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The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:
If the system of linear equations
is consistent and has infinite number of solutions, then:
Given sum of the first n terms of an A.P. is 2n + 3n2. Another A.P. is formed with the same first term and double of the common difference, the sum of n terms of the new A.P. is:
Statement 1: The function x2 (ex + e–x) is increasing for all x > 0.
Statement 2: The functions x2ex and x2e–x is increasing for all x > 0 and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b)
Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is:
The area of the region (in sq. units), in the first quadrant, bounded by the parabola y = 9x2 and lines x = 0, y = 1 and y = 4, is:
If the x-intercept of some line L is double as that of the line, 3x + 4y = 12 and the y-intercept of L is half as that of the same line, then the slope of L is:
The sum upto 11-terms is:
The integral
Let R = {(3, 3), (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)} be a relation on the set A = {3, 5, 9, 12}. Then, R is:
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