List of practice Questions

You are asked to copy this letter word by word:

Let us quickly:

Florid means:

Verity means:

Perspicuity means:

In a triangle ABC, if \( A = a \), \( B = 60^\circ \), and \( C = 75^\circ \), then \( b \) equals:

Prabhat wants to invest the total amount of ₹15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least ₹2,000 in saving certificates and ₹2,500 in national saving bonds. The interest rate is 8% on saving certificates and 10% on national saving bonds per annum. He invests \( x \) in saving certificate and \( y \) in national saving bonds. Then the objective function for this problem is:

For the function \[ f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} - x^2 + x + 1, \] \( f'(1) = mf'(0) \), where \( m \) is equal to:

If the line \( x \cos \alpha + y \sin \alpha = p \) represents the common chord of the circles \( x^2 + y^2 = a^2 \) and \( x^2 + y^2 + b^2 = 2b \), where \( a > b \), where A and B lie on the first circle and P and Q lie on the second circle, then \( AP \) is equal to:

Let \( a_1, a_2, a_3, \dots \) be terms on A.P. If \[ a_1 + a_2 + \dots + a_p = p^2, \, p \neq q, \, \text{then} \, a_q = \frac{p^2}{q^2} \] Then \( a_q \) equals:

If \( \mathbf{a} = \mathbf{c} \) and \( \mathbf{b} = \mathbf{a} \times \mathbf{c} \), then the correct statement is:

What is the value of \( n \) so that the angle between the lines having direction ratios \( (1, 1, 1) \) and \( (1, 1, n) \) is \( 60^\circ \)?

The foot of the perpendicular from the point \( (7, 14, 5) \) to the plane \( 2x + 4y - z = 7 \) is:

Find the coordinates of the point where the line joining the points \( (2, -3, 1) \) and \( (3, -4, -5) \) cuts the plane \( 2x + y + z = 7 \):

A boy is throwing stones at a target. The probability of hitting the target at any trial is \( \frac{1}{2} \). The probability of hitting the target 5th time at the 10th throw is:

Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is:

Evaluate: \[ \int_0^{\pi/2} \frac{x}{\sqrt{4 - x^2}} \, dx \]

The area bounded by the curve \( y = \sin x \), x-axis and the ordinates \( x = 0 \) and \( x = \pi/2 \) is:

The differential equation whose solution is \( Ax^2 + Bx + C = 1 \) where A and B are arbitrary constants is of:

The unit vector perpendicular to the vectors \( 6i + 2j + 3k \) and \( 3i - 6j - 2k \) is:

If \( x = a \sin \theta \) and \( y = b \cos \theta \), then \( \frac{d^2y}{dx^2} \) is:

If \( f(x) = x^\alpha \log x \) and \( f(0) = 0 \), then the value of \( \alpha \) for which Rolle's theorem can be applied in \( [0, 1] \) is:

If the function \( f(x) = ax + b \), \( 2 < x < 4 \), is continuous at \( x = 2 \) and 4, then the values of \( a \) and \( b \) are:

If \( f(x) = a^2 - 1 \), \( x^3 - 3x + 5 \) is a decreasing function of \( x \in R \), then the set of possible values of \( a \) (independent of \( x \)) is:

The diagonal of a square is changing at the rate of \( 0.5 \, \text{cm/sec} \). Then the rate of change of area, when the area is 400 \( \text{cm}^2 \), is equal to: