The numbers of pairs (a, b) of real numbers, such that whenever $\alpha$ is a root of the equation x² + ax + b = 0, $\alpha$² $-$ 2 is also a root of this equation, is :

1

The distance of line $3y - 2z - 1 = 0 = 3x - z + 4$ from the point (2, $-$1, 6) is :

Topic: JEE Main 2021 (1 September Evening Shift)

2

The area, enclosed by the curves $y = \sin x + \cos x$ and $y = \left| {\cos x - \sin x} \right|$ and the lines $x = 0,…

Topic: JEE Main 2021 (1 September Evening Shift)

3

Let ${J_{n,m}} = \int\limits_0^{{1 \over 2}} {{{{x^n}} \over {{x^m} - 1}}dx} $, $\forall$ n > m and n, m $\in$$ N. C…

Topic: JEE Main 2021 (1 September Evening Shift)

4

The function $f(x) = {x^3} - 6{x^2} + ax + b$ is such that $f(2) = f(4) = 0$. Consider two statements : Statement 1 : t…

Topic: JEE Main 2021 (1 September Evening Shift)

5

If y = y(x) is the solution curve of the differential equation ${x^2}dy + \left( {y - {1 \over x}} \right)dx = 0$ ; x &…

Topic: JEE Main 2021 (1 September Evening Shift)

6

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Topic: JEE Main 2021 (1 September Evening Shift)

7

Consider the system of linear equations$-$x + y + 2z = 0 3x $-$ ay + 5z = 12x, $-$ 2y $-$ az = 7, Let S1 be the set of…

Topic: JEE Main 2021 (1 September Evening Shift)

8

${\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12))$ is equal to : (The inverse trigono…

Topic: JEE Main 2021 (1 September Evening Shift)

9

Let f : R $\to$ R be a continuous function. Then $\mathop {\lim }\limits_{x \to {\pi \over 4}} {{{\pi \over 4}\int\li…

Topic: JEE Main 2021 (1 September Evening Shift)

1

Let P1, P2, ......, P15 be 15 points on a circle. The number of distinct triangles formed by points Pi, Pj, Pk such tha…

Topic: JEE Main 2021 (1 September Evening Shift)

2

The range of the function,$f(x) = {\log _{\sqrt 5 }}\left( {3 + \cos \left( {{{3\pi } \over 4} + x} \right) + \cos \lef…

Topic: JEE Main 2021 (1 September Evening Shift)

3

Let a1, a2, ..........., a21 be an AP such that $\sum\limits_{n = 1}^{20} {{1 \over {{a_n}{a_{n + 1}}}} = {4 \over 9}} …

Topic: JEE Main 2021 (1 September Evening Shift)

4

The function f(x), that satisfies the condition $f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $, is :

Topic: JEE Main 2021 (1 September Evening Shift)