NTA JEE Main 8th April 2019 Shift 1

The sum of the solutions of the equation $$\left|\sqrt{x}-2\left|+\sqrt{x}\left(\sqrt{x}-4\right)+2=0\right|\right|$$, $$x > 0$$ is equal to:

If $$\alpha$$ and $$\beta$$ be the roots of the equation $$x^{2} - 2x + 2 = 0$$, then the least value of $$n$$ for which $$\left(\frac{\alpha}{\beta}\right)^{n} = 1$$ is:

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:

The sum of all natural numbers $$n$$ such that $$100 < n < 200$$ and H.C.F. $$(91, n) > 1$$ is:

The sum of the co-efficient of all even degree terms in $$x$$ in the expansion of $$\left(x + \sqrt{x^{3} - 1}\right)^{6} + \left(x - \sqrt{x^{3} - 1}\right)^{6}$$, $$x \gt 1$$ is equal to:

The sum of the series $$2 \cdot {}^{20}C_0 + 5 \cdot {}^{20}C_1 + 8 \cdot {}^{20}C_2 + 11 \cdot {}^{20}C_3 + \ldots + 62 \cdot {}^{20}C_{20}$$ is equal to:

If $$\cos\alpha + \beta = \frac{3}{5}$$, $$\sin(\alpha - \beta) = \frac{5}{13}$$ and $$0 < \alpha, \beta < \frac{\pi}{4}$$, then $$\tan 2\alpha$$ is equal to:

A point on the straight line, $$3x + 5y = 15$$ which is equidistant from the coordinate axes will lie only in:

The sum of the squares of the lengths of the chords intercepted on the circle, $$x^{2} + y^{2} = 16$$, by the lines, $$x + y = n$$, $$n \in N$$, where N is the set of all natural numbers is:

Let $$O(0,0)$$ and $$A(0,1)$$ be two fixed points. Then, the locus of a point P such that the perimeter of $$\triangle AOP$$ is 4 is: