Question # 1

The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is

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x²+ y²+ z²+ 2 ax +2 by + 2cz = 0

x²+ y²+ z²- 2ax - 2 by - 2cz = 0

x²+ y²+ z²- ax - by - cz = 0

x²+ y²+ z²+ ax + by + cz = 0

A number A is said to be the A.M between the two numbers a and b if a, A, b are in

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A.M

A.P

G.P

G.M

The period of 2 cos x is

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30π

7π

5π

2π

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5

25

3

If origin is the mid point of (a,3) and (5,b) then

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a = -5 , b = -3

a = 5 , b =3

a = -5 , b = 3

a = 5 , b = -3

The magnitude of a vector can never be

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Zero

Negative

Positive

None of these

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One-to-one and onto

One-to-one but not on to

Onto but not one-to-one

Neither one-to-one nor onto

Probability of an impossible event is

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0

-1

1

∞

Number of conics is

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1

3

2

4

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A = B

B = C

A = C

None of these

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

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p²- q²+ 2pr = 0

(p + r)²= q²- r²

p²+ q²- 2pr = 0

(p - r)²= q²+ r²

The upper 3/4 the portion of a vertical pole subtends an angle tan^-13/5 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

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20 m

40 m

60 m

80 m

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0

1

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direction ratios

direction cosines

direction angles

none of these

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The distance between the points (0 , 0) and (1, 2) is

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5

0

3

The identity element with respect to subtraction is

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0

1

-1

Does not exist

The transport of a rectangular matrix is a

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Square matrix

Rectangular matrix

Row matrix

Column matrix

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1 / 2

1 / 3

1 / 4

None of these

Domain of cot x is ______

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For an A.P common difference d

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Can be zero

May or may not zero

Cannot be zero

None of these

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sin x + c

-sin x + c

cos x + c

-cos x + c

In R, the multiplicative identity is

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0

1

-1

None

The set of all antiderivaties of f(= ∫f(x)dx) is the

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Definite integral

Indefinite integral

Integral

Area

A circle which touches one side of a triangle extermally and the other two sides produced is called

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In-circle

Circumcircle

e-circle

Point circle

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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

cos 3a =_______;

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3sin a - 4sin3 a

4sin a - 3sin3 a

3cos3 a - 4cos a

4cos3a - 3cos a

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