Engineering Maths MCQ with Answers Set-1

This post contains a computer network related to 20 multiple-choice questions (EM SET-1) that help you to go through the subject and prepare you for engineering maths-related questions in a competitive exam.

Engineering Maths MCQ Test Series Set-1

Total Number of Questions: 20
Each question carries equal marks i.e 1
No Negative Marking

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1. Consider the function

Which of the above functions is/are increasing everywhere in [0,1]?

e^{-x}
x^{2}-sin x
\sqrt{x^{3}+1}

A.3 only

B.2 only

C.2 and 3 only

D.1 and 3 only

2. Let U = {1,2, ..., n}. Let A = $\left \{ (x,X)|x \in X,X\subseteq U\right \}$.Consider the following two statements on $\left| A \right|$.

$\left| A \right|$ = $n2^{n-1}$
$\left| A \right|$ =$\sum_{n}^{k} = 1^{k}\left( \frac{n}{k} \right)$

Which of the above statements is/are TRUE?

A.Only 1

B.Only 2

C.Both 1 and 2

D.Neither 1 nor 2

3. Let X be a square matrix. Consider the following two statements on X.

X is invertible.
Determinant of X is non-zero.

Which one of the following is TRUE?

A.1 implies 2; 2 does not imply 1.

B.2 implies 1; 1 does not imply 2.

C.1 does not imply 2; 2 does not imply 1.

D.1 and 2 are equivalent statements.

In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.

If the first question is answered wrong, the student gets zero marks.
If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.
If both the questions are answered correctly, the student gets the sum of the marks of the two questions.

The following table shows the probability of correctly answering a question and the marks of the question respectively.

question	Probability of answering correctly	marks
QuesA	0.8	10
QuesA	0.5	20

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

A.First QuesA and then QuesB. Expected marks 14.

B.First QuesB and then QuesA. Expected marks 14.

C.First QuesB and then QuesA. Expected marks 22.

D.First QuesA and then QuesB. Expected marks 16.

A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?

A.$\frac{r}{r+b}$

B.$\frac{r}{r+b+3}$

C.$\frac{r+3}{r+b+3}$

D.$\left (\frac{r}{r+b} \right )\left (\frac{r+1}{r+b+1} \right )\left (\frac{r+2}{r+b+2} \right )\left (\frac{r+3}{r+b+3} \right )$

6. Let A and B be two n x n matrices over real numbers, Let rank (M) and det (M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.

rank (AB)=rank (A) rank (B)
det (AB)=det(A) det (B)
rank (A+B)< rank (A)+rank (B)
det (A+B)<det (A) + det (B)

Which of the above statements are TRUE?

A.1 and 2 only

B.1 and 4 only

C.2 and 3 only

D.3 and 4 only

7. Consider the two statements

$S_1$:There exist random variables X and Y such that

$(\mathbb{E}[X-\mathbb{E}(X))(Y-\mathbb{E}(Y))] )^2>Var[X]Var[Y]$

$S_2$:For All random variables X and Y,

$Cov\left[X,Y\right]=\mathbb{E}[|X-\mathbb{E}\left[X\right]||Y-\mathbb{E}\left[Y\right]|]$

Which one of the following choices is correct?

A.Both $S_1$ and $S_2$ are true

B.$S_1$ is true but $S_2$ is false

C.$S_1$ is false but $S_2$ is true

D.Both $S_1$ and $S_2$ are false

8. For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows:
$s(P,Q)\sum_{t=1}^{n} (P[i].Q[i])$
let L be a set of 10-dimensional non-zero vectors such that for every pair if distinct vectors
$P, Q \epsilon L,s(P,Q) = 0$. What is the maximum cardinality possible for the set L?

A.9

B.10

C.11

D.100

9. A relation R is said to be circular if aRb and bRc together imply cRa.

Which of the following options is/are correct?

A.If a relation S is reflexive and symmetric, then S is an equivalence relation.

B.If a relation S is circular and symmetric, then S is an equivalence relation.

C.If a relation S is reflexive and circular, then S is an equivalence relation

D.(D) If a relation S is transitive and circular, then S is an equivalence relation.

10.

Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (Round off to 3 decimal places) is

A.0.225

B.0.125

C.0.175

D.0.205

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11.

Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is

A.7

B.5

C.6

D.4

12. The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is

A.Between 0.27 to 0.29

B.Between 0.35 to 0.39

C.Between 0.21 to 0.24

D.Between 0.31 to 0.34

13. Consider the following expression:

$\lim _{r\rightarrow -3} \frac{\sqrt{2x+22-4}}{x+3}$

The value of the above expression (rounded to 2 decimal places) is

A.0.24

B.0.25

C.0.30

D.0.36

14.

For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is

A.15 to 16

B.14 to 15

C. 12 to 13

D.10 to 11

15.

For $n\gt 2,\in \left\{ 0,1 \right\}^{n}$ be a non-zero vector. Suppose that x is chosen uniformly at random from $\left\{0,1\right\}^{n}$. Then, the probability that $\sum_{i=1}^{n}a_{i}x_{i}$ is an odd number is

A.0.5

B.0.7

C.1

D.0.9

16. Suppose that P is a 4x5 matrix such that every solution of the equation Px=0 is a scalar multiple of $[2 5 4 3 1]^{T}$. the rank is

A.6

B.5

C.4

D.7

17.

Suppose that f: R→R is a continuous function on the interval [-3, 3] and a differentiable function in the interval (-3, 3) such that for every x in the interval, ${f}'(x)\leq 2, if f(-3)=7$ is at most

A.17

B.22

C.19

D.24

18. Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B are subsets of S, and A ⊑ B is

A.50049

B.59049

C.10489

D.60842

19. Consider the following matrix.

$\begin{pmatrix}
0 & 1 & 1 & 1\\
1 & 0 & 1 & 1\\
1 & 1 & 0 & 1\\
1 & 1 & 1 & 0
\end{pmatrix}$

The largest eigenvalue of the above matrix is

A.2

B.3

C.4

D.5

20. A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities of 0.1 and 0.9 respectively, to a receiver (R).
In the graph below, the weight of edge (u,v) is the probability of receiving u when u is transmitted, where u,$\ v\in\left\{H, L\right\}$. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.

If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is

A.0.04

B.0.08

C.0.12

D.0.16

Engineering Maths MCQ Test Series Set-1

Total Number of Questions: 20

Each question carries equal marks i.e 1

No Negative Marking

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