List of top Mathematics & Statistics Questions

Find the cartesian and vector equations of the line passing through \( A(1, 2, 3) \) and having direction ratios \( 2, 3, 7 \).
Find the \( n \)th order derivative of \( \log x \).
Find the vector equation of the plane passing through points \( A(1, 1, 2) \), \( B(0, 2, 3) \), and \( C(4, 5, 6) \).
Divide the number 20 into two parts such that the sum of their squares is minimum.
Find the vector equation of the plane passing through the point having position vector \( 2\hat{i} + 3\hat{j} + 4\hat{k} \) and perpendicular to the vector \( 2\hat{i} + \hat{j} - 2\hat{k} \).
Find the area of the region bounded by the parabola \( y^2 = 16x \) and its latus rectum.
Evaluate: \( \int \frac{1}{25 - 9x^2} \, dx \)
Evaluate: \( \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{1}{1 - \sin x} \, dx \)
Evaluate: \( \int x^9 \cdot \sec^2(x^{10}) \, dx \).
A line makes angles of measure 45° and 60° with the positive directions of the \( Y \) and \( Z \) axes respectively. Find the angle made by the line with the positive direction of the \( X \)-axis.
Find the general solution of \( \tan^2 \theta = 1 \).
Write the order of the differential equation \[ \sqrt{1 + \left( \frac{dy}{dx} \right)^2} = \left( \frac{d^2y}{dx^2} \right)^{\frac{3}{2}}. \]
Write the unit vector in the opposite direction to \( \vec{u} = 8\hat{i} + 3\hat{j} - \hat{k} \).
Using truth table, prove that the statement patterns \( p \leftrightarrow q \) and \( (p \land q) \lor (\sim p \land \sim q) \) are logically equivalent.
The value of \( \int x^x(1 + \log x) \, dx \) is equal to ...........
The vector equation of the line passing through the point having position vector \( 4\hat{i} - \hat{j} + 2\hat{k} \) and parallel to vector \( -2\hat{i} - \hat{j} + \hat{k} \) is given by .........
Let \( f(1) = 3 \), \( f'(1) = -\frac{1}{3} \), \( g(1) = -4 \), and \( g'(1) = -\frac{8}{3} \). The derivative of \( \sqrt{[f(x)]^2 + [g(x)]^2} \) w.r.t. \( x \) at \( x = 1 \) is ........
The area bounded by the line \( y = x \), X-axis and the lines \( x = -1 \) and \( x = 4 \) is equal to .......... (in square units).
Select and write the correct answer of the following multiple choice type questions:
(i) If \( A = \{1, 2, 3, 4, 5\} \), then which of the following is not true?
Show that: \( \int_0^\pi \log (1 + \tan x) \, dx = \frac{\pi}{8} \log 2 \)
Find the area of region between parabolas \( y^2 = 4ax \) and \( x^2 = 4ay \).
Solve the L.P.P. by graphical method. Minimize \( z = 8x + 10y \) subject to \( 2x + y \geq 7 \), \( 2x + 3y \geq 15 \), \( y \geq 0 \), \( x \geq 0 \).
Using vectors prove that the altitudes of a triangle are concurrent.
Solve the following system of equations by the method of inversion:
\( x - y + z = 4 \)
\( 2x + y - 3z = 0 \)
\( x + y + z = 2 \)
A wire of length 36 meters is bent to form a rectangle. Find its dimensions if the area of the rectangle is maximum.