MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

A random variable X bas the following probability distribution: 

The value of P (X > 0) is 

A random variable X has the probability distribution:

Then the value of P(X < 1) is ______.

Let y = `cot^-1((5x^2 + 1)/(4x)) + cot^-1((2x - 3)/(2 + 3x))`, then `dy/dx` = ______ 

In order to get a head at least once probability ~ 0.9, the minimum number of time a unbiased coin needs to be tossed is ______.

Differential coefficient of `sin^-1(sqrtx)` with respect to `sqrt(1 - x)` is ______ 

If A ≡ {7, 8, 10, 12}, determine which of the following quantified statement is true.

The p.m.f. of a r.v. X is as follows:
P(X = 1) = 5k³, P(X = 2) = 10k – 16k² – 1
P(X = 3) = 2k, P(X = 4) = k, P(X = x) = 0 for any other value of x. Then the value of k is ______.

Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = ______.

Determine which of the following quantified statement is false ______.

The point of contact of the tangent lo the circle x² + y² = 5 at the point (1, –2) which touches the circle, x² + y² – 8x + 6y + 20 = 0 is ______.

If for x ∈ `(0, 1/4)`, the derivative of `tan^-1((6xsqrt(x))/(1 - 9x^3))` is `sqrt(x) * "g"(x)`, then g(x) equals ______.

Which of the following quantified statement is True?

The equation of the tangent to the curve x = 2 cos³ θ and y = 3 sin³ θ at the point θ = `pi/4` is ______.

If y = `sin^-1 (xsqrt(1 - x) + sqrt(x) sqrt(1 - x^2))`, then `("d"y)/("d"x)` = ______.

The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.

If y = `cos^-1 ((x + 1)/(x - 1)) + "cosec"^-1 ((x - 1)/(x + 1))`, then `("d"y)/("d"x)` is ______.

If b², a², c² are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______

The gradient of the curve passing through (4, 0) is given by `"dy"/("d"x) - "y"/x + (5x)/((x + 2)(x - 3))` = 0 if the point (5, a) lies on the curve, then the value of a is ______.

The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.