NTA JEE Main 8 April 2018 Offline

Two sets A and B are as under: $$A = \{(a, b) \in R \times R : |a - 5| < 1$$ and $$|b - 5| < 1\}$$; $$B = \{(a, b) \in R \times R : 4(a - 6)^2 + 9(b - 5)^2 \leq 36\}$$. Then:

Tangents are drawn to the hyperbola $$4x^2 - y^2 = 36$$ at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $$\triangle PTQ$$ is:

For each $$t \in R$$, let $$[t]$$ be the greatest integer less than or equal to t. Then $$\lim_{x \to 0^+} x\left(\left[\frac{1}{x}\right] + \left[\frac{2}{x}\right] + \ldots + \left[\frac{15}{x}\right]\right)$$

The Boolean expression $$\sim(p \vee q) \vee (\sim p \wedge q)$$ is equivalent to:

If $$\sum_{i=1}^{9}(x_i - 5) = 9$$ and $$\sum_{i=1}^{9}(x_i - 5)^2 = 45$$, then the standard deviation of the 9 items $$x_1, x_2, \ldots, x_9$$ is:

PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45$$^\circ$$, 30$$^\circ$$ and 30$$^\circ$$, then the height of the tower (in m) is:

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is:

If the system of linear equations
$$x + ky + 3z = 0$$
$$3x + ky - 2z = 0$$
$$2x + 4y - 3z = 0$$
has a non-zero solution (x, y, z), then $$\frac{xz}{y^2}$$ is equal to:

If $$\begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix} = (A + Bx)(x - A)^2$$, then the ordered pair (A, B) is equal to:

Let $$S = \{t \in R : f(x) = |x - \pi| \cdot (e^{|x|} - 1)\sin|x|$$ is not differentiable at $$t\}$$. Then the set S is equal to: