The value of \(\int_{-3}^2 x^2|2 x| d x\) is :

\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) \(dx\) is equal to

Given \(X=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]\), then value of K if \(X^2=8 X+K I\) is :

A 95% confidence interval states that the population mean is greater than 152 and less than 160.
If \(\sigma=15\) and \(Z_{0.025}=1.96\), then what sample size was used in the study?

The value of \(\int e^x\left[f(x)+f^{\prime}(x)\right] d x\) is :

In a box containing 100 bulbs, 10 are defective.
The probability that out of a sample of 5 bulbs none is defective is:

If \(A\) is a square matrix and \(|A|=4\), then the value of \(\left|A A^{\prime}\right|\) where \(A^{\prime}\) is transpose of \(A\) is:

The resistivity of a wire depends on :
(A) its length
(B) its area of cross-section
(C) its temperature
(D) nature of material
(E) voltage applied across it
Choose the correct answer from the options given below :

At what speed should a galaxy move with respect to earth so that spectral line of \( 600.0 \text{ nm} \) appears as \( 600.6 \text{ nm} \) ?

Read the passage carefully and answer the Questions
Molar conductivity \(\Lambda_m^0\)of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\Lambda_m^0\) . For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, they value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
If the molar conductance values of Ca²⁺ and Cl^- at infinite dilution are, respectively, 118.8 × 10^-4 ohm^-1 m² mol^-1 and 77.33 × 10^-4 ohm^-1 m² mol^-1, then the molar conductance of CaCl₂ at infinite dilution will be :

The component of electromagnetic wave having wavelength range from 1 nm to \(10^{-3}\) nm is:

Geometry of \(\left[ Ni ( CN )_4\right]^{2-}\) and \(\left[ NiCl _4\right]^{2-}\) are

A proton is projected with a speed of \( v = 4 \times 10^6 \text{ m s}^{-1} \) horizontally from east to west. A uniform magnetic field \( \vec{B} \) of strength \( B = 1.5 \times 10^{-3} \text{ T} \) exists in the vertically upward direction. What is the acceleration produced? (Use charge on the proton \( q = 1.6 \times 10^{-19} \text{ C} \) and mass of the proton \( m = 1.67 \times 10^{-27} \text{ kg} \))