List of practice Questions

If \( A \) and \( B \) are two independent events such that \( P(A) = 0.3 \), \( P(B) = x \), and \( P(A \cup B) = 0.44 \), then \( x = \):
For the differential equation \( \frac{d^3 y}{dx^3} = 0 \), \( y = ax^2 + bx + c \) is:
There are 10 points in a plane, out of which 6 are collinear. If $ N $ is the number of triangles that can be formed, then $ N = $ ?
Evaluate: $$ \int \frac{dx}{(x - 3)^{4/5} (x + 1)^{6/5}} = ? $$
During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6. The probability that in a given week there will be exactly two days with severe fog is
If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]
The pairs of straight lines \( 2x^2 + axy + 3y^2 = 0 \) and \( 2x^2 + bxy - 3y^2 = 0 \) share a common line, and the other lines are perpendicular. Then values of \( a \) and \( b \) are?
Find the distance between the directrices of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{20} = 1 \]
The maximum value of the variance of a Binomial distribution with parameters \( n \) and \( p \) is:
The sum of the real roots of the equation: $$ x^4 - 2x^3 + x - 380 = 0 $$ is:
If $$ ^{10}C_2 = ^{3^{n+1}}C_3 $$ then the value of $ n $ is:
In any triangle $ ABC $, evaluate: $$ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} $$
Sides passing through vertex $ (\alpha, \beta) $ of a triangle are bisected at right angles by the lines: $$ y^2 - 8xy - ax^2 = 0 $$ Find the coordinates of the centroid of the triangle.
If $ a, b>0 $, then the minimum value of: $$ y = \frac{b^2}{a - x} + \frac{a^2}{x},\quad \text{for } 0<x<a $$
The anions (A) of \( \text{C}_p\text{A}_q \) molecule form an fcc lattice. Cations (C) are positioned at the body center and half of the edge centers. The formula of the molecule is:
Given: \[ \text{CH}_3\text{COOC}_2\text{H}_5 + \text{H}_2\text{O} \rightarrow \text{CH}_3\text{COOH} + \text{C}_2\text{H}_5\text{OH} \] Initial concentrations: Ethyl acetate = 0.001 M, Water = 2 M 99% hydrolyzed in 10 s. Find rate constant \( k \).
The pH of 0.01 N lime water is
The major product of the following reaction is (Grignard Reagent with D2}O)
Grignard Reagent with D2O
The standard Gibbs energy ($\Delta G^\ominus$) for the following reaction is A(s) + B$^{2+}$ (aq) $\rightleftharpoons$ A$^{2+}$ (aq) + B(s), K$_c$=10$^{12}$ at 25$^\circ$C (K$_c$= equilibrium constant)
Which of the following reactions takes places when tertiary butanol passed over heated copper at 573 K ?
If \( \Delta x \) is the uncertainty in position and \( \Delta v \) is the uncertainty in velocity of a particle and both are equal, then the correct expression for uncertainty in momentum for the same particle is:
A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is
A cubic lattice has A atoms at the body center, B atoms at the corners, C atoms at half of the face centers. The formula of the lattice is
Carbohydrates are stored in plants and animals in which of the following forms respectively?

Identify the major product from the following reaction sequence: