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

The equation of a plane containing the point (1, - 1, 2) and perpendicular to the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8 is ______.

If the volume of the parallelepiped whose conterminus edges are along the vectors a, b, c is 12, then the volume of the tetrahedron whose conterminus edges are a + b, b + c and c + a is ______.

The rational form of a number 1.41 is ______.

`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.

If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = ____________.

If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x² + y² = ____________.

The approximate value of the function f(x) = x³ − 3x + 5 at x = 1.99 is ____________.

If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.

`int cot "x".log [log (sin "x")] "dx"` = ____________.

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 = ______.