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

A rectangle with one side lying along the x-axis is to be inscribed in the closed region of the xy plane bounded by the lines y = 0, y = 3x and y = 30 – 2x. The largest area of such a rectangle is ______.

∼ ((∼ p) ∧ q) is equal to ______.

The maximum value of z = 6x + 8y subject to constraints 2x + y ≤ 30, x + 2y ≤ 24 and x ≥ 0, y ≥ 0 is ______.

The volume of the greatest cylinder which can be inscribed in a cone of height 30 cm and semi-vertical angle 30° is ______.

If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = ______.

The minimum value of the function f(x) = xlogx is ______.

The maximum value of f(x) = `logx/x (x ≠ 0, x ≠ 1)` is ______.

If x = `a(t - 1/t)`, y = `a(t + 1/t)`, where t is the parameter, then `dy/dx` =?

If random variable waiting time in minutes for bus and probability density function of x is given by

f(x) = `{{:(1/5",", 0 ≤ x ≤ 5),(0",", "otherwise,"):}`

then probability of waiting time not more than 4 minutes is equal to ______.

If the probability density function of a random variable X is given as

then F(0) is equal to

If A + B + C = π, then sin 2A + sin 2B + sin 2C is equal to ______.

If A + B = C, then cos² A + cos² B + cos² C – 2 cos A cos B cos C is equal to ______.

If α + β – γ = π, then sin² α + sin² β – sin² γ is equal to ______.

If A + B + C = 180°, then `sum tan  A/2 tan  B/2` is ______.

In a ΔABC, `cos((B + 2C + 3A)/2) + cos((A - B)/2)` is ______.

Let A, B and C are the angles of a triangle and `tan(A/2) = 1/3, tan(B/2) = 2/3`. Then, `tan(C/2)` is equal to ______.

If A + B + C = 270°, then cos 2A + cos 2B + cos 2C is equal to ______.

If A + B + C = π, then sin 2A + sin 2B – sin 2C is equal to ______.

In a ΔABC, if cos A cos B cos C = `(sqrt(3) - 1)/8` and sin A sin B sin C = `(3 + sqrt(3))/8`, then the angles of the triangle are ______.

If A + B + C = π, then cos² A + cos² B + cos² C is equal to ______.