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

The value of `lim_(x rightarrow 0) 1/x^3 int_0^x (t log (1 + t))/(t^4 + 4) dt` is ______.

With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.

The mean and variance of n observations x₁ ,x₂, x₃, ..., x_n are 5 and 0, respectively. If `sum_(x = 1)^n x_i^2` = 400, then the value of n is equal to ______.

`lim_(x rightarrow 0) (1 - cos x)/x^2` is equal to ______.

The value of x obtained from the equation `|(x + a, b, c),(c, x + b, a),(a, b, x + c)|` = 0 will be ______.

The value of determinant `|((α^x + a^-x)^2, (α^x - α^-x)^2, 1),((β^x + β^-x)^2, (β^x - β^-x)^2, 1),((γ^x + γ^-x)^2, (γ^x - γ^-x)^2, 1)|`

In ΔABC, a(cos²B + cos²C) + cos A(c cos C + b cos B) = ?

In ΔABC, if (a+ b - c)(a + b + c) = 3ab, then ______.

Degree of the given differential equation

`(("d"^3"y")/"dx"^2)^2 = (1 + "dy"/"dx")^(1/3)` is

The probability distribution of a r.v. X is

Then F (-1) = ?

In a ΔABC, cot `(("A - B")/2)* tan (("A + B")/2)` is equal to

If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?

In a ΔABC, c² sin 2B + b² sin 2C = ?

A coin is tossed 10 times. The probability of getting exactly six heads is ______.

A square plate is contracting at the uniform rate of 3cm²/sec. The rate at which the perimeter is decreasing when the side of the square is 12 cm long is

The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is

A random variable X has the following probability distribution:

Then the value of k is

The maximum value of Z = 3x + 5y, subject to 3x + 2y ≤ 18, x ≤ a, y ≤ 6, x, y ≥ 0 is ______.

In a ΔABC if 2 cos C = sin B · cosec A, then ______.

The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.