List of practice Questions

If \( f(x) = \frac{x}{\sqrt{1 + x^2}} \), then \( (f \circ f)(x) \) is:

Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?

If \( \sec^2 \theta = \frac{4}{3} \), then the general value of \( \theta \) is:

If the coordinates of the points A and B are (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is:

A circle touches both the y-axis and the line \( x + y = 0 \). Then the locus of its center is:

An object moves with speed \( v_1 \), \( v_2 \), and \( v_3 \) along a line segment \( AB \), \( BC \), and \( CD \) respectively as shown in the figure. Where \( AB = BC \) and \( AD = 3 AB \), then the average speed of the object will be:

If one root of the equation \( x^2 + px + 12 = 0 \) is \( 4 \), while the equation \( x^2 + px + q = 0 \) has equal roots, then the value of \( q \) is:

If the sum of an infinite GP \( a, ar, ar^2, ar^3, \dots \) is 15 and the sum of the squares of each term is 150, then the sum of the series \( ar^2, a r^4, ar^6, \dots \) is:

If \[ A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix} \] and \[ kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}, \] then the values of \( k \), \( a \), and \( b \) respectively are:

If \( \int \frac{e^x (1 + \sin x)}{1 + \cos x} \, dx = e^x f(x) + C \), then \( f(x) \) is equal to:

Amar is 16^th from the left end in a row of boys and Vishal is 18^th from the right end. Satish is 11th towards the right of Amar and 3^rd towards the right of Vishal side end. How many boys are there is a row?

Electrode potential data are given below: \[ {Fe}^{3+}({aq}) + e^- \rightarrow {Fe}^{2+}({aq}); E^\circ = +0.77 \, {V} \] \[ {Al}^{3+}({aq}) + 3e^- \rightarrow {Al}({s}); E^\circ = -1.66 \, {V} \] \[ {Br}_2({aq}) + 2e^- \rightarrow 2{Br}^-({aq}); E^\circ = +1.08 \, {V} \] Based on the data, the reducing power of \( {Fe}^{2+} \), Al, and \( {Br}^- \) will increase in the order:

Element with electronic configuration \( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^3 \) belongs to the following group of the periodic table:

Following question is based on the information given below:
(i) 'R×S' means 'R is father of S'
(ii) 'R-S' means 'R is sister of S'
(iii) 'R+S' means 'R is mother of S'
(iv) 'R÷S' means 'R is brother of S'
In the expression A+B×C÷D how is C related to A ?

The interval in which the function \( f(x) = 4x^2 + x \) is decreasing is:

What is the angle between the two straight lines \( y = (2 - \sqrt{3})x + 5 \) and \( y = (2 + \sqrt{3})x - 7 \)?

The lines \[ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-k} \] and \[ \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1} \] are coplanar if:

The magnetic moment of an electron (e) revolving in an orbit around the nucleus with an orbital angular momentum is given by:

The maximum value of \( z = 5x + 2y \) subject to the constraints: \[ x + y \leq 7, \quad x + 2y \leq 10, \quad x, y \geq 0 \]

The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10} \) is:

Pick a word that means the same as 'readable' :

Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows the Arrhenius equation is:

The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is: