Question # 1

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

Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is

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375

500

625

150

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0

1

13

Let a₁, a₂, a₃, a₄and a₅be such that a₁, a₂, and a₃are in A.P., a₂, a₃and a₄are in G.P and a₃, a₄and a₅are in H.P. Then, a₁, a₃and a₅are in

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G.P.

A.P.

H.P.

None of these

Which of the following is a quadrantal angle

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30°

45°

60°

90°

√x = ______ if is a prime number

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Rational no

Natural no

Irrational no

Complex no

If a force F = 2i + j +3k acts at point (1,-2,2) of a body then the moment of F about a pint lying on the line of action of the force is

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5

Equal to the moment of the force about origin

0

Cannot be found

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A quadratic equation in x is an equation that can be witten in the form

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ax²+ b = 0

ax³ +b²+c=0

ax² +bx+c=0

ax³ +bx³+cx=0

The ratio in which the line y- x+ 2 =0 divides the line joining (3,-1) and (8,9) is

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2:3

-2:3

3:2

-3:2

A square matrix A = [aij] is upper triangular when

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

d/dx (3y⁴) =

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12y³ dy/dx

8y³

8y³ dy/dx

12y³

The general solution of the differential equation dy/dx = log x is

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Y = -x log x- x +c

Y = x log x + x²

Y = x log x -x +c

Y= 2x log x + 2x +c

Domain of Y = csc x is

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R - nπ, n ε I

R

R -nπ/2,nεI

All negative Integers

The point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is

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2

13

7

8

If a and b are any two distinct negative real numbers and G-ab where A.G.H represent arithmetic geometric and harmonic means then

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1

ω²

ω

0

Complex roots of real quadratic equation occur in

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

A die is thrown what is the probability that there is a prime number on the top?

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1/2

1/3

1/6

2/3

The angle a (0° < a< 180°) measured counterclockwise from positive x-axis to a non-horizontal straight line / is called the

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Rotation

Inclination

Radian

None

The sum of the series 1+5+9+13+17+21+25+29 is:

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10 cm

20 cm

30 cm

40 cm

P(x) = 2x⁴ -3x³ +2x-1 is polynomial of degree

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1

2

3

4

An m x n matrix is said to be rectangular if

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Forms a group w.r.t. addition

Non commutative group w.r.t. multiplication

Forms a group w.r.t. multiplication

Doesn't form a group

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