HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the value of c for which the conclusion of the mean value theorem holds for the function f(x) = log x on the interval [1, 3]

If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.

An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.

Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 and 3. Let X denote the sum of numbers. Find expected value of the sum.

The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.

For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.

Find `dy/dx`, if y = (log x)^x.

Evaluate:

`int log x dx`

The dual of statement t ∨ (p ∨ q) is ______.

If y=e^ax ,show that  `xdy/dx=ylogy`

Price P for demand D is given as P = 183 +120D - 3D² Find D for which the price is increasing

Show that the lines ` (x+1)/-3=(y-3)/2=(z+2)/1; ` are coplanar. Find the equation of the plane containing them.

If x^py^q = (x + y)^p+q then Prove that `dy/dx = y/x`

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

Find dy/dx if x sin y + y sin x = 0.

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 

The function f (x) = x³ – 3x² + 3x – 100, x∈ R is _______.

(A) increasing

(B) decreasing

(C) increasing and decreasing

(D) neither increasing nor decreasing

Differentiate tan^-1 (cot 2x) w.r.t.x.

If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of the following statement:

∃ x ∈ A such that x + 8 = 15

If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of the following statement:

∀ x ∈ A, x + 5 < 12.