(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Marks for each question are indicated against it.
(iv) Questions 1 to 6 in Section-A are Very Short Answer Type Questions carrying one mark each.
(v) Questions 7 to 19 in Section-B are Long Answer I Type Questions carrying 4 marks each.
(vi) Questions 20 to 26 in Section-C are Long Answer II Type Questions carrying 6 marks each.
(vii) Please write down the serial number of the Question before attempting it.
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- Q1VIEW SOLUTION
- Q2VIEW SOLUTION
- Q3VIEW SOLUTION
- Q4VIEW SOLUTION
- Q5VIEW SOLUTION
- Q6VIEW SOLUTION
- Q7VIEW SOLUTION
Three machines E1, E2 and E3 in a certain factory producing electric bulbs, produce 50%, 25% and 25% respectively, of the total daily output of electric bulbs. It is known that 4% of the bulbs produced by each of machines E1 and E2 are defective and that 5% of those produced by machine E3 are defective. If one bulb is picked up at random from a day's production, calculate the probability that it is defective.
Two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X. VIEW SOLUTION
- Q9VIEW SOLUTION
- Q10VIEW SOLUTION
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
If , then find the value of θ. VIEW SOLUTION
If and I is the identity matrix of order 2, then show that A2= 4 A − 3 I. Hence find A−1.OR
If , then find the values of a and b. VIEW SOLUTION
- Q13VIEW SOLUTION
Evaluate :VIEW SOLUTION
- Q15VIEW SOLUTION
In a parliament election, a political party hired a public relations firm to promote its candidates in three ways − telephone, house calls and letters. The cost per contact (in paise) is given in matrix A asVIEW SOLUTION
The number of contacts of each type made in two cities X and Y is given in the matrix B as
Find the total amount spent by the party in the two cities.
What should one consider before casting his/her vote − party's promotional activity or their social activities ?
Evaluate :VIEW SOLUTION
- Q18VIEW SOLUTION
Find the minimum value of (ax + by), where xy = c2.
Find the coordinates of a point of the parabola y = x2 + 7x + 2 which is closest to the straight line y = 3x − 3. VIEW SOLUTION
- Q21VIEW SOLUTION
- Q22VIEW SOLUTION
- Q23VIEW SOLUTION
- Q24VIEW SOLUTION
- Q25VIEW SOLUTION
Solve the following differential equation :
ORSolve the following differential equation :
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