An experiment consists of flipping a coin and then flipping it a second time if head occurs. If a tail occurs on the first flip, then a six-faced die is tossed once. Assuming that the outcomes are equally likely, what is the probability of getting one head and one tail?
In an examination, there are 3 multiple-choice questions and each question has 4 choices. If a student randomly selects an answer for all the three questions, what is the probability that the students will not answer all the three questions correctly?
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A lot of 4 white and 4 red balls is randomly divided into two halves. What is the probability that there will be 2 red and 2 white balls in each half?
The average marks obtained by the students in a class are 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?
The mean of 10 observations is 5. If 2 is added to each observation and then multiplied by 3, then what will be the new mean?
For what value of m are the point with position vectors 10i + 3j, 12i – 5j and mi + 11j collinear?
For what value of m are the vector 2i – 3j + 4k, i + 2j – k and mi – j + 2k coplanar?
What is the projection of the vector i – 2j + k on the vector 4i – 4j + 7k?
If the vector a lies in the plane of vectors b and c, then which one of the following is correct?
What is the sine of angle between the vectors i + 2j + 3k and – i + 2j + 3k?
Consider a differential equation of order m and degree n. Which one of the following pairs is not feasible?
For the differential equation which one of the following is not its solution?
What is the area bounded by the curves y = ex, y = e–x and the straight line x = 1?
What is the area enclosed between the curves y2 = 12x and the lines x = 0 and y = 6?
If f and g are two increasing functions such that fog is defined, then which one of the following is correct?