Free Printable Quiz for PG students

1.

When a particle is thrown with a velocity in a particular direction then path gain by the particle is called-

a)

Straight line

b)

Projectile

c)

Catenary

d)

All of the above

2.

Assignment problem is a kind of

a)

Transportation problem

b)

Linear programming problem

c)

Both

d)

None

3.

$x_{n+1}=x_n-\frac{f\left(x_n\right)}{f'\left(x_n\right)}\$ is used to solve

a)

Transcendental equations

b)

Algebraic equations

c)

Both

d)

None

4.

Path of brachistochrone problem is

a)

Catenary

b)

Cycloid

c)

Circle

d)

All of the above

5.

In three dimensions, locus of a point whose distance from a fixed point remains always constant,is

(a)

6.

$x^2+y^2+z^2-ax-by-cz=0,\ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

is equation of

a)

Sphere

b)

Plane

c)

Circle

d)

Cone

7.

Finite difference methods for equal intervals is/are

a)

Newton Gregory forward

b)

Lagrange's

c)

Newton's divided difference

d)

Newton Gregory backward

8.

$\mu=\tan\lambda$ is called

a)

Radial acceleration

b)

Coefficient of friction

c)

Lami theorem

d)

None

9.

$\lim_{n\rightarrow\infty}\left(-1\right)^n$

a)

1

b)

-1

c)

Doesn't exist

d)

$\infty$

10.

The empty relation f on a non-empty set is

a)

equivalence relation

b)

partial order relation

c)

total order relation

d)

symmetric, anti-symmetric and transitive

11.

Which of the following statements is false?

a)

No point of the set is an interior points of Q

b)

Every point of the open interval (a, b) is an interior point of (a,b)

c)

Every point of the set R is an interior point of (a,b)

d)

Every point of the closed interval [a,b] is an interior point of [a,b]

12.

Which of the following set is bounded below but not bounded above?

a)

N

b)

Z

c)

Q

d)

R

13.

Which of the following set is nbd of each of its points?

a)

N

b)

Q

c)

z

d)

(a,b)

14.

If A and B are symmetric matrices and AB=BA, then

$A^{-1}$ B is a

a)

symmetric matrix

b)

skew-symmetric matrix

c)

identity matrix

d)

None of the above

15.

Check the correct statement.

a)

The identity of a subgroup is the same as that of the group

b)

The inverse of any element of a subgroup is the same as the inverse of the same regarded as an element of the group

c)

The order of any element of a subgroup is the same as the order of the element regarded as a member of the group

16.

If '0' is a binary operation such that a0b = ab +1, where

a,b $\in$ Z then the given operation is

a)

commutative and associative

b)

commutative but not associative

c)

associative but not commutative

d)

neither associative nor commutative

17.

Which of the following statements is true?

a)

Left cosets of a subgroup are neither disjoint nor identical

b)

Left cosets of a subgroup are either disjoint or identical

c)

Left cosets of a subgroup are always disjoint

d)

Left cosets of a subgroup are always identical

18.

Let order of a group G be prime number P, then

a)

G does not possess proper subgroups

b)

P is prime, it is divisible by 2

c)

G possess proper subgroups

d)

None of the above!

19.

Ring of polynomials over a field is a

a)

prime field

b)

group

c)

unique factorisation domain

d)

irreducible

20.

If u is a homogeneous function of x and y of degree n, then $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}$ is equal to

a)

n

b)

nu

c)

n/u

d)

u

21.

The asymptote of the curve y²(a + x) = (a − x)x² is

a)

x+a=0

b)

x-a=0

c)

x = 0

d)

y = 0

22.

what is the value of gamma 1/2

a)

$\sqrt{\pi}$

b)

$\sqrt{\frac{\pi}{2}}$

c)

$\sqrt{\frac{2}{\pi}}$

d)

$\sqrt{\frac{1}{\pi}}$

23.

$\int_0^1x^2\left(1-x^{ }\right)^3dx$

the value of the integralis

a)

1/6

b)

1/160

c)

1/16

d)

1/60

24.

A general solution of a linear differential equation with

constant coefficients is

a)

sum of particular solution and complementary function

b)

product of particular solution and complementary function

c)

quotient of particular solution and complementary function

d)

None of the above

25.

The relation z=(x+ a)(y+b) represents the partial differential equation

a)

z=p/q

b)

z = p q

c)

z=p-q

d)

None of these

26.

$\lim_{z\rightarrow0}\ \frac{\overline{z}}{z}$ is equal to

a)

0

b)

1

c)

1/2

d)

none of these

27.

The function f(z)=|z|² is

a)

everywhere analytic

b)

nowhere analytic

c)

analytic for z = 0

d)

None of these

28.

consider the function f(z)= $\frac{1}{z^4},\ z\ne0$

Which of the following is not correct?

a)

f(z) is continuous

b)

Cauchy-Riemann equations are satisfied

c)

f'(z) exists and equal to $-\frac{4}{z^5}$

d)

f(z) is differentiable only at origin

29.

The complex line integral is

a)

dependent of path

b)

independent of path

c)

independent of end points

d)

None of the above

30.

$\oint_{ }^{ }\ \ \frac{4z^2+9z+5}{\left(z+1\right)^2}dz\ ;\left|z\right|=2,\ z=-1$ is

a)

a pole of order 1

b)

a pole of order 3

c)

a pole of order 2

d)

not a pole

31.

Which one is greater?

a)

$2^{3^4}$

b)

$4^{3^2}$

32.

Write ramanujan number

(a)

33.

Which one is smallest among

a)

AM

b)

GM

c)

HM

34.

Fundamental period of sinx.cosx

a)

0

b)

π

c)

2π

d)

-2π

35.

Which year is known as National Mathematics Year?

a)

1887

b)

2012

c)

2020

d)

1947

36.

There is only one number in the entire Hindu Arabic number system which can be spelled with the same number of letters as itself. The number is

a)

one

b)

two

c)

three

d)

four

37.

It takes a 360 m long train 12 seconds to pass a pole. How seconds will it take to pass a platform 900 m long?

(a)

38.

What is ((-3, 6) ∩ (0, 3)) ∪ (-2, 1) in interval notation?

a)

(-2, 3)

b)

(-2, 1)

c)

(0, 3)

d)

(-3, 6)

39.

Generating function of sequence 2,6,18,54,162...... is

a)

$\frac{1}{1-3x}$

b)

$\frac{2}{1-3x}$

c)

$\frac{1}{1-x}$

d)

all of the above

40.

$Value\ of\ P\left(\phi\right)$ is

a)

$\left\{\phi\right\}$

b)

$\phi$

c)

U

d)

none

41.

2+4+6+8+10+.....2n=

a)

2n

b)

n(n-1)

c)

n(n+1)/2

d)

$n^2$

42.

In Boolean algebra a+b'=

(a)

43.

In how many ways digits 0,1,2.....,9 can be arranged so that 0 and 1 always come together?

a)

10!

b)

2(9)!

c)

9!

d)

8!

44.

Write the equation of plane parallel to XOY plane and at distance c from it.

(a)

45.

The smallest number which can be divided by each number from 1 to 10

(a)

Quiz for PG students

Total questions: 45

Worksheet time: 30mins

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