \(\text{C}_5\text{H}_{10}\). On reductive ozonolysis X and Y gave four compounds: \(\text{CH}_3\text{CHO}\) (ethanal), \(\text{CH}_3\text{COCH}_3\) (propanone), \((\text{CH}_3)_2\text{CHCHO}\) (3-methylbutanal), and \(\text{HCHO}\) (methanal). The alkyl halide is:

Three identical resistors are connected first in series to an electrical voltage V. Let I be the total current flowing in the circuit. These resistors are disconnected and again connected in parallel with the same source. Which of the following statements are true?
(A) The potential difference across each resistor is V/3 in series connection
(B) The potential difference across all three resistors in parallel connection is 3V
(C) The current flowing in each resistor in series connection is the same as I
(D) The current flowing through each resistor in parallel combination is equal to 31
Choose the correct answer from the options given below:

The standard Gibbs energy of the following reaction is \(-610 kJ mol ^{-1}\)
\(Mg(s)+2 Ag^{+}(aq) \rightarrow Mg^{2+}(aq)+2 Ag(s)\)
What is the standard EMF for the cell correspondng to the above reaction?
Given: Faraday's constant \(=96500 C mol ^{-1}\)

Bt toxins are insect group specific proteins. Gene named crylAc and cryllAb control:

\(\text { If } I=\int \frac{x}{x-\sqrt{x^2-4}} d x=\alpha x^3+\beta\left(x^2-4\right)^{\frac{3}{2}}+\gamma\) where \(\gamma\) is a constant of integration, then