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

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

Q1. The differential coefficient of log (| log x |) w.r.t. log x is

A. 1x|logx|

B. none of these

C. 1logx

D. 1xlogx

Answer : Option C
Explaination / Solution:

Let y =

\log (| l o g x |) a n d z = l o g x,

then , we have ;

\frac{d y}{d z} = \frac{\frac{d y}{d x}}{\frac{d z}{d x}} = (\frac{1}{\log x} . \frac{1}{x}) / (\frac{1}{x})

\Rightarrow \frac{1}{\log x}

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

Q2. Consider the line integral

The line C is shown in the figure below.

A. (1/2)i

B. (2/3)i

C. (3/4)i

D. (4/5)i

Answer : Option B
Explaination / Solution:

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

Q3. Find the distance of the point (2, 3, – 5) from the plane x + 2y – 2z = 9

A. 2

B. 4

C. 3

D. 5

Answer : Option C
Explaination / Solution:

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

Q4. If

ω

is a cube root of unity , then the linear factors of

x^{3} + y^{3}

in complex numbers are

A. (x+y)(x+yω)(x−yω2)

B. (x−y)(x+yω)(x+yω2)

C. (x+y)(x+yω)(x +yω2)

D. (x+y)(x−yω)(x−yω2)

Answer : Option C
Explaination / Solution:

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

Q5. At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (– 4, –3). Find the equation of the curve given that it passes through (–2, 1).

A. (x + 3)2= y + 4

B. (x + 5)2= 2y + 3

C. (x + 5)2= 2y + 3

D. (x + 4)2= y + 3

Answer : Option D
Explaination / Solution:

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

Q6. The index of the power of x that occurs in the

6^{t h}

term in the expansion of

{(\frac{4 x}{5} - \frac{8}{5 x})}^{9}

A. 3

B. 2

C. -1

D. 1

Answer : Option C
Explaination / Solution:

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

Q7. Sets A and B have 3 and 6 elements respectively . What can be the minimum number of elements in A U B

A. 18

B. 3

C. 9

D. 6

Answer : Option D
Explaination / Solution:

n(A) = 3

n(B)=6

n(AUB) = n(A)+n(B)-n(A $\begin{array}{l} \cap \end{array}$ B)

for minimum number of elements in $A U B$

n(A $\begin{array}{l} \cap \end{array}$ B)= 3

so n(AUB = 6

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

Q8. If

y = \sin^{- 1}

x and z =

\cos^{- 1} \sqrt{1 - x^{2}},

then

\frac{d y}{d z} =

A. tan−1x1−x2√

B. 0

C. 1

D. -1

Answer : Option C
Explaination / Solution:

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

Q9. A pack of coffee powder contains a mixture of x grams of coffee and y grams of choco. The amount of coffee is greater than that of choco and each coffee powder pack is atmost 10 grams. Which of the following inequations describe the conditions given ?

A. None of these

B. x + y < 10 ; x < y

C. x + y ≤ 10 ; x > y

D. x + y < 12 ; x > y

Answer : Option C
Explaination / Solution:

Given in the mixture ,amount of coffee= x grams

Amount of choco=y grams

Amount of coffee is greater than that of choco $\Rightarrow$ $x > y$

Each coffee powder pack is atmost 10 grams $\Rightarrow$ $x + y \leq 10$

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

Q10. The sum of first three terms of a G.P. is to the sum of next three terms is 125 : 27. The common ratio of the G.P. is

A. 53

B. 12

C. None of these

D. 35

Answer : Option D
Explaination / Solution:

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