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DSSSB PGT Mathematics Mock Test - 1 - DSSSB TGT/PGT/PRT MCQ


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30 Questions MCQ Test DSSSB PGT Mock Test Series 2024 - DSSSB PGT Mathematics Mock Test - 1

DSSSB PGT Mathematics Mock Test - 1 for DSSSB TGT/PGT/PRT 2024 is part of DSSSB PGT Mock Test Series 2024 preparation. The DSSSB PGT Mathematics Mock Test - 1 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB PGT Mathematics Mock Test - 1 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 - 1 below.
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DSSSB PGT Mathematics Mock Test - 1 - Question 1

Four positions of a dice are shown below. What number must be at the bottom face when the dice is in the position as shown in the figure(iii)

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

From figures (i), (ii), (iv) we conclude that 5, 6, 1 and 2 lie adjacent to 4. Hence, 3 must lie opposite 4 and vice-versa. In fig. (iii), 3 is at the top and consequently 4 must lie at the bottom face.

DSSSB PGT Mathematics Mock Test - 1 - Question 2

A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?

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

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DSSSB PGT Mathematics Mock Test - 1 - Question 3

Study the following information carefully to answer the given questions
P × Q means P is father of Q
P ÷ Q means P is daughter of Q
P + Q means P is sister of Q
P – Q means P is husband of Q
In M ÷ N × O – P, How O related to M ?

Q.

In G×T+Q÷M, how is M related to G ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 3

Correct Answer :- B

Explanation : G×T+Q÷M

G(male) is father of T

T(female) is sister of Q

Q(female) is daughter of M

From the equations, we came to know, M is the wife of G.

DSSSB PGT Mathematics Mock Test - 1 - Question 4

Direction: Read the following passages carefully and answer the question that follows.
The ancient Harappan Civilization emerged, flourished and collapsed under a steadily weakening monsoon, according to new research findings, that scientists say, provide the strongest evidence yet to link its risk and fall to changing climate. A team of scientists has combined multiple sets of date to show that weakening monsoon and reduced river water initially stimulated intensive agriculture and urbanisation, but later precipitated the decline and collapse of the subcontinent's earliest cities. The scientist said their research also suggests that a larger river, summed to be the mythical Saraswati, which once watered the Harappan Civilization's heartland between the suggests it was a glacier fed river with origins in the Himalyas. The findings appear today in the US Journal Proceedings of the National Academy of Science

Q. What was the controversy in the passage?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 4

The controversy is about the monsoon fed river and the glacier fed river.

DSSSB PGT Mathematics Mock Test - 1 - Question 5

Statements:
Some mangoes are yellow.
Some tixo are mangoes.

Conclusions:
(1) Some mangoes are green.
(2) Tixo is a yellow.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 5

From the image:

  • Some mangoes are green. No
  • Tixo is a yellow. maybe or may not be

Neither of the conclusions follows.

DSSSB PGT Mathematics Mock Test - 1 - Question 6

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was: 

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 6

Total Valid votes are = 80% of 7500= 6000
If one has 55% vote then the other has left with 45% votes
Hence, 45% of 6000= 2700

DSSSB PGT Mathematics Mock Test - 1 - Question 7

If p = – 7 and q = 12 and x2+px+q=0, then the value of ‘x’ is

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 7

DSSSB PGT Mathematics Mock Test - 1 - Question 8

निम्नलिखित में से कौन सा शब्द "सोना” का पर्यायवाची नहीं है?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 8

वपु शब्द "सोना” का पर्यायवाची नहीं है। हाटक, हेम, कनक, "सोना" के पर्यायवाची शब्द हैं। वपु, शरीर का पर्यायवाची शब्द है।

DSSSB PGT Mathematics Mock Test - 1 - Question 9

इनमें से कौन सा विलोम-युग्म सही नहीं है?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 9

तिमिर का विलोम शब्द आलोक है। तिमिर, अंधकार का पर्यायवाची शब्द है तथा आलोक, प्रकाश का पर्यायवाची शब्द है।

DSSSB PGT Mathematics Mock Test - 1 - Question 10

Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 10

CD = AC = r units

DSSSB PGT Mathematics Mock Test - 1 - Question 11

What is the number of ways that 4 boys and 3 girls can be seated in a row so that boys and girls alternate?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 11

Number of ways to arrange n items = n!

Given: 4 boys and 3 girls can be seated in a row so that boys and girls alternate

The only pattern in which they can sit according to the given situation is

B G B G B G B

4 boys can be seated in 4! Ways

Girl can be seated in 3! Ways

Required number of ways,

= 4! × 3!

= 144

DSSSB PGT Mathematics Mock Test - 1 - Question 12

The base of a pyramid is a square whose area is 864 sq.cm, if the volume of the pyramid is 1296 cm3. Then find the height of the pyramid?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 12

The volume of a pyramid 

= 1/3 x  area of the base x height of the pyramid

⇒ 1/3 x 864 x  height = 1296

⇒  Height = 1296 x 3 / 864 = 4.5 cm

DSSSB PGT Mathematics Mock Test - 1 - Question 13

Let and be functions such that ,



and   

Which of the following statements is TRUE?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 13




hence option (D) is wrong







⇒ option (B) is wrong

has one solution

DSSSB PGT Mathematics Mock Test - 1 - Question 14

By mathematical induction is divisible by:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 14

Given:

f(n) = 

We have f(1) p2 + p + 1 which is divisible by p2 + p + 1..

Now, assume that f(m) is divisible by p2 + p + 1.

For f(m + 1) :

So, f(m + 1) is divisible by p2 + p + 1.

By mathematical induction f(n) is divisible by p2 + p + 1. for all n ∈ N.

DSSSB PGT Mathematics Mock Test - 1 - Question 15

If  Find the angle between the vectors and .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 15

Given: 

As we know that, the scalar product between any two vectors and is given by:

DSSSB PGT Mathematics Mock Test - 1 - Question 16

Out of 6 teachers and 8 students a committee of 11 is to be formed. In how many ways can this be done such that the committee has exactly 4 teachers?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 16

Given: There are 6 teachers and 8 students  out of which we need to form a committee of 11 members such that the committee has exactly 4 teachers in it.

If out 11 members of committee 4 are teachers then 7 members are students.

So, the committee compromises of 4 teachers and 7 students.

No. of ways in which 4 teachers can be selected from 6 teachers

No. of ways in which 7 students can be selected from 8 students

So, the number of ways in which the committee can be formed

As we know that,



So, the committee can be formed in 120 ways.

DSSSB PGT Mathematics Mock Test - 1 - Question 17

Find if the and terms of the expansion are equal.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 17

We know that,
General term of expansion (a+b)n is:

Finding 18th  term

Now it is given that:

DSSSB PGT Mathematics Mock Test - 1 - Question 18

If the fifth term of a GP is 2, then what will be the product of its first 9 terms?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 18

Given:

Let 'a' be the first term and 'r' the common ratio.

We know that,


Now, the product of 9 terms


DSSSB PGT Mathematics Mock Test - 1 - Question 19

If be given by then is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 19

DSSSB PGT Mathematics Mock Test - 1 - Question 20

The coefficient of in the expansion of is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 20

To find the coefficient of the terms in the expansion of , we will use .

Required power of is 11.

Thus, the coefficient of in the expansion of is 120.

DSSSB PGT Mathematics Mock Test - 1 - Question 21

Find the foot of the perpendicular of the point (4, 5, 4) on the plane x + 2y + z = 2.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 21

Let A (a, b, c) is foot of perpendicular of point P (4, 5, 4)

Given plane is x + 2y + z = 2.

So, PA will be normal to the given plane, so direction ratios of PA will be proportional to (1, 2, 1).

∵ PA passes from (4, 5, 4) and have direction ratios (1, 2, 1).

Equation of line PA (say)

So, point A (a, b, c) in the form of r is (r + 4, 2r + 5, r + 4).

Since A (a, b, c), lies on the given plane, so,

Plane x + 2y + z = 2 

⇒ 1 (r + 4) + 2 (2r + 5) + r + 4 – 2 = 0

∴ r = -3

So, foot of perpendicular A (r + 4, 2r + 5, r + 4) will be (1, -1, 1).

DSSSB PGT Mathematics Mock Test - 1 - Question 22

If  then value of Δ is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 22

By operating we get,

DSSSB PGT Mathematics Mock Test - 1 - Question 23
The domain of the derivative of the function
Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 23
Given:
We have to find the domain of the function
Using the definition of modulus function , we have
(i)
It is clear from equation (i) that is discontinuous at and .
is not differentiable at
Not continuous not differentiable]
is differentiable at all except and
Therefore, domain of .
DSSSB PGT Mathematics Mock Test - 1 - Question 24

How many words with or without meaning, can be formed by using all the letters of the word, ‘DELHI’, using each letter exactly once?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 24

The word 'DELHI', contains different letters.

Required number of words Number of arrangements of letters, taken all at time


DSSSB PGT Mathematics Mock Test - 1 - Question 25

Find the integer value of for which the equation has equal roots.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 25

As given,

has equal roots.

DSSSB PGT Mathematics Mock Test - 1 - Question 26

If , then the matrix A is a/an:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 26

Singular Matrix: Any square matrix of order n is said to be singular if |A| = 0.

Involuntary Matrix: Any square matrix of order n is said to be an involuntary matrix if A2 = I, where I is the identity matrix of order n.

Nilpotent Matrix: Any square matrix of order n is said to be nilpotent matrix if there exist least positive integer m such that Am = O, where O is the null matrix of order n.

Idempotent Matrix: Any square matrix of order n is said to be an idempotent matrix if A2 = A.

Given: ,

Hence, A is an involuntary matrix as A2 = I.

DSSSB PGT Mathematics Mock Test - 1 - Question 27

Differentiate x-ln x with respect to ex2.

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 27

Let z = x-ln x 

Taking log both sides, we get

ln z = ln x-ln x

ln z = - (ln x)2                       (∵ ln mn = n ln m)

Differentiating with respect to x

Also y = ex2

Taking log both sides, we get

ln y = ln ex2

ln y = x2 ln e               (∵ ln mn = n ln m)

ln y = x2                      (∵ ln e = 1)

Differentiating with respect to x

The required result is

DSSSB PGT Mathematics Mock Test - 1 - Question 28

Consider three sets and . Two elements are chosen at random, without replacement, from the set , and let denote the set of these chosen elements. Let and Now two elements are chosen at random, without replacement, from the set and let dentoe the set of these chosen elements.

Let . Finally, two elements are chosen at random, without replacement from the set and let denote the set of these chosen elements.

Let . Given that , let be the conditional probability of the event . Then the value of is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 28

Given:

Three sets and

and

, let

We will follow the tree diagram,


Required probability

DSSSB PGT Mathematics Mock Test - 1 - Question 29

In and , then equals:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 29

Given: and

To Find:

We know that:

DSSSB PGT Mathematics Mock Test - 1 - Question 30

Find the angle between the planes whose vector equations are and .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 1 - Question 30

The equations of the given planes are and .

It is known that if and are normal to the planes and then the angle between them, , is given by, 

....(1)

Here, and

and

Substituting the value of and in equation (1), we have

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