List of practice Questions

The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:
The number of nonzero terms in the expansion of \[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \] is:
The particular solution of \[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \] is:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:
The sum of the series \[ \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots \] up to 15 terms is:
The angle between the two lines: \[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \] is:
The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:
The argument of the complex number \[ \left( \frac{i}{2} - \frac{2}{i} \right) \] is equal to:
The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is:
The derivative of \[ \sin^{-1} \left(\frac{2x}{1 + x^2} \right) \] with respect to \[ \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) \] is equal to:

The determinant of the matrix:

is:

The domain of the function \[ f(x) = \frac{1}{\sqrt{9 - x^2}} \] is:
Negation of the Boolean expression \[ p \Leftrightarrow (q \Rightarrow p) \] is:
The equation of the circle with centre (0,2) and radius 2 is \[ x^2 + y^2 - my = 0. \] The value of \( m \) is:
The general solution of the differential equation given by: \[ \tan^{-1} x + \tan^{-1} y = c \]
If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:
If the vertex of a parabola is \( (2, -1) \) and the equation of its directrix is \[ 4x - 3y = 21, \] then the length of its latus rectum is:
In a certain coding system, if 2 = 5, 4=18, 6=39 then 10 = ?
Arrange the following in increasing order of ionic radii: \( C^{4-}, N^{3-}, F^{-}, O^{2-} \).
2-Pentene contains:

Choose the correct option for the following reactions. 
 

Cuprous ion is colourless while cupric ion is coloured because:

For the below-given cyclic hemiacetal (X), the correct pyranose structure is: 
 

\( P_A \) and \( P_B \) are the vapor pressures of pure liquid components A and B, respectively, in an ideal binary solution. If \( X_A \) represents the mole fraction of component A, the total pressure of the solution will be: