JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year BASIC MATHEMATICS Previous Question Paper (March/April - 2023 - R22)

B.Tech | I Year | I-I | R22 | March/April - 2023

Answer PaperPaper Code: 181ACMaximum Marks: 60Time: 3 Hours

Note: This question paper contains two parts A and B. i) Part- A for 10 marks, ii) Part - B for 50 marks. Part-A is a compulsory question which consists of ten sub-questions from all units carrying equal marks. Part-B consists of ten questions (numbered from 2 to 11) carrying 10 marks each. From each unit, there are two questions and the student should answer one of them. Hence, the student should answer five questions from Part-B.

Part A

110 marks

Define a square matrix.

1 marks

Answer

A square matrix is a matrix in which the number of rows is equal to the number of columns, denoted as an n × n matrix.

Find the root of the equation

3x + 6=0

1 marks

Answer

Given 3x + 6 = 0, then 3x = -6, which implies x = -2.

Multiply

3 + 4i

7 - 3i

1 marks

Answer

Write the number of quadrants and octants in a cartesian coordinate system.

1 marks

Answer

Define

tan(x)

in terms of

sin(x)

and

cos(x)

1 marks

Answer

Find A and B in

A/(x+1) + B/(x-1) = 2/(1-x^2)

1 marks

Answer

Write the domain of the function

f : {(1,2),(2,3),(3,4),(4,5)}

1 marks

Answer

Find the differentiation of

sin(x)

1 marks

Answer

Write an example of a first order and first degree differential equation.

1 marks

Answer

Define an event of a random experiment.

1 marks

Answer

Part B

210 marks

A = [[2,-3,1],[7,8,5]]

and

B = [[1,0,1],[2,4,1]]

then find A+B and A-B.

6 marks

Answer

Solve the equation

x^4 + x^3 + 4x^2 + 6x + 5 = 0

given one root is i.

4 marks

Answer

A = [[2,-1,2],[1,3,-4]]

and

B = [[1,2],[3,-0],[5,4]]

then verify that

(AB)' = B'A'

10 marks

Answer

410 marks

z = cos(theta) + i sin(theta)

prove that

(1+z)/(1-z) = i cot(theta/2)

5 marks

Answer

Evaluate

((1+i sin alpha + cos alpha)/(1+i sin alpha - cos alpha))^n

5 marks

Answer

a = a_1 i + a_2 j + a_3 k

and

b = b_1 i + b_2 j + b_3 k

then find

a.b

and

a x b

10 marks

Answer

610 marks

Prove that

sin^2(theta) + sin^2(theta + pi/3) + sin^2(theta - pi/3) = 3/2

5 marks

Answer

Explain the graph of

y = cos(x)

5 marks

Answer

Resolve

x^2 / ((x+1)(x-2)(x+3))

into partial fractions.

10 marks

Answer

f(x) = { 3x^2-2, x > 3; 3, -2 <= x <= 3; 2x+1, x < -2 }

then find

f(4), f(2.5), f(-2), f(-4)

and

f(-7)

10 marks

Answer

910 marks

Find the differentiation of a function

x^2 + 3x + 2

5 marks

Answer

Find the integration of a function

e^(25x) + x^2

5 marks

Answer

1010 marks

Form a differential equation by the elimination of arbitrary constant from

y=mx+c

5 marks

Answer

Solve the differential equation

xdx + ydy = 0

5 marks

Answer

1110 marks

Write the axioms of probability.

5 marks

Answer

State and prove addition theorem of probability.

5 marks

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year BASIC MATHEMATICS Previous Question Paper (March/April - 2023 - R22)

Part A

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Part B

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