Let $u = {{2z + i} \over {z - ki}}$, z = x + iy and k > 0. If the curve represented
by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :

1

If $A = \left[ {\matrix{ {\cos \theta } & {i\sin \theta } \cr {i\sin \theta } & {\cos \theta } \cr } } …

Topic: JEE Main 4 September 2020 (Morning)

2

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14,…

Topic: JEE Main 4 September 2020 (Morning)

3

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground.…

Topic: JEE Main 4 September 2020 (Morning)

4

If $\left( {a + \sqrt 2 b\cos x} \right)\left( {a - \sqrt 2 b\cos y} \right) = {a^2} - {b^2}$ where a > b > 0, th…

Topic: JEE Main 4 September 2020 (Morning)

5

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read…

Topic: JEE Main 4 September 2020 (Morning)

1

Let $\alpha $ and $\beta $ be the roots of x2 - 3x + p=0 and $\gamma $ and $\delta $ be the roots of x2 - 6x + q = 0. I…

Topic: JEE Main 4 September 2020 (Morning)

2

Let f be a twice differentiable function on (1, 6). If f(2) = 8, f’(2) = 5, f’(x) $ \ge $ 1 and f''(x) $ \ge $ 4, for a…

Topic: JEE Main 4 September 2020 (Morning)

3

Let $f\left( x \right) = \int {{{\sqrt x } \over {{{\left( {1 + x} \right)}^2}}}dx\left( {x \ge 0} \right)} $. Then f(…

Topic: JEE Main 4 September 2020 (Morning)

4

Let $f(x) = \left| {x - 2} \right|$ and g(x) = f(f(x)), $x \in \left[ {0,4} \right]$. Then $\int\limits_0^3 {\left( {g(…

Topic: JEE Main 4 September 2020 (Morning)

5

The integral $\int {{{\left( {{x \over {x\sin x + \cos x}}} \right)}^2}dx} $ is equal to (where C is a constant of inte…

Topic: JEE Main 4 September 2020 (Morning)

6

Let ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$ (a > b) be a given ellipse, length of whose latus rectum…

Topic: JEE Main 4 September 2020 (Morning)

7

Let y = y(x) be the solution of the differential equation, xy'- y = x2(xcosx + sinx), x > 0. if y ($\pi $) = $\pi $ …

Topic: JEE Main 4 September 2020 (Morning)

8

Let [t] denote the greatest integer $ \le $ t. Then the equation in x, [x]2 + 2[x+2] - 7 = 0 has :

Topic: JEE Main 4 September 2020 (Morning)