List of top Mathematics Questions

The line which passes through the origin and intersects the two lines \[ \frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z - 14}{4} \] is
The condition that the line \( \frac{x}{p} + \frac{y}{q} = 1 \) be normal to the parabola \( y^2 = 4ax \) is
If \( x = -\frac{7}{3} \), then \( x^4 \) is
A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is \( x \) and the probability that B will speak the truth is \( y \). A and B agree in a certain statement. The probability that the statement is true is
A and B are events such that \( P(A \cup B) = 3/4 \), \( P(A) = 1/4 \), and \( P(A \cap B) = 2/3 \). Then the probability that \( P(A \cap B) \) is
The difference between greatest and least value of \[ f(x) = 2 \sin x + \sin 2x, \, x \in \left[ 0, \frac{3\pi}{2} \right] \] is
\[ \int \left[ f'(x) \left( g(x) \right)^2 \right] dx \] is equal to:
Let A be the centre of the circle \( x^2 + y^2 - 2x - 4y - 20 = 0 \), and B(1, 7) and D(4, -2) are points on the circle then, if tangents are drawn at B and D, which meet at C, then area of quadrilateral ABCD is
The value of \( x \) obtained from the equation \[ \frac{x + \alpha}{\gamma} = \frac{x + \beta}{\alpha} = \frac{x + \gamma}{\beta} \] will be
The solution of the differential equation \[ \log x \frac{dy}{dx} + x = \sin 2x \] is
The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is
\[ \lim_{x \to \infty} \frac{x^2}{3x - 3} = ? \]
If \( \vec{a} \times \vec{b} \) and \( \vec{c} \times \vec{d} \) are perpendicular, then which of the following is always true?
The area bounded by \( y = |x| \), \( y = 0 \) and \( |x| = \frac{1}{2} \) will be:
Value of \[ \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sin x + \cos x} \, dx \]
The acceleration of a sphere falling through a liquid is \( (30 - 3y) \, \text{cm/s}^2 \) where \( y \) is speed in cm/s. The maximum possible velocity of the sphere and the time when it is achieved are
The function \( f(x) = \sin x - kx - c \), where \( k \) and \( c \) are constants, decreases always when
Negation of the proposition: If we control population growth, we prosper is
The equation \( z^2 + (2 - 3i)z + (2 + 3i) = 4 = 0 \) represents a circle of radius
Equation \( \frac{1}{8} \sin^3 x = \cos 6x \) represents
A value of \( c \) for which conclusion of Mean Value Theorem holds for the function \( f(x) = \log x \) on the interval [1, 3] is
A straight line parallel to the line \( 2x + y - 5 = 0 \) is also a tangent to the curve \( y^2 = 4x + 5 \). Then the point of contact is
\( \sin\left( \sin 5 \right) = x^2 - 4x \) holds if
If '' > 0$ for all $

Let \(f(x)=x+log_{e}​x−xlog_{e}​x,\text{ }x∈(0,∞)\).

  • Column 1 contains information about zeros of \(f(x)\), \(f'(x)\) and \(f''(x)\).
  • Column 2 contains information about the limiting behavior of \(f(x)\), \(f'(x)\) and \(f''(x)\) at infinity.
  • Column 3 contains information about increasing/decreasing nature of \(f(x)\) and \(f'(x)\).