Question # 1

If n is any positive integer then n! > n²for

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Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21

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-3x + 4y =21

4x - 3x = 0

-3x + 4y = 25

None of these

The proposition S(k+1) is true when ______ is true∀K∈N

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S(n)

S(k)

S(1)

S(k-1)

The conic ax2+2hxy+by2+2gx+2fy+c= 0 never represent a circle if

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a≠ b,h≠0

a=b

h≠0

h=0

The coefficient of the third term of (8a-b)^1/3, after simplification is

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-228

1/288

1/220

-1/177

Let A be a square matrix. Then, 1/2 (A-A') is

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Skew-symmetric

Symmetric

Null

None of the above

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Rule of quotient of fraction

Golden rule of fraction

Rule for product of fraction

Principle for equality of fraction

Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

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7 / 40

5 / 40

11 / 40

None of these

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If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

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an ellipse

a hyperbola

a circle

a parabola

Given X, Y are any two sets such that number of elements in X=28, number of elements in set Y=28, and number of elements in set X∪Y=54, then number of elements in set X∩Y=

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-7 + 2i

7 + 2i

7-2i

√53

The value of the polynomial 3x³ + 4x² - 5x + 4 at x = -1 is

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A² + B²

A² + B²+ 2AB

A + B

A² + B² + AB+BA

If in isosceles right angled triangle one side is a then hypotenuse is

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a√2

a/2

a

Cannot be determined by given

If a rectangle has an area 81x² and length of 27x. then what is its width?

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3x

9x

3x²

9x²

Sec^-1 x=

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Cos^-1 1/x

Cosec^-1 1/x

Cos-1 (-x)

Tan^-1 x

What is the domain of y = Cot^-1 x?

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Set of irrational numbers only

Set of all real numbers

Set of integers only

Set of complex numbers only

If Z₁ = √-36, Z₂=√-25, Z₃= √-16, then what is the sum of Z₁, Z₂ and Z₃ ?

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√3 I

√7

-2-1

√5

Complex roots of real quadratic equation occur in

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

AreCot √3 =?

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π/2

π

2π

π/6

The complement of set A relative to universal set U is the set

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X

φ

Universal set

If the vector 2i+4j-2k and 2i +6j+xk are perpendicular then x-7

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4

8

14

7

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