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

The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on ______.

The general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.

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

The joint equation of pair of straight lines passing through origin and having slopes `(1 + sqrt2) and (1/(1 + sqrt2))` is ______.

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 ______

The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, 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 minimum value of z = 10x + 25y subject to 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≥ 5 is ______.

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 = ______

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 ______

Negation of the statement 'A is rich but silly' 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 ______