List of top Mathematics Questions asked in IPU CET

If the arithmetic mean of the following data is 7, then \( a + b = \) \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 4 & 6 & 7 & 9 \\ f_i & a & 4 & b & 5 \\ \hline \end{array} \]

Choose the most appropriate option. If \(y = a^b x\), then

In how many ways can 3 blue, 4 white and 2 red balls be distributed into 4 distinct boxes?

Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]

Choose the most appropriate option. \(\lim_{x \to 1} x^{(1-x)}\) is equal to:

Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]

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,

Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]

In how many ways can 10 identical objects be put in 8 distinct boxes in such that no box is empty?

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?

Solve for $x \ (a \neq 0)$ $$ \sqrt{(a + x)^2 + 4\sqrt{(a - x)^2}} = 5\sqrt{a^2 - x^2} $$

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 \( S \)?

In how many ways can 5 men and 3 women be seated in a row such that no two women sit adjacent?

\[ \left| \begin{matrix} x+1 & x+2 & x+4 \\ x+3 & x+5 & x+8 \\ x+7 & x+10 & x+14 \end{matrix} \right| \]