List of practice Questions

The solution of the differential equation \( x \frac{dy}{dx} = \cot y \) is
If \( ^nC_3 = 220 \), then \( n = \ ? \)
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is
If \( \sin A + \sin B = a \) and \( \cos A + \cos B = b \), then \( \cos(A + B) \) equals?
What is \( \frac{\cos \theta}{1 - \tan \theta} + \frac{\sin \theta}{1 - \cot \theta} \) equal to?
Find the general solution of \( \sin 2x + \cos x = 0 \).
If \( f(x) + 2f(1 - x) = x^2 + 5 \) for all real values of \( x \), then \( f(x) \) is given by:
Total number of elements in the power set of a set $A$ containing 17 elements is
Evaluate $\left[i^{22} + \left(\dfrac{1}{i}\right)^{25}\right]^3$
There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?
How many numbers greater than 50000 can be formed by using digits 2, 5, 5, 6, 7?
A regular polygon of \( n \) sides has 170 diagonals. Then \( n \) is equal to:
The equation of the pair of angle bisectors of the line \( x^2 - 4xy - 5y^2 = 0 \) is:
The distance of point \( (1, 2) \) from line \( x + y + 2 = 0 \) measured along the line parallel to \( 2x - y = 5 \) is equal to:
The slope of lines which makes an angle \( 45^\circ \) with the line \( 2x - y = -7 \)
If 2 and 3 are intercepts of a line \( L = 0 \), then the distance of \( L \equiv 0 \) from the origin is
KMnO$_4$ acts as an oxidising agent in acidic medium. The number of moles of KMnO$_4$ that will be required to react with one mole of oxalate ions (to form CO$_2$) in acidic solution is:
What can be A and B in the following reaction?
Which of the following is a false statement?
Which of the following molecules does not exhibit dipole moment?
(i) CCl$_4$
(ii) CO$_2$
(iii) NH$_3$
(iv) CHCl$_3$
(v) H$_2$O
(vi) CH$_3$–O–CH$_3$
Which of the following is highly basic?
The relation between work done in reversible and irreversible process is
What is the function of platelets?
The monosaccharides of maltose is
Which of the following does not affect solubility of a gas in liquid?