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DSSSB PGT Mathematics Mock Test - 3 - DSSSB TGT/PGT/PRT MCQ


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30 Questions MCQ Test - DSSSB PGT Mathematics Mock Test - 3

DSSSB PGT Mathematics Mock Test - 3 for DSSSB TGT/PGT/PRT 2024 is part of DSSSB TGT/PGT/PRT preparation. The DSSSB PGT Mathematics Mock Test - 3 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB PGT Mathematics Mock Test - 3 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 - 3 below.
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DSSSB PGT Mathematics Mock Test - 3 - Question 1

If LMNO is written as GHIJ, how will STUV be written?

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

L - 5 = G
M - 5 = H
N - 5 = I
O - 5 = J
LMNO → GHIJ

Similarly,
S - 5 = N
T - 5 = O
U - 5 = P
V - 5 = Q
STUV → NOPQ

DSSSB PGT Mathematics Mock Test - 3 - Question 2

Directions to Solve

In each of the following questions there are three statements. Which are followed by three or four conclusions. Choose the conclusions which logically follow from the given statements.

Question -

Statements: Some envelops are gums. Some gums are seals. Some seals are adhesives.

Conclusions:

  1. Some envelopes are seals.
  2. Some gums are adhesives.
  3. Some adhesives are seals.
  4. Some adhesives are gums.

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

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DSSSB PGT Mathematics Mock Test - 3 - Question 3

In insects, air enters the body through

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

Insect bodies have openings, called spiracles, along the thorax and abdomen. These openings connect to the tubular network, allowing oxygen to pass into the body, regulating the diffusion of CO2 and water vapor. 

DSSSB PGT Mathematics Mock Test - 3 - Question 4

Direction: Read the following passages carefully and answer the question that follows.
Knowledge means knowing the things in an appropriate and better way. A man of knowledge can understand the circumstances more wisely, so can decide the things favorably. Knowledge inspired. confidence and courage to act at a right time. A man of knowledge possesses immense influence in society. He has the capacity to lead the society, mold the society in a positive direction and keeps away the society from the many social evils. A man of knowledge can turn the sleeping people into a thundering force. Whatever the inventions and discoveries are seen today. from needle to the jet planes. are the result of proper use of knowledge. Human being is the only creature who can use his brain wisely, rationally, selectively and can do wonders.

Q. What is the reformative activity of a man of knowledge according to the given passage?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 4

The author considers that a man of knowledge is reformative in his approach. He can tun the sleeping people into a thundering force.

DSSSB PGT Mathematics Mock Test - 3 - Question 5

Direction: Read the following passage carefully and answer the questions. Your answer to these questions should be based on passage only.
Shouldn't we then live in harmony with nature and evolve with it? Our brains, too, are wired to enjoy the beauty of nature. No man-made systems can complete with the joy and well-being. we feel in observing nature's display all year round. We recover rapidly from physical stress when exposed to pleasing natural environmental beauty. We take holidays amidst natural scenic wonders and we retreat to nature to recover and recoup from stress. Yet, we choose to destroy nature with our wasteful lifestyles and our burgeoning population. We use natural resources inefficiently and destroy them for technological development. We think we can change the natural resources inefficiently and destroy them for technological development. We think we can change the natural tapestry, and have even started playing God !

Q. What is the human weakness?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 5

Nature has given us everything to survive on this Earth. But human lifestyle does not allow him to nature efficiently and not to destroy nature for his personal use.

DSSSB PGT Mathematics Mock Test - 3 - Question 6

The manager of a circus decides to buy some animals for the show. He buys 10 giraffes costing as much as 24 dogs, 16 dogs costing as much as 4 oxen and 6 oxen costing as much as 4 elephants. If the cost of 10 elephants is Rs. 1,70,000, what is the cost of a giraffe?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 6

Cost of a giraffe = P
10 giraffes = 24 dogs
16 dogs = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs. 1,70,000
P = Rs. [(24 × 4 × 4 × 1,70,000)/(10 × 16 × 6 × 10)]
P = Rs. (6,52,80,000/9600)
P = Rs. 6800

DSSSB PGT Mathematics Mock Test - 3 - Question 7

What is the least number that can be added to 7218 make it a perfect square ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 7

85*85 = 7225

DSSSB PGT Mathematics Mock Test - 3 - Question 8

निर्देश: निम्नलिखित गद्यांश को ध्यानपूर्वक पढ़िए और प्रश्न का उत्तर दीजिए।
महिला आरक्षण विधेयक पर हर कोई अपने विचार व्यक्त कर रहा है। कोई इससे सहमत है तो कोई असहमत। लोकतंत्र में सबका अपना विचार हो सकता है, लेकिन इसका अथ यह कदापि नहीं कि हम महिलाओं का विरोध करें। जातिगत आरक्षण जैसे सुधार तो आवश्यकता होने पर बाद में भी किए जा सकते हैं। हर बार विरोध करना घोर वैचारिक पिछड़ापन है। जो दल विभिन्न आधार सुझा रहे हैं, वे अपनी पार्टी में उसको लागू करने के लिए स्वतंत्र है। बार-बार विरोध करने से नीयत पर शक होना जरूरी है। हो-हल्ला करके कई वषों से इस बिल को रोकने का प्रयास किया जा रहा है। महिलाओं ने भी आज़ादी के लिए पुरुषों के साथ मिलकर संघर्ष किया था। क्या आज़ाद भारत में आज अपने अधिकारों के लिए उन्हें याचना करनी पड़ेगी? बेहतर होगा कि सभी दल इस दिशा में सहयोग करें और सर्वमान्य समाधान निकालें।

Q. आज़ादी के लिए महिलाओं ने क्या किया था?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 8

आज़ादी के लिए महिलाओं ने पुरुषों के साथ मिलकर संघर्ष किया था।

DSSSB PGT Mathematics Mock Test - 3 - Question 9

‘से’ किस कारक का चिह्न है? 

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 9

दिए गए विकल्पों में ‘से’ ‘करण कारक’ का चिह्न है।
संज्ञा या सर्वनाम के जिस रूप की सहायता से क्रिया सम्पन्न होती हैं, उसे करण कारक कहते हैं। जैसे- रामा ने मोहन को डंडे से मारा।

DSSSB PGT Mathematics Mock Test - 3 - Question 10

ठकुराइन शब्द किस प्रत्यय से बना हुआ है?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 10

ठकुराइन शब्द ठाकुर+आइन प्रत्यय से बना हुआ है।

DSSSB PGT Mathematics Mock Test - 3 - Question 11

A circle is circum-scribed of ΔABC. 0 is the centre of the circle and CP is the tangent of the circle at the point C. If BC bisects the ∠OCP, then what is the supplementary angle of ∠BAC?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 11

As we know,

As we know,

Sum of two supplementary angle is 180o.

Let the supplementary angle of ∠BAC be x, then

DSSSB PGT Mathematics Mock Test - 3 - Question 12

Find the value of .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 12

Given,

For two functions,

Thus,

As we know,

DSSSB PGT Mathematics Mock Test - 3 - Question 13

Apply Chinese Remainder theorem to solve (mod13). the common solution is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 13

Given:

m1= 9 and m2 = 13 which are relatively co-prime.

Also, a1 = 3 and a2 = 7, which are integer.

Hence the condition of the Chinese  Remainder Theorem satisfied.
So, according to the theorem, there will be the unique solution of x for modulo

M = 9 x 13 = 117

Now, using the relation,

We will get

M1 = 13 and M2 = 9

To calculate X1 and X2 we can use the relation,

Multiplying both sides with 7, we will get

Again, using the above relation

Thus the unique solution of x will be:

DSSSB PGT Mathematics Mock Test - 3 - Question 14

The solution of the inequality is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 14

Given,

⇒ 3(x – 2) × 3 ≥ 5(2 – x) × 5

⇒ 9(x – 2) ≥ 25(2 – x)

⇒ 9x – 18 ≥ 50 – 25x

⇒ 9x – 18 + 25x ≥ 50

⇒ 34x – 18 ≥ 50

⇒ 34x ≥ 50 + 18

⇒ 34x ≥ 68

⇒ x ≥ 2

⇒ x ∈ [2, ∞)

DSSSB PGT Mathematics Mock Test - 3 - Question 15

If , then what is the value of ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 15

If

Where, and are Pythagorean triples

We have,

and are Pythagorean triples

DSSSB PGT Mathematics Mock Test - 3 - Question 16

The average of nine numbers is 60, that of the first five numbers is 55 and the next three is 65. The ninth number is 10 less than the tenth number. Then the tenth number is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 16

Given,

Average of nine numbers = 60

Average of first five numbers = 55 

Average of next three numbers = 65

Tenth number = Ninth number + 10

As we know,

Average = 

The sum of nine numbers = 60 × 9 = 540

The sum of the first five numbers = 55 × 5 = 275

The sum of the next three numbers = 65 × 3 = 195

Ninth number = (540 – 275 – 195) = (540 – 470) = 70

∴ Tenth number = 70 + 10 = 80

DSSSB PGT Mathematics Mock Test - 3 - Question 17

Find sin θ if  is the angle between the vectors  and 

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 17

Given:

and

DSSSB PGT Mathematics Mock Test - 3 - Question 18

is equal to_______:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 18

Given,


As we know,

DSSSB PGT Mathematics Mock Test - 3 - Question 19

If , then what is the value of

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 19

Given:

DSSSB PGT Mathematics Mock Test - 3 - Question 20

Solve .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 20

L-Hospital Rule:

Let and be two functions

Suppose that we have one of the following cases,

I.

II.

Then we can apply L-Hospital Rule

Apply L hospital;

Again apply L hospital rule;

DSSSB PGT Mathematics Mock Test - 3 - Question 21
Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 21
Given:

According to the question,






DSSSB PGT Mathematics Mock Test - 3 - Question 22

A linear congruence has:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 22

Given that,


Greatest common divisor(GCD) of and :

So,

We can see that, 

is with a remainder of .

Thus, is not evenly .

So, linear congruence has no solution.

DSSSB PGT Mathematics Mock Test - 3 - Question 23

Let and be functions such that ,

and

Which of the following statements is TRUE?

DSSSB PGT Mathematics Mock Test - 3 - Question 24

Let A be a point in space such that where is the origin. If is inclined at angles and with -axis and y-axis respectively, then what is equal to?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 24

Given that, OA is inclined at angles and with -axis and -axis respectively.

We know that,

where are the angles which inclined with

and axis respectively.

According to the question,

So,

DSSSB PGT Mathematics Mock Test - 3 - Question 25

If the lines and are coplanar then find the value of ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 25

Given:

The lines and are coplanar

Here, we have to find the value of

As we know that, if two lines and are coplanar then

Here,

Similarly, and

DSSSB PGT Mathematics Mock Test - 3 - Question 26

Point A(10, 5), B(8, 4) and C(6, 6) are vertices of a triangle, then length of median from A is-

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 26

It is given that point A(10, 5), B(8, 4) and C(6, 6) are vertices of a triangle, 

Let D be the midpoint on the line BC.

Its coordinates are given by,


So, the length of median 


Point A(10, 5), B(8, 4) and C(6, 6) are vertices of a triangle, then length of median from A is 3 units.

DSSSB PGT Mathematics Mock Test - 3 - Question 27

If and if , then the value of x is equal to

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 27

Given,

DSSSB PGT Mathematics Mock Test - 3 - Question 28

How many terms are there in the expansion of

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 28

We know that,
The total number of terms in the binomial expansion of is , i.e., one more than the exponent n.
Now,
can be written as

We know that,

So, Total number of the terms = 9 + 1 = 10
There are 10 terms in the expansion of

DSSSB PGT Mathematics Mock Test - 3 - Question 29

The sine of the angle between vectors and is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 29

Given,

and

As we know,

If and then

As we know,

DSSSB PGT Mathematics Mock Test - 3 - Question 30

What is the value of ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 3 - Question 30

Given,

Put value in equation

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