List of top Questions asked in JEE Main- 2020

If the sum of the coefficients of all even powers of x in the product
(1 + x + x² + ....+ x²ⁿ)(1 - x + x² - x³ + ...... + x²ⁿ) is 61, then n is equal to _______.

The logical statement (p \( \Rightarrow \) q) \( \Lambda \) ( q \( \Rightarrow \) ~p) is equivalent to :

If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c \( \in \) R are non-zero distinct; has a non-zero solution, then:

If g(x) = x² + x - 1 and
(goƒ) (x) = 4x² - 10x + 5, then ƒ\( \left( {{5 \over 4}} \right) \) is equal to:

Let \( \alpha \) and \( \beta \) be two real roots of the equation
(k + 1)tan²x - \( \sqrt 2 \) . \( \lambda \)tanx = (1 - k), where k(\( \ne \) - 1) and \( \lambda \) are real numbers. if tan² (\( \alpha \) + \( \beta \)) = 50, then a value of \( \lambda \) is:

A vector \( \overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k\left( {\alpha ,\beta \in R} \right) \) lies in the plane of the vectors, \( \overrightarrow b = \widehat i + \widehat j \) and \( \overrightarrow c = \widehat i - \widehat j + 4\widehat k \). If \( \overrightarrow a \) bisects the angle between \( \overrightarrow b \) and \( \overrightarrow c \), then:

Let x^k + y^k = a^k, (a, k > 0 ) and \( {{dy} \over {dx}} + {\left( {{y \over x}} \right)^{{1 \over 3}}} = 0 \), then k is:

If ƒ(a + b + 1 - x) = ƒ(x), for all x, where a and b are fixed positive real numbers, then

\( {1 \over {a + b}}\int_a^b {x\left( {f(x) + f(x + 1)} \right)} dx \) is equal to:

Let S be the set of points where the function, ƒ(x) = |2-|x-3||, x \( \in \) R is not differentiable. Then \( \sum\limits_{x \in S} {f(f(x))} \) is equal to_____.

The area of the region, enclosed by the circle x² + y² = 2 which is not common to the region bounded by the parabola y² = x and the straight line y = x, is:

The greatest positive integer k, for which 49^k + 1 is a factor of the sum
49¹²⁵ + 49¹²⁴ + ..... + 49² + 49 + 1, is:

If \( {\mathop{\rm Re}\nolimits} \left( {{{z - 1} \over {2z + i}}} \right) = 1 \), where z = x + iy, then the point (x, y) lies on a :

If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to_____.

If \( y\left( \alpha \right) = \sqrt {2\left( {{{\tan \alpha + \cot \alpha } \over {1 + {{\tan }^2}\alpha }}} \right) + {1 \over {{{\sin }^2}\alpha }}} ,\alpha \in \left( {{{3\pi } \over 4},\pi } \right) \)

\( {{dy} \over {d\alpha }}\,\,at\,\alpha = {{5\pi } \over 6}is \) :

\( \mathop {\lim }\limits_{x \to 2} {{{3^x} + {3^{3 - x}} - 12} \over {{3^{ - x/2}} - {3^{1 - x}}}} \) is equal to_______.

Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is -\( {1 \over 2} \) , then the greatest number amongst them is:

Let \( \alpha \) be a root of the equation x² + x + 1 = 0 and the
matrix A = \( {1 \over {\sqrt 3 }}\left[ {\matrix{ 1 & 1 & 1 \cr 1 & \alpha & {{\alpha ^2}} \cr 1 & {{\alpha ^2}} & {{\alpha ^4}} \cr } } \right] \)

then the matrix A³¹ is equal to

If y = y(x) is the solution of the differential equation, \( {e^y}\left( {{{dy} \over {dx}} - 1} \right) = {e^x} \) such that y(0) = 0, then y(1) is equal to:

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :

The purest from of commercial iron is :

A solution of m-chloronailimne, m-chlorophenol and m-chlorobenzoic acid in ethyal acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The left over organic phase was extracted with dilute NaoH solution tio give fraction B. The final organiic layer was labelled as fraction C. Fractions A,B and C, contain respectively :

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is :

The atomic radius of Ag is closed to :

The number of chiral carbons in chloramphenicol is

Amongst the following statements, that which was not proposed by Dalton was :