In the first four examinations, each of 100 marks, Hamid got 94,73,72, 84 marks if the final average is greater than or equal to 80 and less than 90 is needed to obtain a final B grade in a course, what range of marks in the fifth (last) examination will result in Hamid receiving 'B' in the course ?

To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita’s marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade ‘A’ in the course.

Rajiv has two courses to prepare for final examination. Each hour of study, he devotes to course A is expected to return Rs.600 in terms of long range job benefits. Each hour devoted to course B Is expected to return Rs.300 in terms of long range job benefits. the stores are closed and Rajiv has only 15 chewing gums. He finds that he consumes one chewing gum every 20 minutes while studying course B and every 12 minutes while studying course A. Time is running short only four hours are left to prepare. Rajiv feels that he must devote atleast two hours to study. using linear programming, determine an optimal policay for Rajiv that would maximise his returns in terms of long range job benefits.

An unbiased die with faced marked 1, 2, 3, 4, 5, and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than five all the 4 times is a. 16//81 b. 1//81 c. 80//81 d. 65//81

Each question contains STATEMENT-1 (Assertion) and STATEMENT-2( Reason). Examine the statements carefully and mark the correct answer according to the instruction given below: STATEMENT-1:For a chemical reaction at initial stage rate of forward reaction ( r_(f) ) is greater than rate of reversed reaction( r_(b) ) STATEMENT-2: When r_(f)=r_(b) ,chemical reaction is at equilibrium.

The final marks in Mathematics of 30 students are as follows (53,61,48,60,78,68,55,100,67,90) (75,88,77,37,84,58,60,48,62,56) (44,58,52,98,59,70,38,50,60) How many have scored less than 50?