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

`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?

If a = `3hat"i" + hat"j" - hat"k"`, b = `2hat"i" - hat"j" + 7hat"k"` and c = `7hat"i" - hat"j" + 23 hat"k"` are three vectors, then which of the following statement is true.

The rate of disintegration of a radio active element at time t is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm. Will disintegrate into its mass of 0.5 gm. is proportional to ______.

The negation of the statement pattern ~ p v(q → ~ r) is ______.

∫ log x · (log x + 2) dx = ?

The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x²). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.

\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?

If `x^2 y^2 = sin^-1 sqrt(x^2 + y^2) + cos^-1 sqrt(x^2 + y^2)`, then `"dy"/"dx"` = ?

`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e^2x dx = ?

The equation of a plane containing the point (1, - 1, 2) and perpendicular to the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8 is ______.

The rational form of a number 1.41 is ______.

`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.

If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = ____________.

If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x² + y² = ____________.

The approximate value of the function f(x) = x³ − 3x + 5 at x = 1.99 is ____________.

If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.

`int cot "x".log [log (sin "x")] "dx"` = ____________.

The differential equation of all lines perpendicular to the line 5x + 2y + 7 = 0 is ____________.

`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______

If the line `(x - 3)/2 = (y + 2)/-1 = (z + 4)/3` lies in the plane lx + my - z = 9, then l² + m² is equal to ______