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

The third order differential equation is ______ 

In Δ ABC; with usual notations, `("b" sin "B" - "c" sin "C")/(sin ("B - C"))` = _______.

X is a continuous random variable with a probability density function

f(x) = `{{:(x^2/4 + k;     0 ≤ x ≤ 2),(0;              "otherwise"):}`

The value of k is equal to ______

The edge of a cube is decreasing at the rate of 0.04 cm/sec. If the edge of the cube is 10 ems, then rate of decrease of surface area of the cube is ______.

The polar co-ordinates of P are `(2, pi/6)`. If Q is the image of P about the X-axis then the polar co-ordinates of Q are ______.

Let X be the number of successes in 'n' independent Bernoulli trials with probability of 3 success p = `3/4`. The least value of 'n' so that P(X ≥ 1) ≥ 0.9375 is ______.

In ΔABC, `(sin(B - C))/(sin(B + C))` = ______

In Δ ABC, with the usual notations, if `(tan  "A"/2)(tan  "B"/2) = 3/4` then a + b = ______.

If sum of the slopes of the lines given by x² - 4pxy + 8y² = 0 is three times their product then p = ______.

`(1 - 2[cos 60^circ - cos 80^circ])/(2 sin 10^circ)` = ______.

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is ______.

If f(x) is continuous at x = 3, where

f(x) = ax + 1, for x ≤ 3

= bx + 3, for x > 3 then.

If A= {x ∈ R/ x² + 5 |x| + 6 = 0} then n(A) = ______.

If f(x) = `[tan (pi/4 + x)]^(1/x)`, x ≠ 0 at

= k, x = 0 is continuous x = 0. Then k = ______.

Let f : [-1, 2] → [0, ∞] be a continuous function such that f(x) = f(1 - x) ∀ x ∈ [-1, 2].

Let R₁ = `int_-1^2 xf(x) dx` and R₂ be the area of the region bounded by y = f(x), x = -1, x = 2 and the X-axis. Then, ______

The general solution of `(1 + e^{x/y})dx + e^{x/y}(1 - x/y)dy = 0` is ______ 

The minimum value of z = 5x + 13y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10, x ≥ 0, y ≥ 2 is ______ 

In ΔABC if sin²A + sin²B = sin²C and l(AB) = 10, then the maximum value of the area of ΔABC is ______ 

If the slope of the tangent to the curve at any point is equal to -y + e^-x, then the equation of the curve passing through the origin is ______  

The probability distribution of a random variable X is given below. If its mean is 4.2, then the values of a and bar respectively