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

`int_0^{pi/2} log(tanx)dx` = ______

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is ______

`int_0^4 1/(1 + sqrtx)`dx = ______.

If p, q and r are non-zero, non-coplanar vectors then [p + q - r  p - q  q - r] = ______.

The equation of the plane passing through the point (– 1, 2, 1) and perpendicular to the line joining the points (– 3, 1, 2) and (2, 3, 4) is ______.

`int_2^3 x/(x^2 - 1)` dx = ______

Adjoint of ______

The value of sin 163° cos 347° + sin 167° sin 73° is ______

Equation of the plane passing through A(-2, 2, 2), B(2, -2, -2) and perpendicular to x + 2y - 3z = 7 is ______ 

If x + y + k = 0 touches the circle x² + y² - 2x - 4y + 3 = 0, then k will be ______

`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______ 

The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through the point (1, 1, 0) is ______

`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"` = ______.