NTA JEE Main 16 th April 2018 Online

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is $$\frac{3}{2}$$ units, then its eccentricity is:

$$\lim_{x \to 0} \frac{(27+x)^{\frac{1}{3}} - 3}{9 - (27+x)^{\frac{2}{3}}}$$ equals:

If $$p \to (\sim p \vee \sim q)$$ is false, then the truth values of p and q are, respectively:

The mean and the standard deviation (S.D.) of five observations are 9 and 0, respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10, then their S.D. is:

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from 30$$^\circ$$ to 45$$^\circ$$, then the time taken (in min) by the car to reach the foot of the tower is:

Let N denote the set of all natural numbers. Define two binary relations on N as $$R_1 = \{(x, y) \in N \times N : 2x + y = 10\}$$ and $$R_2 = \{(x, y) \in N \times N : x + 2y = 10\}$$. Then:

Let $$A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$$ and $$B = A^{20}$$. Then the sum of the elements of the first column of B is:

The number of values of k for which the system of linear equations $$(k+2)x + 10y = k$$ and $$kx + (k+3)y = k - 1$$ has no solution is:

If the function f defined as $$f(x) = \frac{1}{x} - \frac{k-1}{e^{2x} - 1}$$, $$x \neq 0$$ is continuous at $$x = 0$$, then ordered pair (k, f(0)) is equal to: 

If $$x = \sqrt{2^{\text{cosec}^{-1}t}}$$ and $$y = \sqrt{2^{\text{sec}^{-1}t}}$$, ($$|t| \geq 1$$), then $$\frac{dy}{dx}$$ is equal to: