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

`int_-9^9 x^3/(4 - x^2)` dx = ______

`int_0^{pi/2} xsinx dx` = ______

The intercepts of the plane 3x - 4y + 6z = 48 on the co-ordinate axes are ______

Equations of planes parallel to the plane x - 2y + 2z + 4 = 0 which are at a distance of one unit from the point (1, 2, 3) are _______.

In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.

Using differentiation, approximate value of f(x) = x² - 2x + 1 at x = 2.99 is ______.

Which of the following statements is contingency?

`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.

`int_0^1 (1 - x)^5`dx = ______.

If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.

The length of the latusrectum of an ellipse is `18/5` and eccentncity is `4/5`, then equation of the ellipse is ______.

`int log x * [log ("e"x)]^-2` dx = ?

`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.

If `hati - 2hatj + hatk`, `2hati + phatj + 3hatk` and `5hati - 9hatj + 4hatk` are coplanar, then the value of p is equal to ______

Equation of plane parallel to ZX-plane and passing through the point (0, 5, 0) is ______

Which of the following statement pattern is a tautology?

If A =`[(1, -1), (2, 3)]` and adj (A) = `[(a, b), (-2, 1)]`, then ______ 

`sqrt3 sin15^circ + cos15^circ` = ______

`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________

`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________