JEE Main 2021 (Online) 17th March Morning Shift

The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is :

If the equation of the plane passing through the line of intersection of the planes 2x \(-\) 7y + 4z \(-\) 3 = 0, 3x \(-\) 5y + 4z + 11 = 0 and the point (\(-\)2, 1, 3) is ax + by + cz \(-\) 7 = 0, then the value of 2a + b + c \(-\) 7 is __...

If (2021)3762 is divided by 17, then the remainder is __________.

If the fourth term in the expansion of \({(x + {x^{{{\log }_2}x}})^7}\) is 4480, then the value of x where x\(\in\)N is equal to :

The line 2x \(-\) y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x \(-\) 2y = 4. Then, the radius of the circle is :

The minimum distance between any two points P1 and P2 while considering point P1 on one circle and point P2 on the other circle for the given circles' equationsx2 + y2 \(-\) 10x \(-\) 10y + 41 = 0x2 + y2 \(-\) 24x \(-\) 10y + 160 = 0 is ___...

Choose the incorrect statement about the two circles whose equations are given below :x2 + y2 \(-\) 10x \(-\) 10y + 41 = 0 and x2 + y2 \(-\) 16x \(-\) 10y + 80 = 0

The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :

If [ . ] represents the greatest integer function, then the value of \(\left| {\int\limits_0^{\sqrt {{\pi \over 2}} } {\left[ {[{x^2}] - \cos x} \right]dx} } \right|\) is ____________.

Which of the following statements is correct for the function g(\(\alpha\)) for \(\alpha\) \(\in\) R such that $$g(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }...

Which of the following is true for y(x) that satisfies the differential equation \({{dy} \over {dx}}\) = xy \(-\) 1 + x \(-\) y; y(0) = 0 :

If \(f(x) = \sin \left( {{{\cos }^{ - 1}}\left( {{{1 - {2^{2x}}} \over {1 + {2^{2x}}}}} \right)} \right)\) and its first derivative with respect to x is \(- {b \over a}{\log _e}2\) when x = 1, where a and b are integers, then the minimum v...

The inverse of \(y = {5^{\log x}}\) is :

The sum of possible values of x for tan\(-\)1(x + 1) + cot\(-\)1\(\left( {{1 \over {x - 1}}} \right)\) = tan\(-\)1\(\left( {{8 \over {31}}} \right)\) is :

If cot\(-\)1(\(\alpha\)) = cot\(-\)1 2 + cot\(-\)1 8 + cot\(-\)1 18 + cot\(-\)1 32 + ...... upto 100 terms, then \(\alpha\) is :

If the function \(f(x) = {{\cos (\sin x) - \cos x} \over {{x^4}}}\) is continuous at each point in its domain and \(f(0) = {1 \over k}\), then k is ____________.

The value of \(\mathop {\lim }\limits_{x \to {0^ + }} {{{{\cos }^{ - 1}}(x - {{[x]}^2}).{{\sin }^{ - 1}}(x - {{[x]}^2})} \over {x - {x^3}}}\), where [ x ] denotes the greatest integer \(\le\) x is :

If the Boolean expression (p \(\Rightarrow\) q) \(\Leftrightarrow\) (q * (\(\sim\)p) is a tautology, then the boolean expression (p * (\(\sim\)q)) is equivalent to :

If \(A = \left[ {\matrix{ 2 & 3 \cr 0 & { - 1} \cr } } \right]\), then the value of det(A4) + det(A10 \(-\) (Adj(2A))10) is equal to _____________.

If \(A = \left( {\matrix{ 0 & {\sin \alpha } \cr {\sin \alpha } & 0 \cr } } \right)\) and \(\det \left( {{A^2} - {1 \over 2}I} \right) = 0\), then a possible value of \(\alpha\) is :

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to :

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :

Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is \(\alpha\), only E2 occurs is \(\beta\) and only E3 occurs is \(\gamma\). Let 'p' denote the probability of none of events occurs that satisfies the...

Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :

The value of \(4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}\) is :

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

In a triangle PQR, the co-ordinates of the points P and Q are (\(-\)2, 4) and (4, \(-\)2) respectively. If the equation of the perpendicular bisector of PR is 2x \(-\) y + 2 = 0, then the centre of the circumcircle of the \(\Delta\)PQR is :

The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y \(\le\) 100 and 4x + 3y \(\le\) 75 for x \(\ge\) 0 and y \(\ge\) 0 is __________.

If \(\overrightarrow a = \alpha \widehat i + \beta \widehat j + 3\widehat k\),\(\overrightarrow b = - \beta \widehat i - \alpha \widehat j - \widehat k\) and \(\overrightarrow c = \widehat i - 2\widehat j - \widehat k\)such that $$\over...

Let \(\overrightarrow a\) = 2\(\widehat i\) \(-\) 3\(\widehat j\) + 4\(\widehat k\) and \(\overrightarrow b\) = 7\(\widehat i\) + \(\widehat j\) \(-\) 6\(\widehat k\).If \(\overrightarrow r\) \(\times\) \(\overrightarrow a\) = $$\overri...