List of practice Questions

Which one of the following sets is not correctly matched?
Arrange the following pesticides in the chronological order of their release into the market: A: Organophosphates
B: Organochlorides
C: Sodium chlorate
Identify the incorrect statements from the following: I. \( \Delta S_{\text{system}} = (\Delta S_{\text{total}} + \Delta S_{\text{sur}}) \) II. \( A(l) \rightarrow A(s) \); for this process entropy change decreases III. Entropy units are \( J \ K^{-1} \ mol^{-1} \)
Drift speed \( v \) varies with the intensity of the electric field \( E \) as per the relation
Two point charges +6 \(\mu\)C and +10 \(\mu\)C kept at a certain distance repel each other with a force of 30 N. If each charge is given an additional charge of -8 \(\mu\)C, the two charges
The moments of inertia of a solid cylinder and a hollow cylinder of the same mass and same radius about the axes of the cylinders are \( I_1 \) and \( I_2 \). The relation between \( I_1 \) and \( I_2 \) is
Find the general solution of the differential equation \( (x - y -1) dy = (x + y + 1) dx \).
Find the area enclosed by the curve \( y = x^3 - 19x + 30 \) and the X-axis.
Evaluate \( \int_{ \log 4}^{ \log 5} \frac{e^{2x} + e^x}{e^{2x} - 5e^x +6} dx \):
Evaluate the integral: \[ I = \int (\tan^7 x + \tan x) dx. \]
Evaluate the integral: \[ I = \int \frac{\csc x}{3\cos x + 4\sin x} dx. \]
By considering \( 1' = 0.0175 \), the approximate value of \( \cot 45^\circ 2' \) is:
Evaluate the limit: \[ \lim_{x \to \infty} \left( \frac{3x^2 - 2x + 3}{3x^2 + x - 2} \right)^{3x - 2} \]
Let \( P(a, 4, 7) \) and \( Q(3, \beta, 8) \) be two points. If the YZ-plane divides the join of the points P and Q in the ratio 2:3 and the ZX-plane divides the join of P and Q in the ratio 4:5, then the length of line segment PQ is:
If the coordinate axes are rotated by \( 45^\circ \) about the origin in the counterclockwise direction, then the transformed equation of \( y^2 = 4ax \) is:
The probability that a person goes to college by car,\(\frac{1}{5}\) bus,\(\frac{2}{5}\) or train \(\frac{3}{5}\) is given. If he reaches college on time, find the probability he traveled by car.
A random variable \( X \) follows a Poisson distribution with mean 5. Find the probability that \( X3 \).
In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).
In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).
Find the value of \( x \) satisfying: \[ 1 + \sin x + \sin^2 x + \sin^3 x + \dots = 4 + 2\sqrt{3} \] where \( 0x\pi, x \neq \frac{\pi}{2} \).
The coefficient of \( x^5 \) in the expansion of \( (3 + x + x^2)^6 \) is:

 If a red eyed male Drosophila and white eyed female Drosophila are crossed, the eye color in their offspring is:

At T(K), the following graph is obtained for an ideal gas.

Which of the following graphs correctly represents the work done on the gas (shaded part)?

With reference to the Fast Fourier Transform, if \( W_4^1 = W_x^2 \), then what is the value of \( x \)?
An organic compound \( C_7H_5N \) on reduction with reagent X gave Y. Reaction of Y with p-toluene sulphonyl chloride gave Z which is insoluble in alkali. X and Y respectively are: