Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Prove `(9pi)/8 - 9/4  sin^(-1)  1/3 = 9/4 sin^(-1)  (2sqrt2)/3`

Solve the following equation:

2 tan⁻¹ (cos x) = tan⁻¹ (2 cosec x)

sin (tan^–1 x), |x| < 1 is equal to ______.

sin^–1 (1 – x) – 2 sin^–1 x = `pi/2`, then x is equal to ______.

Solve  `tan^(-1) -  tan^(-1)  (x - y)/(x+y)` is equal to

(A) `pi/2`

(B). `pi/3` 

(C) `pi/4` 

(D) `(-3pi)/4`

Write Minors and Cofactors of the elements of the following determinant:

`|(2,-4),(0,3)|`

Write Minors and Cofactors of the elements of the following determinant:

`|(a,c),(b,d)|`

Write Minors and Cofactors of the elements of the following determinant:

`|(1,0,0),(0,1,0),(0,0,1)|`

Write Minors and Cofactors of the elements of the following determinant:

`|(1,0,4),(3,5,-1),(0,1,2)|`

Using Cofactors of elements of second row, evaluate Δ = `|(5,3,8),(2,0,1),(1,2, 3)|`.

Using Cofactors of elements of third column, evaluate Δ = `|(1,x,yz),(1,y,zx),(1,z,xy)|`.

If Δ = `|(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and A_ij is Cofactors of a_ij, then the value of Δ is given by ______.

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 What is the probability that the student knows the answer given that he answered it correctly?

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (that is, if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

There are three coins. One is two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that was produced by machine B?

Two groups are competing for the position on the board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.