JEE Main Maths Mock Test- 5 - JEE MCQ

The differential equation which represents the family of plane curves y=exp. (cx) is

If the domain of function f(x) = x² - 6x + 7 is (-∞, ∞), then the range of function is :

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-
Let a, b, c, p, q be real numbers. Suppose α,β are the roots of the equation x² + 2px + q = 0 and a, 1/β are the roots of the equation ax² + 2bx + c = 0, where β² ∉ {-1, 0, 1}
Statement-1:
(p²-q)(b²-ac)≥0
Statement-2:
b≠pa or c≠qa

The angle between the pair of tangents drawn from the point (1,2) to the ellipse 3x² + 2y²= 5 is

(d/dx)[cos(1-x²)²]=

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): e^x , log_e x are two functions such that each is the image of the other with respect to the line x = y
Reason (R): The inverse of every bijective function is symmetric about the line x = y

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)² rupees. The dimensions of the tank for the least total cost are

The same roots of 3-4 i are

Everybody in a room shakes hands with every body else. The total number of hand shakes is 66. Then the number of persons in the room is

If the sum of the squares of the roots of x² + px - 3 = 0 is 10, then the values of p =

Three identical dice are rolled. The probability that the same number will appear on each of them, is

If A is the single A.M. between two numbers a and b and S is the sum of n A.M.'s between them, then S/A depends upon

M telegrams are distributed at random over N communication channels (N > M). The probability of the event
A = {not more than one telegram will be sent over any channel} is

The equation of a line passing through (-a,0) and form a triangle of area 'T' with coordinates axes, is

If  then value of L/128 is :-

If the function is continuous in the interval (–∞, 6) then value of  is

Value of is equals to
(where [.] denotes greatest integer function)

If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4 is equals to

If value of is k then k/4 is