Mathematics | ECE Electronics and Communication Engineering | TANCET Anna University Online Objective Test

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Three Dimensional Geometry Prepare / Learn

Q1.

Find the values of p so that the lines

\frac{1 - x}{3} = \frac{7 y - 14}{2 p} = \frac{z - 3}{2} a n d \frac{7 - 7 x}{3 p} = \frac{y - 5}{1} = \frac{6 - z}{5}

are at right angles.

A. p=7012

B. p=7215

C. p=7113

D. p=7011

Answer : Option B
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Permutations and Combinations Prepare / Learn

Q2.

If $^{n} P_{5} = 60^{n - 1} P_{3},$ then n is

A. 10

B. none of these

C. 12

D. 6

Answer : Option A
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Introduction to Three Dimensional Geometry Prepare / Learn

Q3. The line

x = x_{1}, y = y_{1}

A. none of these.

B. parallel to x axis

C. parallel to z axis

D. parallel to y axis

Answer : Option C
Explaination / Solution:

The line

x = x_{1}, y = y_{1}

is parallel to Z- axis as here value of x and y is fixed . Here whatever be the value of z , x and y will be fixed So it represent a plane parallel to Z axis

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Matrices Prepare / Learn

Q4.

then B equals

[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

[\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}]

[\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}]

A. - I cosθ+Jsinθ

B. I sin θ+Jcosθ

C. I cosθ−Jsinθ

D. I cosθ+Jsinθ

Answer : Option D
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Differential Equations Prepare / Learn

Q5. General solution of

\frac{d y}{d x} = (1 + x^{2}) (1 + y^{2})

c o t^{- 1} y

= x +

\frac{x^{3}}{3} + C

c o t^{- 1} y

= x +

\frac{x^{3}}{3} + C

c o t^{- 1} y

= x +

\frac{x^{3}}{3} + C

c o t^{- 1} y

= x +

\frac{x^{3}}{3} + C

Answer : Option B
Explaination / Solution:

\frac{d y}{d x} = (1 + x^{2}) (1 + y^{2}) \int \frac{1}{1 + y^{2}} d y = \int (1 + x^{2}) d x \tan^{- 1} y = x + \frac{x^{3}}{3} + C

Since

\int \frac{d x}{1 + x^{2}} = t a n^{- 1} x + c

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Complex Numbers and Quadratic Equations Prepare / Learn

Q6. he locus of the equation

| \frac{3 z - 1}{z - 1} | = 1

A. a circle

B. a straight line

C. an ellipse

D. none of these.

Answer : Option A
Explaination / Solution:

We have this is a circle with centre (1/4,0) and radius =1/4.

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Binomial Theorem Prepare / Learn

Q7. 5th term from the end in the expansion of

{(\frac{x^{3}}{2} - \frac{2}{x^{2}})}^{12}

A. 7920x4

B. −7920x4

C. −7920x−4

D. 7920x−4

Answer : Option D
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Maths Sets Prepare / Learn

Q8. If A = { 1,2,3,4 } and B = { 4,5,6,7 } then A−B =

A. { 1,2,3,4 }

B. { 5,6,7 }

C. { 1,2,3 }

D. { 4 }

Answer : Option C
Explaination / Solution:

Given A={1,2,3,4} and B={4,5,6,7}

A-B set will contain those elements which are present in A but not in B

we can see $A \cap B = {4}$

Now $A - B = A - (A \cap B)$

so $A - B = {1, 2, 3, 4} - {4} = {1, 2, 3}$

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Application of Derivatives Prepare / Learn

Q9. The equation of the normal to the curve y = sinx at (0, 0) is

A. x=0

B. y=0

C. x+y=0

D. x-y=0

Answer : Option C
Explaination / Solution:

Since ,

\frac{d y}{d x} = \cos x,

therefore , slope of tangent at ( 0 , 0 ) = cos 0 = 1 and hence slope of normal at ( 0 , 0 ) is - 1 .

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Application of Integrals Prepare / Learn

Q10. The area bounded by the parabola

y^{2}

= x and the straight line 2y = x is

A. 1 sq. units

B. 2/3 sq. units

C. 4/3 sq. units

D. 1/3 sq. units

Answer : Option C
Explaination / Solution:

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