List of top Mathematics Questions

Find the absolute maximum and minimum values of the function: \[ f(x) = 12x^{4/3} - 6x^{1/3}, \quad x \in [0, 1]. \]
(a) If \( y = \sqrt{\cos x + y} \), prove that \[ \frac{dy}{dx} = \frac{\sin x}{1 - 2y}. \]
(b) Show that the function \( f(x) = |x|^3 \) is differentiable at all points of its domain.
If \( \vec{a} \) and \( \vec{b} \) are two non-zero vectors such that \( (\vec{a} + \vec{b}) \perp \vec{a \) and \( (2\vec{a} + \vec{b}) \perp \vec{b} \), then prove that \( |\vec{b}| = \sqrt{2} |\vec{a}| \).}
The number of points, where \( f(x) = \lfloor x \rfloor \), \( 0 < x < 3 \) (\(\lfloor \cdot \rfloor\) denotes the greatest integer function), is not differentiable is:
Let \( f(x) \) be a continuous function on \([a, b]\) and differentiable on \((a, b)\). Then, this function \( f(x) \) is strictly increasing in \((a, b)\) if:
The distance of the point \( P(a, b, c) \) from the y-axis is:
The number of corner points of the feasible region determined by the constraints \( x \geq 0, y \geq 0, x + y \geq 4 \) is:
The vector with terminal point \( A(2, -3, 5) \) and initial point \( B(3, -4, 7) \) is:
The derivative of \( \sin(x^2) \) w.r.t. \( x \), at \( x = \sqrt{\pi} \), is:
A linear programming problem deals with the optimization of a/an:
The order and degree of the differential equation: \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^3 = \frac{d^2y}{dx^2}, \] respectively, are:
If \( P(A \mid B) = P(A' \mid B) \), then which of the following statements is true?
The integrating factor of the differential equation \( x \frac{dy}{dx} - y = x^4 - 3x \) is:
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
Let \( \theta \) be the angle between two unit vectors \( \hat{a} \) and \( \hat{b} \) such that \( \sin \theta = \frac{3}{5} \).
Then, \( \hat{a} \cdot \hat{b} \) is equal to:
\( \int_a^b f(x) \, dx \) is equal to:
Let \( \theta \) be the angle between two unit vectors \( \mathbf{\hat{a}} \) and \( \mathbf{\hat{b}} \) such that \( \sin \theta = \frac{3}{5} \). Then, \( \mathbf{\hat{a}} \cdot \mathbf{\hat{b}} \) is equal to:
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
A linear programming problem deals with the optimization of a/an:
The determinant \(\begin{vmatrix} x+1 & x-1 \\ x^2+x+1 & x^2-x+1 \end{vmatrix}\) is equal to:
The derivative of \( \sin(x^2) \) w.r.t. \( x \), at \( x = \sqrt{\pi} \), is:
The order and degree of the differential equation: \[ \left[ 1 + \left(\frac{dy}{dx}\right)^2 \right]^3 = \frac{d^2y}{dx^2} \] respectively are:
The vector with terminal point \( A(2, -3, 5) \) and initial point \( B(3, -4, 7) \) is:
The distance of point P(a, b, c) from the y-axis is: