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

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 ______

The maximum value of z = 6x + 8y subject to x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0 is ______.

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 _______.

For L.P.P. maximize z = 4x₁ + 2x₂ subject to 3x₁ + 2x₂ ≥ 9, x₁ - x₂ ≤ 3, x₁ ≥ 0, x₂ ≥ 0 has ______.

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 ______.

`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.

`int_0^1 (1 - x)^5`dx = ______.

If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.

Area of the region bounded by y = cos x, x = 0, x = π and X-axis is ______ sq.units.