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

The principal solutions of cot x = `sqrt3` are ______.

If 2 cos² θ + 3 cos θ = 2, then permissible value of cos θ is ________.

The radius of the circle passing through the points (5, 7), (2, -2) and (-2, 0) is ______.

The cartesian coordinates of the point on the parabola y² = x whose parameter is ____________.

The vector equation of the line passing through `4hati - hatj + 2hatk` and parallel to `-2hati - hatj + hatk` is ______ 

The sum of intercepts on co-ordinate axes made by the tangent to the curve `sqrtx + sqrty = sqrta` is ______

The mean of 5 observations is 4.8 and their variance is 4.56. If three observations are 2, 3, and 5, the other two observations are ______

The cartesian equation of the line `overliner = (hati + hatj + hatk) + lambda(hatj + hatk)` is ______

If f(x) = 3x - 2 and g(x) = x², then (fog)(x) = ________.

If line joining points A and B having position vectors `6overlinea - 4overlineb + 4overlinec` and `-4overlinec` respectively, and the line joining the points C and D having position vectors `-overlinea - 2overlineb - 3overlinec` and `overlinea + 2overlineb - 5overlinec` intersect, then their point of intersection is ______

The equation of normal to the curve y = log_e x at the point P(1, 0) is ______.

The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.

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

`intx/(x + 2)dx` = ______

If the line passes through the points P(6, -1, 2), Q(8, -7, 2λ) and R(5, 2, 4) then value of λ is ______.

If the function f(x) = `(log (1 + "ax") - log (1 - "bx))/x, x ≠ 0` is continuous at x = 0 then, f(0) = _____.

The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is ______ 

The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.

Which of the following equations has no solution?

The value of `tan^-1  1/3 + tan^-1  1/5 + tan^-1  1/7 + tan^-1  1/8` is ______.