List of top Mathematics Questions asked in Guru Gobind Singh Indraprastha University Common Entrance Test

The value of \( \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx \) is
It is known that \( AB = 2a - 6b \) and \( AC = 3a + b \), where \( a \) and \( b \) are mutually perpendicular unit vectors. Determine the angles of the AABC.
Given the vertices of a triangle are \( A(1, -1, -3) \), \( B(2, 1, -2) \), and \( C(-5, 2, -6) \). Compute the length of the bisector of the interior angle at vertex A.
Negation of the statement \( (\rho \land r) \rightarrow (r \lor q) \) is
Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]
For real \( x \), let \( f(x) = x^3 + 5x + 1 \), then:
Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]
Find the limit \[ \lim_{x \to 0} \left( 1 + \tan^2 \sqrt{x} \right)^{3/x} \]
If the line \( x - 1 = 0 \) is the directrix of the parabola \( y^2 - kx + 8 = 0 \), then one of the values of \( k \) is
Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?
A line segment with the end points \( A(3,-2) \) and \( B(6,4) \) is divided into three equal parts. Find the coordinates of the division points.
If \( \tan \frac{\pi}{18}, x \) and \( \tan \frac{\pi}{18} \) are in AP and \( \tan \frac{5\pi}{18} \) are in AP, then the value of \( \frac{x}{y} \) will be
Let \( n \) be a 5-digit number and let \( q \) and \( r \) be the quotient and remainder respectively, when \( n \) is divided by 100. For how many values of \( n \) is \( q + r \) divisible by 11?
Let \( f(x) = x^2 + 6x + 1 \) and let \( R \) denote the set of points \( (x, y) \) in the coordinate plane such that \( f(x) + f(y) \) so and \( f(x) - f(y) \leq 0 \). Which of the following is closest to the area of \( R \)?
The exradii of a triangle \( r_1, r_2, r_3 \) are in harmonic progression, then the sides \( a, b \) and \( c \) are in
Consider sequences of positive real numbers of the form \( x, 2000, y, \dots \), in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of \( x \) does the term 2001 appear somewhere in the sequence?
The eccentricity of the hyperbola \( \frac{\sqrt{1999}}{3} \left( x^2 - y^2 \right) = 1 \) is
Find the area of the figure bounded by the parabola \( y^2 = 4x \) and \( x^2 = 4y \).
The value of \( \int_0^{\frac{\pi}{2}} e^x \cos x \, dx \) is equal to:
Solve for \( x \left( a \neq 0 \right) \) \[ \sqrt{(a + x)^2 + 4\sqrt{(a - x)^2}} = 5\sqrt{a^2 - x^2} \]
The integral \( \int e^{\sec x} \tan x \sec x \, dx \) is equal to
The integral \( \int 34x^4 dx \) is equal to
If the arithmetic mean of the following data is 7, then \( a + b = \) \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 4 & 6 & 7 & 9 \\ f_i & a & 4 & b & 5 \\ \hline \end{array} \]
Find \( \frac{dy}{dx} \) where \( a^y = \left( \frac{x}{y} \right)^a \)
Let \( T_n \) denote the number of triangles which can be formed using the vertices of a regular polygon of \( n \) sides. If \( T_{n+1} - T_n = 21 \), then \( n \) equals