NTA JEE Main 12th January 2019 Shift 2

Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If $$\Delta S'BS$$ is a right angled triangle with right angle at B and area ($$\Delta S'BS$$) = 8 sq. units, then the length of a latus rectum of the ellipse is:

$$\lim_{x \to 1^-} \frac{\sqrt{\pi} - \sqrt{2\sin^{-1}x}}{\sqrt{1-x}}$$ is equal to

The expression $$\sim(\sim p \to q)$$ is logically equivalent to

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is:

If the angle of elevation of a cloud from a point P which is 25 m above a lake be $$30°$$ and the angle of depression of reflection of the cloud in the lake from P be $$60°$$, then the height of the cloud (in meters) from the surface of the lake is:

Let Z be the set of integers. If $$A = \{x \in Z : 2^{(x+2)(x^2-5x+6)} = 1\}$$ and $$B = \{x \in Z : -3 < 2x - 1 < 9\}$$, then the number of subsets of the set $$A \times B$$, is:

If $$A = \begin{bmatrix} 1 & \sin\theta & 1 \\ -\sin\theta & 1 & \sin\theta \\ -1 & -\sin\theta & 1 \end{bmatrix}$$, then for all $$\theta \in \left(\frac{3\pi}{4}, \frac{5\pi}{4}\right)$$, det(A) lies in the interval:

The set of all values of $$\lambda$$ for which the system of linear equations $$x - 2y - 2z = \lambda x$$, $$x + 2y + z = \lambda y$$, $$-x - y = \lambda z$$ has a non-trivial solution:

Let f be a differentiable function such that $$f(1) = 2$$ and $$f'(x) = f(x)$$ for all $$x \in R$$. If $$h(x) = f(f(x))$$, then $$h'(1)$$ is equal to:

The tangent to the curve $$y = x^2 - 5x + 5$$, parallel to the line $$2y = 4x + 1$$, also passes through the point: