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

Compute the determinant of the \(n \times n\) matrix whose elements are identified by the condition \(a_{ij} = \min(i,j)\), where \(i\) is the row number and \(j\) is the column number.
The standard deviation of a data is 6, when each observation is increased by 1, then the standard deviation of the new data is
The determinant of the matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \] is equal to
If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^{10} \theta + \csc^{10} \theta \) is
Find the distance from the point \( A(2, 3, -1) \) to the given straight lines \( 2x - 2y + z + 3 = 0 \) and \( 3x - 2y + 2z + 17 = 0 \).
Choose the most appropriate options. If \(a, b, c\) are positive real numbers, then \[ \frac{1}{\log_{abc}} + \frac{1}{\log_{abc}} + \frac{1}{\log_{abc}} = \]
\( 8 \cos^4 x - 8 \cos^2 x + 1 \) is equal to
Choose the most appropriate options. Let \( P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} \) and \( Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} \). Then,
Determine the form of the conic section described by the equation \( x^2 + y^2 + 2xy - 8x + 8y = 0 \)
The line \( y = mx + C \) will be tangent to the ellipse \( \frac{x^2}{9} + \frac{y^2}{4} = 1 \) if \( C \) is equal to
The series \( 1 + 1 + \frac{3}{2^2} + \frac{4}{2^3} + \frac{5}{2^4} + \cdots \) is equal to
If A and B are independent events such that \( P(B) = \frac{2}{7} \), \( P(A \cup B) = 0.8 \), then \( P(A) = \)?
Six ants simultaneously stand on the six vertices of a regular octahedron with each ant at a different vertex. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. What is the probability that no two ants arrive at the same vertex?
The value of the integral \( \int_{-3}^{5} |x - 3| \, dx \) is
Let \( S \) be the set of all points with coordinates \( (x, y, z) \), where \( x, y, z \) are each chosen from the set \([0, 1, 2]\). How many equilateral triangles have all their vertices in \( S \)?
Choose the most appropriate option. If \(y = a^b x\), then
Is equal to \[ \left| \begin{matrix} b^2 + c^2 & c^2 + b^2 \\ c^2 & c^2 + a^2 \\ b^2 & a^2 + b^2 \end{matrix} \right| \]
In a class, there are 10 boys and 8 girls. When 3 students are selected at random, the probability that 2 girls and 1 boy are selected, is
\[ \left| \begin{matrix} x+1 & x+2 & x+4 \\ x+3 & x+5 & x+8 \\ x+7 & x+10 & x+14 \end{matrix} \right| \]
Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]
In how many ways can 5 men and 3 women be seated in a row such that no two women sit adjacent?

If \( \alpha \) and \( \beta \) are non-real numbers satisfying \( x^3 - 1 = 0 \), then the value of \[ \left| \begin{matrix} \lambda+1 & \alpha & \beta \\ \beta & \lambda + \beta & 1 \\ 1 & \lambda + \alpha & \lambda + \alpha \end{matrix} \right| \] is:

In how many ways can 3 blue, 4 white and 2 red balls be distributed into 4 distinct boxes?
Choose the most appropriate option. \(\lim_{x \to 1} x^{(1-x)}\) is equal to:
In how many ways can 10 identical objects be put in 8 distinct boxes in such that no box is empty?