The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x\) is:

If \(A^{-1}\) exists for the matrix \(A=\left[\begin{array}{ccc}1 & \lambda & -1 \\ -1 & 1 & 0 \\ \lambda & 1 & 1\end{array}\right]\) then

A and B are two students. Their chances of solving a problem correctly are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively.
If the probability of their making a common error is \(\frac{1}{20}\) and they obtain the same answer, then the probability that their answer is correct is:

The value of the determinant \(\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|\) is:

The area (in sq. units) of a triangle formed by vertices \(O, A\), and \(B\) where \(\overrightarrow{O A}=\hat{i}+2 \hat{j}+3 \hat{k}\) and \(\overrightarrow{O B}=-3 \hat{i}-2 \hat{j}+\hat{k}\) is

The minimum value of \(Z = 3x + 2y\) subjected to the constraints \(2x + y ≥ 7, x + 2y ≥ 8 x, y ≥ 0\) is:

If the objective function Z = px + qy is maximum at (2,-2) and the maximum value is 8, such that p = 3q, then the values of p and q respectively are:

Which one of the following step is not involved in the genetic modification of an organism?

'GEAC' stands for -

A ray incident at 50° on one refracting surface of a prism of angle 60°, suffers a deviation of 40°. The angle of emergence is:

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom \(X\) is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
Which of the following bromo isomer of butane will react at a faster rate towards SN2 reaction?

Which of the following is an example of 'Ex-situ Conservation' of threatened animals and plants?

In the atomic hydrogen line spectrum, the wavelength of the first line of the Lyman series is (Given: Rydberg constant R = \( 1.097 \times 10^7 \, m^{-1} \))