The value of a washing machine purchased two years ago depreciates at the annual rate of 10%. If its present value is ₹ 50,000, then its value after two years will be :

The value of \(\int \frac{x^5}{\sqrt{1+x^3}}\)dx is

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of k/4 is

A vector of magnitude 8 units in the direction perpendicular to both the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}+\hat{k}\) is

Integrating factor of \(\frac{dy}{dx} + y \cot x = 2x + x^2 \cot x\) (\(x \neq 0\)) is:

If \(\left[\begin{array}{ll}1 & 0 \\ b & 5\end{array}\right]+2\left[\begin{array}{cc}a & 0 \\ 1 & -2\end{array}\right]=I\), where \(I\) is the unit matrix of order 2 , then the value of \((a-b)\) is :

The value of which of the following integrals is zero?
(A) \(\int_0^1 x d x\)
(B) \(\int_{-1}^1 x d x\)
(C) \(\int_{-1}^1 x^2 d x\)
(D) \(\int_0^1 \log \left(\frac{x}{1-x}\right) d x\)
Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) 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 \(\left(\Lambda_m^0\right)\). 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, the value of \(\left(\Lambda_m^0\right)\) 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.
The unit of constant A is :

Consider the function \(f(x)=\sin x\) in the interval \([\pi, 2 \pi]\), then which of the following statements are correct?
(A) \(x=\frac{3 \pi}{2}\) is its stationary point.
(B) Its maximum value is 1
(C) Its minimum value is -1
(D) It attains its maximum value at \(\pi\) and \(2 \pi\)
Choose the correct answer from the options given below:

Which of the following enzyme is used during isolation of DNA from plant cell ?

20 g of binary electrolyte (Molecular mass = 100) are dissolved in 500 g of water. The freezing point of the solution is -0.74°C and \(K_f \) is 1.86 K kg mol⁻¹. The degree of ionisation of the electrolyte is:

For any two matrices A and \(B , AB + BA\) is a possible matrix, then :

Match List-l with List-II

List-l	List-II
A. Methyl alcohol	I. Highly poisonous
B. Ethyl alcohol	II. Carbolic acid
C. Phenol	III. Highly soluble in water
D. Picric acid	IV. Turns blue litmus red

Choose the correct answer from the options given below :