JEE Main Maths Mock Test- 4 - JEE MCQ

If is a purely imaginary number, then is equal to

If f (x) = cos [π²] x + cos [− π²] x where [x] is the step function, then 

The sum of the focal distances from any point on the ellipse 9x² + 16y² = 144 is

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): f (x) = log x³ and g (x) = 3 log x are equal.
Reason(R) : Two functions f and g are said to be equal if their domains, ranges are equal and f (x) = g (x)∀ x in the domain .

Determinant   is not equal to

Solution of the differential equation 

If is continuous at x = x₀ , then f ′ (x₀) is equal to

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-
Tangents are drawn from the point (17,7) to the circle x²+y²=169.
Statement-1:
The tangents are mutually perpendicular.
Statement-2:
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x²+y²=338.

If z² = -i, then z is equal o

If θ + Φ = π/3 then sin θ . sinΦ has a maximum value at θ =

The sum of the digits in the unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is

An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points is

The probability of A = probability of B = probability of C = 1/4, P(A∩B) = P(C∩B) = 0 and P(A∩C) = 1/8, then P(A∪B∪C) is equal to:

If the equations x²+ ba + a = 0 and x² + ax + b = 0 have a common root, then a + b =

If a, b, c, d, e, f are in A.P., then e - c is equal to

If a line passes through points (4,3) and (2,λ) and perpendicular to y=2x+3, then λ=

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

If a, b are odd integers then number of integral root, of equation x¹⁰ + ax⁹ + b = 0 is equal to :

If the number of distinct positive rational numbers p/q smaller than 1, where  p, q ∈ {1, 2, 3 ....., 6} is k then k is :

If two distinct chords of a parabola y² = 4ax passing through (a, 2a) are bisected on the line x + y = 1, then the sum of integral values of the length of possible latus rectums is equal to :

If  the value of  is e^–A then ‘A’ is :

If  be three vectors of magnitude √3, 1, 2, such that   is the angle between  is equal  to:-