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

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

If A = `[(1, -1, 3), (2, 5, 4)]`, then R₁ ↔ R₂ and C₃ → C₃ + 2C₂ gives ______

`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 ______

The following statement (p → q) → [(∼p → q) → q] is ______ 

If `[(1, -1, x), (1, x, 1), (x, -1, 1)]` has no inverse, then the real value of x is ______ 

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` = ______

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 ______