JEE Main Maths Mock Test- 9 - JEE MCQ

The limiting point of the system of co-axial circles x²+y²-6x-6y+4=0, x²+y²-2x-4y+3=0 is

[(1-i)/(1+i)] =

The number of tangents drawn from the point (-1,2) to x²+y²+2x-4y+4=0 is

The conjugate of complex number [(2+5i)/(4-3i)] is

The solution of differential equation

The maximum value of the function f(x)=[(x)/(4+x+x²)] at the interval [-1,1] will be

sin⁻¹ (cos(sin⁻¹ x) + cos⁻¹ (sin(cos⁻¹ x) is equal to

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): y = sin (ax + b) is a general solution of y" + a^2y = 0 .
Reason(R) : y = sin (ax + b)  is a trigonometric function.

The inverse of the converse of a conditional statement is the _______________.

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): The domain of the function
Reason (R): The domain of the function

If A is a square matrix such that A² = I, then A⁻¹ is equal to

The equation of the directrix to the parabola y² − 2x − 6y − 5 = 0 is

Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively

A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is

If in a moderately asymmetrical distribution mode and mean of the data are 6λ and 9λ respectively, then median is

The sides of a parallelogram are lx + ny + n = 0, lx + my + n' = 0, mx + ly + n = 0, mx + ly + n' = 0, the angle between its diagonals is

Let f : (–3, 3) → R be a differentiable function with f(0) = – 2 and f'(0) = – 1 and g(x) = (f(3f(x) + 6))³ then g'(0) is equal to.

At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100 - 12√x. If the firm employs 25 more workers, then the new level of production of items is:

It is given that events A and B of an experiment are such that P(A / B) = 1 / 4 and P (B / A) = 1/12 and chance of occurence of an event "only A" is 1/12  (where P(x) denote the probability of occurence of event 'x'). Value of 22P(B) equals

If the function ƒ(x) = 2 + x² – e^–x and g(x) = ƒ^–1(x), then the value of  equals