Let f be a real valued continuous function on [0, 1] and $f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $.

Then, which of the following points (x, y) lies on the curve y = f(x) ?

1

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $-$ 1) $-$ arg(z + 1) = ${…

Topic: JEE Main 2022 (29 June Evening Shift)

2

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $-$ 1) $-$ arg(z + 1) = ${…

Topic: JEE Main 2022 (29 June Evening Shift)

3

Let $\alpha$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $\alpha$1011 + $\alpha$2022 $-$ $\alpha$3033…

Topic: JEE Main 2022 (29 June Evening Shift)

1

If $\int\limits_0^2 {\left( {\sqrt {2x} - \sqrt {2x - {x^2}} } \right)dx = \int\limits_0^1 {\left( {1 - \sqrt {1 - {y^…

Topic: JEE Main 2022 (29 June Evening Shift)

2

If y = y(x) is the solution of the differential equation $\left( {1 + {e^{2x}}} \right){{dy} \over {dx}} + 2\left( {1 +…

Topic: JEE Main 2022 (29 June Evening Shift)

3

Let a triangle ABC be inscribed in the circle ${x^2} - \sqrt 2 (x + y) + {y^2} = 0$ such that $\angle BAC = {\pi \over…

Topic: JEE Main 2022 (29 June Evening Shift)

4

The distance of the origin from the centroid of the triangle whose two sides have the equations $x - 2y + 1 = 0$ and $2…

Topic: JEE Main 2022 (29 June Evening Shift)

5

$ \text{Let A, B, C be three points whose position vectors respectively are } \vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}, …

Topic: JEE Main 2022 (29 June Evening Shift)

6

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :

Topic: JEE Main 2022 (29 June Evening Shift)

7

The number of values of a $\in$ N such that the variance of 3, 7, 12, a, 43 $-$ a is a natural number is :

Topic: JEE Main 2022 (29 June Evening Shift)