JEE Main 2020 (Online) 7th January Morning Slot

Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point
(2, 1, 6). Then the image of R in the plane P is :

Let the function, ƒ:[-7, 0]\(\to\)R be continuous on [-7,0] and differentiable on (-7, 0). If ƒ(-7) = -
3 and ƒ'(x) \(\le\) 2, for all x \(\in\) (-7,0), then for all such functions ƒ, ƒ(-1) + ƒ(0) lies in the interval:

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:

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 greatest positive integer k, for which 49k + 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 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:

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:

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

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\...

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 :

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

\(\mathop {\lim }\limits_{x \to 2} {{{3^x} + {3^{3 - x}} - 12} \over {{3^{ - x/2}} - {3^{1 - x}}}}\) 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 logical statement (p \(\Rightarrow\) q) \(\Lambda\) ( q \(\Rightarrow\) ~p) is equivalent to :

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 ...

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 y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b 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 :

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k
consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected
value of X, is :

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 $$...

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:

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_____.

Let A(1, 0), B(6, 2) and C \(\left( {{3 \over 2},6} \right)\) be the vertices of a triangle ABC. If P is a Point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, wher...

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 = \wideha...