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

Negation of the statement (ρ∧r)→(r∨q) (\rho \land r) \rightarrow (r \lor q) is
Evaluate the limit: lim⁡x→alog⁡(xa−1)x−a \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a}
Find the limit lim⁡x→0(1+tan⁡2x)3/x \lim_{x \to 0} \left( 1 + \tan^2 \sqrt{x} \right)^{3/x}
Find the area of the figure bounded by the parabola y2=4x y^2 = 4x and x2=4y x^2 = 4y .
The value of ∫0π2excos⁡x dx \int_0^{\frac{\pi}{2}} e^x \cos x \, dx is equal to:
Choose the most appropriate options. Let P={θ:sin⁡θ−cos⁡θ=2cos⁡θ} P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} and Q={θ:sin⁡θ+cos⁡θ=2sin⁡θ} Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} . Then,
The series 1+1+322+423+524+⋯ 1 + 1 + \frac{3}{2^2} + \frac{4}{2^3} + \frac{5}{2^4} + \cdots is equal to
The value of the integral ∫−35∣x−3∣ dx \int_{-3}^{5} |x - 3| \, dx is
Choose the most appropriate option. ∫−223x7−2x5+x3−3x4+3x2+1 dx \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx