Question # 1

Water seeps out of a conical filter at eh constant rate of 5 cm/sec. the height of the cone of water in the filter is 15 cm. the height of the filter is 20 cm and radius of the base is 10 cm. the rate at which the height of the water decreases is

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8 . 7 . 6. 5 in factorial form is

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A monoid (G, *) is said to be group if

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have identity element

is commutative

have inverse of each element

None of these

The probability to get an odd number in a dice thrown once is

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6

1

1/6

1/2

2x + 3y > 4 is a linear inequality in

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one variable

two variables

three variables

none of these

The expansion of (1 - 3x)^-1is valid if

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| x | < 1

| x | < 3

| x | < 1/3

None of these

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

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The domain of y = cos-1 x is

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-∞ < x < ∞

-1≤ x≤ 1

x≤ -1 or x ≥ 1

None of these

csc(-π/2) = __________;

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0

1

-1

Undefined

Given X.Y are any two sets such that number of elements in X = 18, number of elements in set Y = 24,and number of elements in set X∪ Y =40,then number of elements in set x∩ Y =

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3

1

2

4

A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is

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50

25

10

100

x = ________ is in the solution of 2x + 3 > 0

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1

-2

-3

-4

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If a≠ , b≠ 0 and|a=b|=|a-b|,then vectors a and b are:

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Parallel to each other

Perpendicular to each other

Inclined at 60^o

neither parallel nor perpendicular

In a triangle ABC, if angle A = 72° , angle B = 48° and c = 9 cm then Ĉ is

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69°

66°

60°

63°

√11 is

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an irrational number

Rational number

odd number

Negative number

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a^xIn a + c

a^x+ c

x a^x+ c

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A

A'

U

U'

When rational fraction is separated into partial fractions, the result is

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an identity

A fraction

A partial sum

Improper fraction

The angle of depression of a point A on the ground from the top of the tower is 30𝜊,then the angle of elevation of the top of the tower at the point A is