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

A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:

If f(x) = `{{:((x - 4)/(|x - 4|) + a",",  "for"  x < 4),(a + b",",  "for"  x = 4  "is continuous at"  x = 4","),((x - 4)/(|x - 4|) + b",",  "for"  x > 4):}`

then ______.

If the water is being poured at the rate 36 m ³/s in a cylindrical vessel of base radius 3 m, then the rate at which water level is rising, is ______.

The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.

For the following shaded region, the linear constraint are:

For x > 0, `lim_(x rightarrow 0) ((sin x)^(1//x) + (1/x)^sinx)` is ______.

If f(x) = `{{:((3 sin πx)/(5x),",", x ≠ 0),(2k,",", x = 0):}`

is continuous at x = 0, then the value of k is ______.

If f(x) = `{{:((sin^3(sqrt(3)).log(1  +  3x))/((tan^-1 sqrt(x))^2(e^(5sqrt(3))  -  1)x)",", x ≠ 0),(                         a",", x = 0):}`

is continuous in [0, 1] then a is equal to ______.

The order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.

If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.

`lim_(x rightarrow 0) (e^(x^2) - cosx)/x^2` is equal to ______.

sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) is ______.

Area bounded by the curve 7xy - 7x - 7y - 2 = 0, X-axis and the lines x = 2, x = 3 is ______.

If `(bar"a" + 2bar"b" - bar"c") * [(bar"a" - bar"b") xx (bar"a" - bar"b" - bar"c")] = "k"[bar"a"  bar"b"  bar"c"]`, then the value of k is

The area bounded by the curve y = f(x), X-axis and ordinates x = 1 and x = a is (a - 1) cos(2a + 7), then f(x) is ______.

If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.

If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.

The number of discontinuities of the greatest integer function f(x) = [x], x ∈ `(- 7/2, 100)` is equal to ______.

y = 3 cos 2x is a solution of the differential equation

If y = sec x + x^logx, then `"dy"/"dx"` is