List of practice Questions

Let \( x \) be a real number and \( -2<x<2 \). When \( \frac{x+1}{(x+3)(x-2)} \) is expanded in powers of \( x \), then the coefficient of \( x^3 \) is:
If \( \vec{a} = t\vec{b} \) where \( t<0 \) is a scalar, then:
If \( \vec{a} \) and \( \vec{b} \) are two unit vectors with \( (\vec{a}, \vec{b}) = 0 \) and \( |\vec{a} - \vec{b}| = 1 \), then: \[ 2|\vec{a} + \vec{b}| \cos\theta = \frac{2}{|\vec{a} + \vec{b}| \cos\theta} \]
Evaluate: \( (1 + \cos\frac{\pi}{8})(1 + \cos\frac{2\pi}{8})(1 + \cos\frac{3\pi}{8}) \ldots (1 + \cos\frac{7\pi}{8}) = \)
If \(3\sin^4 x + 2\cos^4 x = \frac{6}{5}\) and \(x\) is an acute angle, then \(\tan 2x =\)
If \( f_n(x) = \frac{1}{2n} \left[ \sin^{2n}x + \cos^{2n}x \right] \), then \( f_1(x) + f_2(x) - f_3(x) = \):
If \( \cosh x = \csc\theta \), then \( \coth^2\left(\frac{x}{2}\right) = \):
If \( P(x) = 0 \) is a polynomial of least degree with integer coefficients and \( \sqrt{2} + \sqrt{3}i \) is one of its roots, then that equation is:
A question paper has two sections A and B. Section A has 8 questions and Section B has 6 questions. A student has to answer 10 questions, choosing at least 4 from section A and at least 3 from section B. The number of ways the student can answer the paper is:
If 5 dice are rolled simultaneously, then the number of ways of getting a total of 7 from the numbers on their faces is:
If \( -3 + ix^2y \) and \( x^2 + y + 4i \) are complex conjugates, then \( x = \):
If \( z = 1 + \cos\theta - i\sin\theta \) and \( 0<\theta<\pi \), then \[ \left[ |z - 1|^2 \cdot \frac{|z|^2}{4} \right]^{1/2} = \]
In the Argand plane, the values of \( z \) satisfying the equation \( |z - 1| = |i(z + 1)| \) lie on:
The sum of the fourth powers of the roots of the equation \( 16x^2 - 10x + 1 = 0 \) is:
If \( f : \mathbb{R} \setminus \{0\} \to \mathbb{R} \) is defined by \( f(x) = x + \frac{1}{x} \), then the value of \( \left(f(x)\right)^2 \) is:
If \( A = \begin{bmatrix} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{bmatrix} \) is expressed as a sum of a symmetric matrix \( P \) and a skew-symmetric matrix \( Q \), then \( P^T - Q^T \) equals:
Which of the following are fibrous proteins? Keratin, Insulin, Myosin, Albumin
Which of the following hormones modulate inflammatory reactions?
Correct statements with respect to morphine (X) and Veronal (Y) are
A) Both X and Y are sleep producing agents
B) X is hypnotic and Y is analgesic
C) X is analgesic and Y is hypnotic
D) X is non-narcotic analgesic and Y is antidepressant
Chlorocyclohexane is
Which of the following reagents will convert isobutyraldehyde to the corresponding acid?
What are 'X' and 'Y' respectively in the following reaction sequence?
styrene
This equation represents the preparation of gold sol by \[ 2 \, \text{AuCl}_3 + 3 \, \text{CHO} + 3 \, \text{H}_2 \text{O} \rightarrow 2 \, \text{Au} + 3 \, \text{HCOOH} + 6 \, \text{HCl} \]
2.0 g of activated charcoal is added to 100 mL of 0.5 M acetic acid (molar mass 60 g mol\(^{-1}\)), shaken well and filtered. The concentration of solution is reduced to 0.4 M. How many grams of acetic acid is adsorbed on charcoal per gram?
Match the following