ECAT Mathematics Online Test

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  D

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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  A
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  B
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  D

n different objects can be arranged taken all at a time in ______

• (n + 1)! ways A
• (n - 1)! ways B
• n! ways C
• n ways D

If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

• 1 A
• 2 B
• 0 C
• -2 D

If a, b, c are in A.P., then 3^a, 3^b, 3^care in

• A.P. A
• G.P. B
• H.P. C
• None of these D

The set {1,-1,i,-i}

• Form a group w.r.t addition A
• Form a group w.r.t multiplication B
• Does not form a group w.r.t multiplication C
• Not closed under multiplication D

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  A
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  B
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  C
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  D

• 3K A
• K2 B
• K3 C
• K D

The sum of indicated terms of a sequence is called

• Arithmetic series A
• Series B
• Harmonic series C
• None of these D

A relation in which the equality is true for all values of the unknown is called ______

• An identity A
• An equation B
• A polynomial C
• None of these D

If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

• -i A
• 2 + i B
• i C
• 2 - i D

The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is

• 2 A
• 1 B
• 0 C
• None of these D

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  A
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  B
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  C
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  D

f(x)g(x)- ∫g(x) f′(x) dx is equal to

• ∫f(x)g′(x)dx A
• ∫f′(x)g(x)dx B
• ∫f′(x)g(x)′dx C
• ∫f(x)g(x)dx D

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  A
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  B
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  C
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  D

A vector of magnitude zero is called

• Position vector A
• Null vector B
• Free vector C
• None of these D

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

• A = x, B = 1 A
• A = 0, B = 2 B
• A = -1, B = 1 C
• A = x-1, B = x + 1 D

• Improper rational fraction A
• Rational fraction B
• Proper rational fraction C
• None of above D

The 60th part of one minute is called

• Degree A
• Second B
• Radiam C
• None of these D

If the intersection of two sets is non-empty, but either is a subset of other are called

• Disjoint sets A
• Over lapping B
• Equal sets C
• None of these D

If the distance of any point on the curve from any of the two lines approaches zero then it is called

• Axis A
• Directrices B
• Asymptotes C
• None D

If ab > 0 and a < 0, which of the following is negative?

• b A
• -b B
• -a C
• (a - b)² D

The set of positive integers, 0 and negative integers is known as the set of

• Natural numbers A
• Rational numbers B
• All integers C
• Irrational numbers D

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  A
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  B
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  C
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  D

• 3x²+ 2 A
• 3x²+ 2x + 3 B
• x³+ x² C
• none of these D

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  B
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  C
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  D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

The area between the x-axis and the curve y = x² + 1 from x = 1 to 2 is:

• 15/6 A
• 15/4 B
• 10/4 C
• 10/3 D

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  B
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  C
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  D