NTA JEE Main 15th April 2018 Shift 2

If $$|z - 3 + 2i| \leq 4$$ then the difference between the greatest value and the least value of $$|z|$$ is:

The number of four letter words that can be formed using the letters of the word BARRACK is:

Let $$A_n = \left(\frac{3}{4}\right) - \left(\frac{3}{4}\right)^2 + \left(\frac{3}{4}\right)^3 - \ldots + (-1)^{n-1}\left(\frac{3}{4}\right)^n$$ and $$B_n = 1 - A_n$$. Then, the least odd natural number p, so that $$B_n > A_n$$, for all $$n \geq p$$ is:

If a, b, c are in A.P. and $$a^2, b^2, c^2$$ are in G.P. such that $$a < b < c$$ and $$a + b + c = \frac{3}{4}$$, then the value of a is:

The coefficient of $$x^{10}$$ in the expansion of $$(1+x)^2(1+x^2)^3(1+x^3)^4$$ is equal to:

The number of solutions of $$\sin 3x = \cos 2x$$, in the interval $$\left(\frac{\pi}{2}, \pi\right)$$ is:

Consider the following two statements.
Statement p: The value of $$\sin 120^\circ$$ can be divided by taking $$\theta = 240^\circ$$ in the equation $$2\sin\frac{\theta}{2} = \sqrt{1 + \sin\theta} - \sqrt{1 - \sin\theta}$$.
Statement q: The angles A, B, C and D of any quadrilateral ABCD satisfy the equation $$\cos\left(\frac{1}{2}(A+C)\right) + \cos\left(\frac{1}{2}(B+D)\right) = 0$$.
Then the truth values of p and q are respectively:

The foot of the perpendicular drawn from the origin, on the line, $$3x + y = \lambda(\lambda \neq 0)$$ is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is:

The sides of a rhombus ABCD are parallel to the lines, $$x - y + 2 = 0$$ and $$7x - y + 3 = 0$$. If the diagonals of the rhombus intersect at P(1, 2) and the vertex A (different from the origin) is on the y axis, then the ordinate of A is:

The tangent to the circle $$C_1: x^2 + y^2 - 2x - 1 = 0$$ at the point (2, 1) cuts off a chord of length 4 from a circle $$C_2$$ whose centre is (3, -2). The radius of $$C_2$$ is: