Free Printable Mock Test

1.

Write the characteristic equation of the matrix

a)

$\lambda^2-4\lambda-17=0$

b)

$\lambda^2+4\lambda-17=0$

c)

$\lambda^2+4\lambda+17=0$

d)

$\lambda^2-4\lambda+17=0$

2.

Find the determinant of the matrix

a)

-6

b)

6

c)

-10

d)

10

3.

Solve $\lambda^2-10\lambda+16=0.$

a)

$\lambda=-2,\ -8$

b)

$\lambda=-2,\ 8$

c)

$\lambda=2,\ 8$

d)

$\lambda=2,\ -8$

4.

Find the sum of the squares of the Eigen values of the matrix

a)

18

b)

7

c)

13

d)

19

5.

Find the sum and product of the Eigen values of the matrix

a)

sum=9

pdt=9

b)

sum=6

pdt=7

c)

sum=7

pdt=8

d)

sum=8

pdt=7

6.

If two Eigen values of the matrix are 1 and 3, then find the third

Eigen value.

a)

3

b)

2

c)

1

d)

-3

7.

The product of 2 Eigen values of the matrix is 6. Find the third Eigen

Value of this matrix.

a)

1

b)

-1

c)

2

d)

-2

8.

Find the sum of the Eigen values of the matrix $A^{-1}$

a)

$\frac{30}{31}$

b)

$\frac{31}{30}$

c)

$\frac{21}{30}$

d)

$\frac{20}{30}$

9.

If 2, -3, 4 are Eigen values of A, then the Eigen values of $A^{-1}$ =--------.

a)

$-2,\ 3,\ -4$

b)

$-\frac{1}{2},\ \frac{1}{3},\ -\frac{1}{4}$

c)

$\frac{1}{2},\ \frac{1}{3},\ \frac{1}{4}$

d)

$\frac{1}{2},\ -\frac{1}{3},\ \frac{1}{4}$

10.

If -1, 2, 3 are Eigen values of the matrix A, then the Eigen values of the matrix A³are ------

a)

-1, 8, 27

b)

1, 6, 9

c)

1, 8, 27

d)

-1, 6, 27

11.

If 1, -3, 4 are the Eigen values of the matrix A, then the Eigen values of the matrix 2A are ---------.

a)

1, -9, 16

b)

1, 9, 16

c)

2, -6, 8

d)

2, 6, 8

12.

State Cayley-Hamilton theorem.

a)

Every matrix satisfies its own characteristic equation

b)

Every square matrix satisfies its own characteristic equation

c)

Every square matrix satisfies its own polynomial equation

d)

Every square matrix satisfies its equation

13.

Write the matrix of the quadratic form $2x^2-3y^2+5z^2+4xy-6yz+16zx$

a)

b)

c)

d)

14.

Write the quadratic form corresponding the the matrix

a)

$6x^2+3y^2+14z^2+4xy+18xz+4yz$

b)

$6x^2+3y^2+14z^2+2xy+9xz+2yz$

c)

$12x^2+6y^2+28z^2+4xy+18xz+4yz$

d)

$6x^2+3y^2+14z^2+4xz+18xy+4yz$

15.

Write the rank of the quadratic form whose canonical form is $3y_1^2-4y_2^2+y_3^2$

a)

0

b)

1

c)

2

d)

3

16.

Find the index of the quadratic form whose canonical form is $y_1^2+2y_2^2-4y_3^2$

a)

2

b)

1

c)

3

d)

4

17.

Find the signature of the quadratic form whose canonical form is $y_1^2+2y_2^2-4y_3^2$

a)

4

b)

3

c)

1

d)

2

18.

Determine the nature of Q.F whose canonical form is $y_1^2+2y_2^2-4y_3^2$

a)

Positive definite

b)

Indefinite

c)

Negative semi-definite

d)

Negative definite

19.

Determine the nature of Q.F whose canonical form is $3y_1^2+5y_2^2+4y_3^2$

a)

Positive semi-definite

b)

Indefinite

c)

Negative definite

d)

Positive definite

20.

If the Eigen values of the matrix are 0, -1, -2 then the nature of the quadratic form is -----

a)

indefinite

b)

negative semi-definite

c)

negative definite

d)

positive semi-definite

21.

If all the Eigen values of the matrix are in negative, then the nature of the quadratic form is -------------.

a)

negative definite

b)

negative semi-definite

c)

positive semi-definite

d)

indefinite

22.

In solving algebraic and transcendental equations, the iteration formula for Newton-Raphson method

is ----------.

a)

b)

c)

d)

23.

Bisection method is also known as ------------ method.

a)

Interval Halving

b)

Newton-Raphson

c)

Regula Falsi

d)

Newton's

24.

In solving the function x² -2=0 using Newton-Raphson method, if the initial guess x₀ =3, then the

subsequent estimate x₁ will be -----.

a)

1

b)

2

c)

1.5

d)

1.83

25.

In the bisection method for root finding, identify the primary requirement for the function

a)

Continuous on the interval [a, b]

b)

Monotonic on the interval [a, b]

c)

Differentiable on the interval [a, b]

d)

Discontinuous on the interval [a, b]

26.

The convergence rate of the Newton-Raphson method is ---------------.

a)

logarithmic convergence

b)

exponential convergence

c)

quadratic convergence

d)

linear convergence

27.

Under what conditions might the Bisection method provide a more accurate result

compared to other root-finding methods?

a)

When the function is linear

b)

When the initial guess is very close to the root

c)

When the function is highly nonlinear

d)

When the function is continuously differentiable

28.

The condition for choosing a new interval in the Bisection method is based on the sign

of f(a) and f(b). The formula for this condition is:

a)

f(a)−f(b)=0

b)

f(a)⋅f(b)=0

c)

f(a)⋅f(b)>0

d)

f(a)⋅f(b)<0

29.

Identify the primary goal of interpolation in numerical analysis.

a)

To estimate the error in a numerical method

b)

To approximate a function at points between known values

c)

To calculate the definite integral of a function

d)

To find the roots of a polynomial

30.

What happens if the derivative of the function is zero at the current approximation in the Newton-

Raphson method?

a)

The method converges to a local minimum

b)

The iteration continues with the next approximation

c)

The method fails to converge

d)

The method converges to a local maximum

Mock Test

Total questions: 30

Worksheet time: 30mins

Similar Resources on Wayground