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

In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?

Let F(x) = e^x, G(x) = e^-x and H(x) = G[F(x)], where x is a real variable. Then `"dH"/"dx"`at x = 0 is ______.

If `bar"a", bar"b", bar"c"` are the three non-coplanar vectors and `bar"p", bar"q", bar"r"` are defined by the relations `bar"p" = (bar"b" xx bar"c")/([(bar"a", bar"b", bar"c")]), bar"q" = (bar"c" xx bar"a")/([(bar"a", bar"b", bar"c")]), bar"r" = (bar"a" xx bar"b")/([(bar"a", bar"b", bar"c")])` then `(bar"a" + bar"b")* bar"p" + (bar"b" + bar"c") * bar"q" + (bar"c" + bar"a") * bar"r"` = ______.

Which of the following pair of straight lines intersect at right angles?

The p.m.f. of a r.v. X is
P(x) = `{:(= 1/13","  "for"  x = 1","  2","  ......","  14","  13),(= 0","  "otherwise."):}`
Then, E(X) is equal to ______.

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.

A pair of dice is thrown and X denotes the absolute difference of the numbers on uppermost faces. Then the expected value of X is ______

`int "e"^x ((cos x - sin x)/(sin^2x)) "d"x` = ______.

If f(x) = `sin^2x + sin^2(x + pi/3) + cosx cos(x + pi/3) and g(5/4) = 1`, then (gof)(x) is equal to: ______ 

The co-ordinates of a point on the line x = 4y + 5, z = 3y – 6 at a distance `3sqrt(26)` from the point (5, 0, –6) are ______.

The p.m.f. of a r.v. X is 

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is ______.

If P₁ and P₂ are the lengths of the perpendiculars from the points (2, 3, 4) and (1, 1, 4) respectively from the plane 3x – 6y + 2z + 11 = 0, then P₁ and P₂ are the roots of the equation ______.

If f(x) =bx - 7 and f(-1) = 4, then b = ______.

If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then ______ 

`int "e"^x [2"cosec"  2x + log(tanx)] "d"x` = ______.

`int("I" - cosx)"cosec"^2x"d"x` = ______.

If `int (sin2x)/(sin^4x + cos^4x) "d"x = tan^-1["f"(x)] + "c"`, then `"f"(pi/3)` = ______.

The Standard deviation of the following frequency distribution

is ______.

If f(x) =x⁴, g(x) = 6x – 2, then g[f(x)] = ______.