List of top Mathematics Questions

If \[ \Delta_r = \begin{vmatrix} 2r - 1 & mC_r & 1 \\ m^2 - 1 & 2^m & m + 1 \\ \sin^2(m^2) & \sin^2(m) & \sin^2(m + 1) \end{vmatrix}, \] then the value of \[ \sum_{r=0}^{m} \Delta_r \text{ is:} \]

Let \( f'(x) \) be differentiable for all \( x \). If \( f(1) = -2 \) and \[ f'(x) \geq 2 \quad \forall x \in [1, 6], \] then:

If \[ \Delta(x) = \begin{vmatrix} 1 & \cos{x} & 1 - \cos{x} \\ 1 + \sin{x} & \cos{x} & 1 + \sin{x} - \cos{x} \\ \sin{x} & \sin{x} & 1 \end{vmatrix}, \] then \[ \int_0^{\frac{\pi}{4}} \Delta(x) \, dx \text{ is equal to:} \]

If there is an error of \( k% \) in measuring the edge of a cube, then the percent error in estimating its volume is:

If \( (m,n) \) is an integer solution of \( \int_1^\infty \left( 1 + y^2 \right) dy \), then the expression for \( (m, n) \) in terms of \( (m+1, n+1) \) is?

If the points \( (1, 2, 3) \) and \( (2, -1, 0) \) lie on the opposite sides of the plane \( 2x + 3y - 2z = k \), then \( k \) is:

If \[ A = \begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}, \] then \( A \cdot \text{(adj A)} \) is equal to:

If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then \( k \) is equal to:

The area in the first quadrant between \( x^2 + y^2 = 4 \) and \( y = \sin x \) is?

The area bounded by \( y = x \) and \( lines |x| = 1 \) is?

The equation of the chord of the hyperbola \( 25x^2 - 16y^2 = 400 \), which is bisected at the point \( (6, 2) \), is?

\( \int_0^\infty \left( \sin x + \left| \sin x \right| \right) dx \) is equal to?

The value of \( \int_0^\infty \left[ \sqrt{x} \right] dx \), where \( \left[ . \right] \) is the greatest integer function, is?

If the area of the triangle on the complex plane formed by the points \( z = x + iy \) and \( z = 1 \) is 200, then the value of \( 3 \times |z| \) must be equal to?

If a plane meets the coordinate axes at \( A, B, C \) such that the centroid of the triangle is \( (1, 2, 4) \), then the equation of the plane is?

The volume of the tetrahedron included between the plane \( 3x + 4y - 5z = 60 \) and the coordinate planes is?

The negation of \( \sim (p \land q) \lor (p \land \sim q) \) is?

The normals at three points P, Q, and R of the parabola \( y^2 = 4ax \) meet at \( (h, k) \). The centroid of the triangle formed by the points P, Q, and R lies on?

The minimum area of the triangle formed by any tangent to the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) with the coordinate axes is?

If the line \( lx + my - n = 0 \) will be a normal to the hyperbola, then \( \frac{a^2}{l^2} + \frac{b^2}{m^2} = k \), where \( k \) is equal to?

If \( \cos \alpha + i \sin \alpha = b \), \( c = \cos \gamma + i \sin \gamma \) and \( b + c + a = 1 \), then \( \cos (\beta - \gamma) + \cos (\alpha - \beta) \) is equal to?

The greatest and the least value of \( z = x + iy \), where \( |z| = 1 \) and \( |x| \leq 3 \), are?

The angle between lines joining the origin to the point of intersection of the line \( \sqrt{3}x + y = 2 \) and the curve \( y^2 = x^3 \) is?

The equation of normal to the curve \( y = (1 + x) + \sin^{-1}(\sin x) \) at \( x = 0 \) is?

The value of from the Lagrange's mean value theorem for which \( f(x) = \sqrt{25 - x^2} \) in the interval \( [1,5] \) is?