List of top Questions asked in IPU CET

A die is thrown twice and the sum of the numbers appearing is 6. Then, the conditional probability that the number 4 has appeared at least once is

For \(x>1\), how many roots/solutions of the following equation exist: \[ \log_2\left( \frac{2}{x} \right)\log^2 x + \log^2 x = 1 \]

Choose the most appropriate options.
\[ \int \frac{x^2 - 2}{x \sqrt{x^2 - 1}}\,dx \text{ equal to} \]

\[ \int_0^1 x e^{2x} dx \text{ is equal to} \]

Evaluate $ \int_0^1 x^5 \sqrt{1 - x^3} \, dx $

\[ \lim_{n \to \infty} \left[ 5 - \frac{1}{5} + \frac{1}{25} - \dots + (-1)^{n-1} \cdot \frac{1}{5^n} \right] \]

If \(x = e^y + e^{-y} - x,\, x>0\) then \(\frac{dy}{dx}\) is

Tangents are drawn from the origin to the curve \(y = \sin x\). Then, the point of contact lie on the curve:

What is the value of \(\tan \left(\frac{\pi}{12}\right)?\)

Find the component of the vector \((-1, 2, 0)\) perpendicular to the plane of the vectors \(\mathbf{e}_1 = (1, 0, 1)\) and \(\mathbf{e}_2 = (1, 1, 1)\).

Angles A, B, and C of a triangle \(\Delta ABC\) are in AP and \( b:c = \sqrt{3} : \sqrt{2} \), then angle \( \angle A \) is given by

At what point of the curve \( y^2 = 2x^3 \) is the tangent line perpendicular to the straight line \[ 4x - 3y + 2 = 0? \]

On the sphere \((x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 25\), compute the distance from the point \(M_0\) to the plane \(3x - 4z + 19 = 0\)

Choose the most appropriate option. Solve for \(x>0\)
\[ \log_3\left( \frac{3}{x} \right) + \log_3 x = 1 \]

\[ \lim_{x \to 0} \frac{\sqrt{1+x} - \sqrt{1 - x}}{x} \]

If the expansion of \(\left(x^2 + \frac{2}{x} \right)^n\) has a term independent of \(x\), then \(n\) is

\[ \int_{-1}^1 \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \text{ is equal to} \]