List of top Questions asked in IPU CET- 2016

Choose the most appropriate options.
The period of the function \(f(x) = |\sin x| - |\cos x|\) is

$ \lim_{x \to 0} \frac{a^x - 1}{x} $ is equal to

$\lim_{x \to 0} \frac{\tan^{-1} \left( \frac{-x}{\sqrt{1 - x^2}} \right)}{\ln(1 - x)} =\ ?$

$ (1 + 2i)^6 $ is equal to:

\(\lim_{x \to \infty} \frac{\ln x}{x^n}\) is equal to
What is the number of ordered pairs of real numbers (a, b) such that \[ (a + bi)^{2002} = a - bi \]
If \(P(x)\) is a polynomial such that \[ P(x^2 + 1) = \{P(x)\}^2 + 1 \] then \(P'(0)\) is equal to
Find the component of the vector a = (-1, 2, 0) perpendicular to the plane of the vectors \(\mathbf{e}_1(1, 0, 1)\) and \(\mathbf{e}_2(1, 1, 1)\)
A real solution of the equation \[ \cosh x - 5 \sinh x - 5 = 0 \text{ is} \]
\[ \frac{1}{2 \sin 10^\circ} - 2 \sin 70^\circ \text{ is equal to} \]
Given \(\varepsilon = \cos\left(\frac{2\pi k}{n}\right) + i \sin\left(\frac{2\pi k}{n}\right)\), find the value of \[ \prod_{k=0}^{n-1} \left( \varepsilon^2k - 2\varepsilon k \cos \theta + 1 \right) \]
Find the derivative of \[ y = (1 - x)^m (1 + x)^n \text{ at } x = 0, \text{ where } m, n>0 \]
The straight line \( r = (i - j + k) + \lambda (2i + j - k) \) and the plane \( r \cdot (2i + j - k) = 4 \) are
\[ \int \frac{x^2}{(x \sin x + \cos x)^2} dx \text{ is equal to} \]
\[ \int_{-\pi/2}^{\pi/2} |\sin x| dx \text{ equals to} \]
Which of the following complex numbers is conjugate to its square?
If \(i = \sqrt{-1}\), then \[ \lim_{n \to \infty} \frac{(n + 2i)(3 + 7in)}{(2 - i)(6n^2 + 1)} \] is equal to:
What is the shape of the figure given by the following equations?
What is the equation of the curve traced by point \(M\), if the sum of distances to \(A(-1, -1)\) and \(B(1, 1)\) is constant and equals \(2\sqrt{3}\)?
Choose the most appropriate options.
The value of \({}^{40}C_0 + {}^{40}C_1 + {}^{40}C_2 + \ldots + {}^{40}C_{20}\) is
If \(y = \sec(\tan^{-1} x)\), then \(y\) at \(x = 1\) is equal to term is the sum of two preceding terms. Then, the common ratio of the G.P. is:
Every term of G.P. is positive and also every term is the sum of two preceding terms. Then, the common ratio of the G.P. is
There are 3 true coins and 1 false coin with 'head' on both sides. A coin is chosen at random and tossed 4 times. If 'head' occurs all the 4 times, then the probability that the false coin has been chosen and used is
Let \( a = \cos \theta_1 + i \sin \theta_1 \), \( b = \cos \theta_2 + i \sin \theta_2 \), \( c = \cos \theta_3 + i \sin \theta_3 \) and \( a + b + c = 0 \), then \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = ? \]
If \(y^{\frac{1}{m}} + x^{\frac{1}{m}} = 2x\) then