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

Twenty meters of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is ______

The S.D. and C.V. for the following frequency distribution is

Coefficients of variation of two distributions are 30 and 40 and their arithmetic means are 10 and 25 respectively. The difference of their standard deviations is ______ 

The value of `[(1 - cos  pi/6 + isin  pi/6)/(1 - cos  pi/6 - isin  pi/6)]^6` = ______

Let y be an implicit function of x defined by `x^{2x} - 2x^x coty - 1 = 0`. Then, y'(1) equals ______ 

If `cos "A" = 3/4,`then 32 sin`"A"/2 cos  (5"A")/2` = ?

The function y = 1 + sin x is maximum, when x = ______ 

The maximum value of function x³ - 15x² + 72x + 19 in the interval [1, 10] is ______.

For all complex numbers z₁, z₂ satisfying |z₁| = 12 and |z₂ - 3 - 4i| = 5, the minimum value of |z₁ - z₂| is ______.

If the probability density function continuous random variable X is

f(x) = k(1 - x₂); 0 < x < 1
      = 0  ;    otherwise

Then P`(0 < X < 1/2)` = ?

The S.D. of 20 items is 15 and if each item is decreased or increased by 1, then standard deviation will be ______.

`(sin20^circ +2sin40^circ)/sin70^circ=` ______.

The standard deviation of the data 8, 7, 1, 15, 14, 10, 12 is ______.

If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+....oo))),` then `dy/dx` equals ______.

If A ≡ {7, 8, 10, 12}, determine which of the following quantified statement is true.

The odds against an event be 3 : 5. Find the probability of occurrence of the event.

The maximum and minimum values for the function f(x) = 4x³ - 6x² on [-1, 2] are ______

An integrating factor of the differential equation `x/y ("d"y)/("d"x) + log x = ("e"^x x^(-tanx))/y, (x > 0)`, is ______.

For certain data, the following information is available. Obtain the combined standard deviation.