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DSSSB PGT Mathematics Mock Test - 2 - DSSSB TGT/PGT/PRT MCQ


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30 Questions MCQ Test - DSSSB PGT Mathematics Mock Test - 2

DSSSB PGT Mathematics Mock Test - 2 for DSSSB TGT/PGT/PRT 2024 is part of DSSSB TGT/PGT/PRT preparation. The DSSSB PGT Mathematics Mock Test - 2 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB PGT Mathematics Mock Test - 2 MCQs are made for DSSSB TGT/PGT/PRT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for DSSSB PGT Mathematics Mock Test - 2 below.
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DSSSB PGT Mathematics Mock Test - 2 - Question 1

Which one will replace the question mark ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 1

(16 + 13) = (14 + 15)

and (28 + 12) = (10 + 30)

Therefore (29 + 16) = (15 + 30).

DSSSB PGT Mathematics Mock Test - 2 - Question 2

Solve problems using substitution (Mathematical Operations): If A > B, B > C and C > D, then which of the following conclusions is definitely wrong?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 2

Given: A > B, B > C and C > D

After combining the operators,

we get: A > B > C > D

Now, checking the options:

Option A: A > D → True (As, A > B > C > D gives A > D)

Option B: A > C → True (As, A > B > C > D gives A > C)

Option C: D > A → False (As, A > B > C > D gives A > D)

Option D: B > D → True (As, A > B > C > D gives B > D)

So, Option C, D > A is definitely wrong.

Hence, the correct answer is "Option c".

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DSSSB PGT Mathematics Mock Test - 2 - Question 3

Who acts as the ex-officio Chairman of the Supreme Court of India?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 3

The Chief Justice of India acts as the ex-officio Chairman of the Supreme Court.

DSSSB PGT Mathematics Mock Test - 2 - Question 4

Cell has ability to extract _____ energy from food molecules:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 4

Cells has ability to extract chemical energy from food molecules. The energy present in food molecules like glucose undergo respiration to produce chemical energy in form of ATP.

DSSSB PGT Mathematics Mock Test - 2 - Question 5

Direction: Read the following passages carefully and answer the question that follows.
"Cloning is an advanced technological invention for producing a genetic twin of a living thing, an organism that starts life with the same genes as its parents. In mammals, DNA is taken from an adult animal and then it is inserted into an egg cell from another animal. This egg then divides into an embryo. The embryo is then transplanted into a surrogate mother and grown to term. This process has worked in animals like cows, sheep, goats, mice, pigs, rats, cat, monkeys, and horses." The opponents of human cloning say that an embryo at any stage of development is a human life. worthy of protection and any kind of research that entails destroying an embryo is immoral, unethical, no matter how worthy the intent may be. It involves using human beings as means; it turns human life into a commodity and fosters a culture of dehumanization.

Q. Find out the false statement out of the given options.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 5

In cloning, embryo is transplanted.

DSSSB PGT Mathematics Mock Test - 2 - Question 6

Direction: Read the following passages carefully and answer the question that follows.
"Cloning is an advanced technological invention for producing a genetic twin of a living thing, an organism that starts life with the same genes as its parents. In mammals, DNA is taken from an adult animal and then it is inserted into an egg cell from another animal. This egg then divides into an embryo. The embryo is then transplanted into a surrogate mother and grown to term. This process has worked in animals like cows, sheep, goats, mice, pigs, rats, cat, monkeys, and horses." The opponents of human cloning say that an embryo at any stage of development is a human life. worthy of protection and any kind of research that entails destroying an embryo is immoral, unethical, no matter how worthy the intent may be. It involves using human beings as means; it turns human life into a commodity and fosters a culture of dehumanization.

Q. What does a 'surrogate mother' mean?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 6

Here the expression surrogate has been used as an adjective meaning replacing someone else (human beings or animals) or used instead of somethings else. In this way option 'd' clears the meaning.

DSSSB PGT Mathematics Mock Test - 2 - Question 7

Sum of the three consecutive number is 1956. What is 23% of the highest number ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 7

X+x+1+x+2 = 1956
3x = 1956 – 3 = 1953
X = 1953/3 = 651
X+3 = 653
23% of largest num = 23*653/100 = 150.19

DSSSB PGT Mathematics Mock Test - 2 - Question 8

In a maternity centre, 5% of all the childbirth cases result in twins. What is the approximate percentage of twins out of total children born?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 8

 Let there be x number of birth cases.
Thus, the number of birth cases of twins = (5*x)/100 = x/20
So the total number of children born are = x + (x/20)(since in cases of twins there is an additional child) = 21x/20
Total number of twin born = (x/20)* 2 = x/10
percentage of twins in the total population born = ((x/10)/(21x/20)) * 100 = 9.5 %

DSSSB PGT Mathematics Mock Test - 2 - Question 9

The geometric mean and arithmetic mean of two non-negative observations are 8 and 12 respectively. Then what is the harmonic mean of the observations equal to?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 9

Given:
G = 8
A = 12
As we know, G2 = AH

⇒ H = G2 / A

= 82 / 12

= 5.3

DSSSB PGT Mathematics Mock Test - 2 - Question 10

If a number is increased by 30% and then it is decreased by 60%. Find the new number is how much percent of the original number:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 10

Let the number be 100

By increasing it by 30% we'll get 

We'll get 130

Again this number is decreased by 60%

⇒ By decreasing it by 60% we'll get

⇒ New number = 52

⇒ Required percentage

⇒ The new number is 52% of the original number

DSSSB PGT Mathematics Mock Test - 2 - Question 11

Write the set A = {1, 4, 9, 16, 25, ...} in set-builder form :

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 11

Given:
If we see the pattern here, the numbers are squares of natural numbers, such as:


And so on,

A = {x : x is the square of a natural number}

Or we can write;

DSSSB PGT Mathematics Mock Test - 2 - Question 12

What is equal to (where )?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 12

Given,

DSSSB PGT Mathematics Mock Test - 2 - Question 13

Rs. 4200 is divided among X,y, and Z in the ratio of 5 : 10 ; 6. What is the share (in Rs.) of X?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 13

Given,

Total amount = Rs. 4200

Ratio of X, Y and Z = 5 : 10 : 6

5 = 10 + 6 = 21 units

According to the question:

21 units = 4200

∴ The share of X is Rs. 1000.

DSSSB PGT Mathematics Mock Test - 2 - Question 14

If 63% of persons like oranges while 76% like apples, what can be said about % of persons who like both oranges and apples? Each person eats at least one fruit.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 14

Given:

So, 39% of people eat both orange and apple.

DSSSB PGT Mathematics Mock Test - 2 - Question 15

Two fair dice are rolled. What is the probability of getting a sum of 7?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 15

According to the question,

Favourable event = 

Probability = 6/36 = 1/6

DSSSB PGT Mathematics Mock Test - 2 - Question 16

Find the conjugate of .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 16

Given:


Conjugate of this complex number is .

DSSSB PGT Mathematics Mock Test - 2 - Question 17

The differential form of the equation :

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 17

Given equation is

There are two constants and so differentiate two times

Differentiating w.r.t

...(1)

Again differentiating w.r.t

From equation (1),

DSSSB PGT Mathematics Mock Test - 2 - Question 18

In , the area of quadrilateral . If , then the area of  is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 18

Given,

the area of quadrilateral .

AN : NC

So,

Area of  unit and area of  unit

Now, Area of quadrilateral area of  - area of

DSSSB PGT Mathematics Mock Test - 2 - Question 19

Find the interval in which the function is strictly increasing ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 19

Concept: 

If f′(x) >  0 at each point in an interval, then the function is said to be strictly increasing.

Calculations:

Given,

Differentiating, we get

is strictly increasing function

DSSSB PGT Mathematics Mock Test - 2 - Question 20

Find the coefficient of in the expansion of .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 20

Suppose occurs in the term of the expansion .

Now,

Comparing the indices of as well as in and in we get .

Thus, the coefficient of is,

DSSSB PGT Mathematics Mock Test - 2 - Question 21

There are 3 coins in a box. One is a two-headed coin; another is a fair coin; and third is biased coin that comes up heads 75% of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 21

Let and be the respective events of choosing a two-headed coin, a biased coin and an unbiased coin.

Let A be the event that coin shows head.

We have to find  So, by using baye's theorem, we obtain:

DSSSB PGT Mathematics Mock Test - 2 - Question 22

A line makes an angle with the , and axes. Then is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 22

Given,

We know that,

Sum of squares of the direction cosines of a line is equal to unity.

So,

DSSSB PGT Mathematics Mock Test - 2 - Question 23

In  the coordinates of are  and the middle point of has the coordinates . The centroid of triangle is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 23

Apollonious's theorem formula:
a,b,c: lengths of sides
m : median

Consider the triangle shown,

The formula for length of median to side BC

In any triangle as shown in fig from Apollonius theorem.

Cosine rule:
Consider the triangle as shown:

Following are the conclusions for the cosine rule

Given coordinates of B(0,0),AB = 2 and ∠ABC = (��/3)
mid point of ���� has coordinates (2,0).

���� = ����
from theorem and equation (1)

Length of median = √2
From the cosine rule mentioned above the length of side AC is:

From the distance formula between AB
y12 + x12 = 4⋯ (i)
From the distance formula between AC

solving (i) and (ii) we get

Substituting this value in (i) we get

The centroid is calculated as:

DSSSB PGT Mathematics Mock Test - 2 - Question 24

Let be the relation in the set given by Choose the correct answer.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 24

Now, Since

Also, as

and, as

Now, consider  

We have and also,


DSSSB PGT Mathematics Mock Test - 2 - Question 25

If and and then

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 25

DSSSB PGT Mathematics Mock Test - 2 - Question 26

If the matrix is singular, then is equal to :

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 26

A matrix is said to be singular if its determinant is zero

i.e. for matrix A to be singular, |A| = 0

For a singular matrix, the inverse doesn't exist

Given that, matrix is singular.

Then,

DSSSB PGT Mathematics Mock Test - 2 - Question 27

Let the curve be the mirror image of the parabola with respect to the line . If and are the points of intersection of with the line , then the distance between and is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 27

The parabola has axis along axis and opens in positive direction of axis. The line cut the and axis at points (-4,0) and (0,4) respectively. 

The graph is shown below:

The given equation of a parabola is .

Compare it with general form to get  

So, its vertex is (0,0) and focus is (1,0) 

It is given that the line intersect the image of parabola at points and

Note that is the latus rectum of the new parabola.

So, we only need to find the image of vertex (0,0) and focus (1,0) 

First find the image of vertex (0,0) about the line .

Let the image of vertex (0,0) be then

So, image of vertex is (-4,-4).

Now find the image of focus (1,0) about the line .

Let it be then

So, image of focus is (-4,-5).

So, the focus of the new parabola is at a distance of 1 unit from the vertex on the axis. 

So, we have  

Therefore, the distance between and is, latus rectum of new parabola


DSSSB PGT Mathematics Mock Test - 2 - Question 28

The roots of quadratic equation are:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 28

Given,

Dividing the equation by , we get

By adding to both sides of the equation, we get

The square root of a negative number is imaginary, therefore, there is no real root for the given equation.

DSSSB PGT Mathematics Mock Test - 2 - Question 29
If and are any three sets, then is:
Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 29

We have to find the value of .



(using distributive law)

DSSSB PGT Mathematics Mock Test - 2 - Question 30

A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows is

Detailed Solution for DSSSB PGT Mathematics Mock Test - 2 - Question 30

The probability of getting a head on tossing a coin
The probability of getting a six on rolling a dice
These two events are independent.
So, the probability that the coin shows the head and the dice shows is given by-

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