1
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Change Language
Let S be the set of all integer solutions, (x, y, z), of the system of equations
x – 2y + 5z = 0
–2x + 4y + z = 0
–7x + 14y + 9z = 0
such that 15 $$ \le $$ x2 + y2 + z2 $$ \le $$ 150. Then, the number of elements in the set S is equal to ______ .
Your input ____
2
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Out of Syllabus
Change Language
If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .
Your input ____
3
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is :
A
1
B
$${1 \over 2}$$
C
$$\sqrt 2 $$
D
$${1 \over {\sqrt 2 }}$$
4
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The mass density of a planet of radius R varies with the distance r from its centre as
$$\rho $$(r) = $${\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$.
Then the gravitational field is maximum at :
A
$$r = {1 \over {\sqrt 3 }}R$$
B
r = R
C
$$r = \sqrt {{3 \over 4}} R$$
D
$$r = \sqrt {{5 \over 9}} R$$
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