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

If `x^2 y^2 = sin^-1 sqrt(x^2 + y^2) + cos^-1 sqrt(x^2 + y^2)`, then `"dy"/"dx"` = ?

`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e^2x dx = ?

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 ______.

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 ____________.

`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 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 ______.