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

`int_0^pi sin^2x.cos^2x  dx` = ______ 

Which one of the following statements is not a tautology?

At any point on a curve, the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point. If the curve passes through (0, 1), then the equation of the curve is ______.

The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.

`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`

`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.

`int_0^1 log(1/x - 1) "dx"` = ______.

If the plane passing through the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is ax + by + cz = d then a + 2b + 3c = ______.

9x² + hxy + y² = 0 represents pair of parallel straight lines, if h is ______.

`int_(pi/4)^(pi/2) sqrt(1-sin 2x)  dx =` ______.

`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = ______

`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.

`int_-1^1x^2/(1+x^2)  dx=` ______.

Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______ 

Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.

Which of the following statement is contradiction?

Which of the following statement is a contingency?

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______ 

If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.