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Five balls are to be placed in three boxes, where each box can contain up to five balls. Find the number of ways if no box is to remain empty.
Concept: undefined >> undefined
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
Concept: undefined >> undefined
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How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficient if a coefficient can be repeated in an equation.
Concept: undefined >> undefined
A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?
Concept: undefined >> undefined
Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. What is the chance that three selected consists of 1 girl and 2 boys?
Concept: undefined >> undefined
A, B, and C are mutually exclusive and exhaustive events associated with the random experiment. Find P(A), given that P(B) = `3/2` P(A) and P(C) = `1/2` P(B).
Concept: undefined >> undefined
Two-third of the students in a class are boys and rest are girls. It is known that the probability of girl getting first class is 0.25 and that of boy getting is 0.28. Find the probability that a student chosen at random will get first class.
Concept: undefined >> undefined
Show that 1 + i10 + i20 + i30 is a real number.
Concept: undefined >> undefined
Find the value of i49 + i68 + i89 + i110
Concept: undefined >> undefined
Find the value of i + i2 + i3 + i4
Concept: undefined >> undefined
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Concept: undefined >> undefined
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Concept: undefined >> undefined
Find the derivative of the following function by the first principle: `(x - 1)/(2x + 7)`
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
(2i3)2
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Concept: undefined >> undefined
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
Concept: undefined >> undefined
