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

In ΔABC, if `"a" cos^2  "C"/2 + "c" cos^2  "A"/2 = (3"b")/2`, then a, b, c are in ______.

In a triangle ABC, b = `sqrt3`, c = 1 and ∠A = 30°, then the largest angle of the triangle is ______ 

The p.d.f. of a continuous random variable X is

f(x) = 0.1 x, 0 < x < 5

= 0, otherwise

Then the value of P(X > 3) is ______ 

The difference between the slopes of lines represented by 6x² – 5.xy + y² = 0 is ______.

In ΔABC, `cos"A"/"a" = cos"B"/"b"  cos"C"/"c"`. If a = `1/sqrt(6)`, then the area of the triangle is ______.

The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.

If a = 13, b = 14, c = 15, then `cos("A"/2)` = ______.

In a ΔABC, if `sin"A"/sin"C" = (sin("A" - "B"))/(sin("B" - "C"))`, then a², b², c² are in ______.

If z₁ = 3 – 2i and z₂ = –1 + 3i, then Im(z₁z₂) = ______.

In a ΔABC, if a = `sqrt(2)` x and b = 2y and ∠C = 135°, then the area of triangle is ______.

The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.

In a ΔABC, if `("b" + "c")/11 = ("c" + "a")/12 = ("a" + "b")/13`, then cos C = ______.

A random variable X has the following probability distribution:

The mean and the variance are respectively ______.

If A and B are sets, then A ∩ (B – A) is ______.

If f(x) = `{{:((sin5x)/(x^2 + 2x)",", x ≠ 0),(k + 1/2",", x = 0):}` is continuous at x = 0, then the value of k is ______.

If I = `int 1/(2p) sqrt((p - 1)/(p + 1))dp` = f(p) + c, then f(p) is equal to ______.

`int_0^1 1/((x^2 + 16)(x^2 + 25))dx` = ______.

The figure shows as triangle AOB and the parabola y = x². The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x² is equal to ______.

The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.

Shamli wants to invest ₹ 50, 000 in saving certificates and PPF. She wants to invest atleast ₹ 15,000 in saving certificates and at least ₹ 20,000 in PPF. The rate of interest on saving certificates is 8% p.a. and that on PPF is 9% p.a. Formulation of the above problem as LPP to determine maximum yearly income, is ______.