List of top Mathematics Questions

The value of \( x \) in the interval \( [4, 9] \) at which the function \[ f(x) = \sqrt{x} \] \text{satisfies the mean value theorem is:}

If the second term in the expansion \[ \left( \frac{3}{\sqrt{4a + \sqrt{a}}} \right)^n \] \text{is} \( 14a^{5/2} \), then \( nC_3 \) is:

The value of the integral \[ \int_1^3 |x| + |x - 1| \, dx \] \text{is:}

Let \( e^{1/c}, e^{b/c}, e^{1/a} \) are in A.P. with a common difference \( d \). Then \( e^{1/c}, e^{b/c}, e^{1/a} \) are in:

The solution of the differential equation \[ \left(1 + x \sqrt{x^2 + y^2}\right) dx + \left( \sqrt{x^2 + y^2} - 1 \right) y dy = 0 \]

The integrating factor of \[ \frac{dy}{dx} - y = x^4 - 3x \] \text{is:}

It is given that the events \( A \) and \( B \) are such that \[ P(A) = \frac{1}{4}, \quad P(A|B) = \frac{1}{2}, \quad P(B|A) = \frac{2}{3}. \] \text{Then \( P(B) \) is:}

Let \( f: \mathbb{R} \to \mathbb{R}, g: \mathbb{R} \to \mathbb{R} \) be two functions such that \[ f(x) = 2x - 3, \quad g(x) = x^3 + 5. \] \text{The function} \( (f \circ g)^{-1}(x) \) is equal to:

The inverse of the statement \[ (p \land \neg q) \to r \] \text{is:}

If \( f(x) = x^3 + bx^2 + cx + d \) and \( 0<b^2<c \), then in \( (-\infty, \infty) \),

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is:

A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90°. What is the maximum area which can be enclosed inside the quadrilateral?

The domain of the function \[ f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}} \] \text{is:}

Value of \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\cot x}} dx \]

The equation of the chord of the hyperbola \( 25x^2 - 16y^2 = 400 \) that is bisected at point \( (5, 3) \) is:

The area under the curve \( y = | \cos x - \sin x | \), where \( 0 \leq x \leq \frac{\pi}{2} \), and the x-axis is:

Evaluate \[ \int \left( 27e^{9x} + e^{12x} \right)^{1/3} dx \]

If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is equal to:

The conic represented by \[ x = 2(\cos t + \sin t), \quad y = 5(\cos t - \sin t) \] \text{is}

The solution of \( \sin x = \frac{-\sqrt{3}}{2} \) is:

Evaluate \( \lim_{x \to 2} \frac{\sqrt{x+7} - 3}{\sqrt{x-3} - 2} \):

At how many points between the interval \( (-\infty, \infty) \) is the function \( f(x) = \sin x \) is not differentiable?

If vector equation of the line \( \frac{x-2}{2} = \frac{2y-5}{-3} = z+1 \), is \[ \mathbf{r} = \left( 2\hat{i} + \frac{5}{2} \hat{j} - k \right) + \lambda \left( 2\hat{i} - \frac{3}{2} \hat{j} + p \hat{k} \right) \] then \( p \) is equal to:

If \( a \), \( b \), and \( c \) are in A.P., then the value of: \[ |x + 1| + |x + 2| + |x + 3| + |x + b| + |x + c| \]

The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm\(^3\)/min, when the radius is 2 cm and the height is 3 cm is: