An urn contains 5 red and 2 black balls. Two balls are drawn at random. X denotes number of black balls drawn. What are the possible values of X?
Concept: Mean of a Random Variable
Find the mean of number of heads in three tosses of a fair coin
Concept: Mean of a Random Variable
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X
Concept: Mean of a Random Variable
Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance of X.
Concept: Mean of a Random Variable
State whether the following is True or False :
X is the number obtained on upper most face when a die is thrown then E(X) = 3.5.
Concept: Mean of a Random Variable
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2ax)dx`
Concept: Properties of Definite Integrals
A random variable X has the following probability distribution:
then E(X)=....................
Concept: Random Variables and Its Probability Distributions
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) 2
(c) 2
(d) ±2
Concept: Properties of Definite Integrals
Evaluate : `int e^x[(sqrt(1x^2)sin^1x+1)/(sqrt(1x^2))]dx`
Concept: Properties of Definite Integrals
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
Concept: Properties of Definite Integrals
Find the value of 'k' if the function
`f(X)=(tan7x)/(2x) , "for " x != 0 `
`=k`, for x=0
is continuos at x=0
Concept: Continuous Function of Point
Price P for demand D is given as P = 183 +120D  3D^{2} Find D for which the price is increasing
Concept: Increasing and Decreasing Functions
Examine the continuity of the following function :
`{:(,,f(x)= x^2 x+9,"for",x≤3),(,,=4x+3,"for",x>3):}}"at "x=3`
Concept: Continuous Function of Point
If 'f' is continuous at x = 0, then find f(0).
`f(x)=(15^x3^x5^x+1)/(xtanx) , x!=0`
Concept: Continuous Function of Point
The ratio of number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, find the percentage of students who are not scholarship holders.
Concept: Ratio, Proportion and Partnership
An agent charges 12% commission on the sales. What does he earn if the total sale amounts to Rs. 36,000? What does the seller get?
Concept: Commission, Brokerage and Discount
The present worth of the sum of Rs. 5,830, due 9 months hence, is Rs. 5,500. Find the rate of interest.
Concept: Commission, Brokerage and Discount
Natarajan and Mr. Gopalan are partners in the company having capitals in the ratio 4 : 5 and the profits received by them are in the ratio 5 :4. If Mr. Gopalan invested capital in the company for 16 months, how long was Mr. Natarajan’s investment in the company?
Concept: Commission, Brokerage and Discount
From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain 
(a) exactly 1 defective bulb.
(b) at least 1 defective bulb.
Concept: Random Variables and Its Probability Distributions
You are given the following information about advertising expenditure and sales:

Advertisement 

Expenditure (Rs. in lakh) (X) 
Sales (Rs. in lakh) (Y) 

Arithmetic mean 
10 
90 
Standard deviation 
3 
12 
Correlation coefficient between X and Y = 0.8.
(a) Obtain the two regression equations.
(b) What is the likely sales when the advertising budget is ? 15 lakh?
(c) What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression