DSSSB PGT Mathematics Mock Test - 9 - DSSSB TGT/PGT/PRT MCQ

Given inequality is: P ≤ Q ≥ R; E ≥ Q; L < Q = D

1. L < P → P ≤ Q, L < Q, data is not sufficient to determine the relation → False

2. E ≥ R → E ≥ Q ≥ R, E ≥ R → True.

3. E < D → E ≥ Q, L < Q = D, E ≥ D → False.

4. Q < R → Q ≥ R → False.

Hence, E ≥ R, is the correct inequality.

The figure may be labelled as shown.

The squares composed of two components each are ABKJ, BCLK, CDEL, LEFG, KLGH and JKHI i.e.6 in number.

There is only one square i.e. CEGK composed of four components.

The squares composed of eight components each are ACGI and BDFH i.e. 2 in number.

There are 6 + 1 + 2 = 9 squares in the figure.

Multicellular glands are formed by the folding of epithelial tissue. Epithelial tissue forms the lining of glands and ducts.

Inertia is the property of a body by virtue of which the body unable to change the state of rest or state of motion and direction as inertia is the tendency to oppose the change in state or direction.

He was satisfied with the condition of his bicycle.

Some heat on the ocean floor comes from radium as more soil gets washed down into the ocean.

x = Rs. 1000 (As 1000 @ 5% for 2 years = 1100).
Similarly y = Rs. 1500. x +y = 2500.

Since, we have to find the minimum percentage, it can be possible that no one has failed in both the subjects.

Efficiency of Chandni = 11.11%
Efficiency of Divakar = 8.33%
They do 19.44% work in 2 days.
∴ They need 10 days to do 97.22% work,
Now the rest work (2.78) was done by Chandni in 2.78 / 11.11 = 1 / 4 days
Therefore total number of days required = 
Alternatively :
Chandni's one day's work = 1 / 9
Divakar's one day's work = 1 / 12
Chandni's and Divakar's (1 + 1) = 2 day's work = 1 / 9 + 1 / 12 = 7 / 36
So, in 10 days they do = 
So, the remaining work will be done by Chandni = 
Thus total number of required days = 
Hint

Monday + Tuesday + Wednesday = 3 x 35 = 105;
Tuesday + Wednesday + Thursday = 3 x 30 = 90.
Thus, Monday – Thursday = 15 and
Thursday = Monday/2 → Monday = 30 and Thursday = 15

4x + 40 = 5(x + 4) → x = 20 (average after 4 innings).

Hence, new average = 20 + 4 = 24.

P : Q : R
= (25 × 1 + 35 × 2) : (35 × 2 : 25 × 1) : (30 × 3)
= 95 : 95 : 90
= 19 : 19: 18

‘अनुराग’ शब्द का उचित विलोम शब्द ‘विराग’ होगा।
अनुराग का अर्थ - प्रेम या भक्ति
विराग का अर्थ - उदासीन या अरुचि
विपरीत (उल्टा) अर्थ बताने वाले शब्दों को विलोम शब्द कहते हैं। विलोम शब्दों को विपर्यायवाची, प्रतिलोमार्थक और विपरीतार्थक शब्द भी कहते हैं।

‘गंगा’ का पर्यायवाची शब्द 'मंदाकिनी' है।
'गंगा' के अन्य पर्यायवाची शब्द - देवनदी, मंदाकनी, भगीरथी, विश्नुपगा, देवपगा, ध्रुवनंदा, सुरसरि, त्रिपथगा, जाह्नवी, सुरसरिता, सुरधुनी।

• लोकोक्ति - दूल्हे को पत्तल नहीं, बरातियों को थाली
• अर्थ - भीड़ के चक्कर में मुख्य व्यक्ति को अनदेखा करना
• वाक्य - स्कूल के सांस्कृतिक कार्यक्र्म में मुख्य अतिथि की उपस्थिति के बावजूद लोगों का ध्यान महिला खिलाड़ी की तरफ ही ज्यादा था। सच में ये तो वो वाली बात हो गई दूल्हे को पत्तल नहीं बरातियों को खाना।

अघोष वर्ण अर्थात जिन वर्णों के उच्चारण में स्वरतन्त्रियों में कम्पन न हो, वह अघोष वर्ण कहलाते हैं। प्रत्येक ‘वर्ग’ का पहला और दूसरा व्यंजन वर्ण अघोष वर्ण होता है, जैसे क, ख, च, छ, ट, ठ, इत्यादि।

Let,

As we know,

So, similarly

Thus equation (1) and equation (2), we get

Give, the total number of tickets = 10

Number of tickets drawn = 2

Prime number between 1 to 10 = {2, 3, 5, 7} = 4

A: The event of getting a prime number in the first draw

B: The event of getting a prime number in the second draw

Event A and B are independent events.

P(A) =  Probability of getting a prime number in the first draw  = 4/10 = 2/5

Number of remaining cards in pack = 9

P(B) = Probability of getting a prime number in the second draw  = 3/9 = 1/3

The probability that both the tickets drawn have prime numbers 
= 2/5 x 1/3
= 2/15
Hence, In a lottery of 10 tickets numbered 1 to 10, two tickets are drawn simultaneously. then the probability that both the tickets are drawn have prime numbers is 2/15

 All students solves the problem independently, so if at least one of them solves the problem then the problem is considered solved.

Probability that the problem is unsolved

= [1 – P(A)][1 – P(B)][1 – P(C)]

= 3/32

The probability that the problem will be solved

= 1 – Probability that the problem is unsolved

= 29/32

We have,

On dividing by i, we get

So, z = 1 or z² = -i.

Now, z = i

And, z² = -i

The distance between the points is given by:

CALCULATION

Let be the point which is equidistant from the points 

As we know that, the distance between the points   is given by:

Similarly, let's find out the distance between the the points P and B

By squaring both the sides we get,

So, the set of the points which are equidistant from the points ��(3,4,−5) and ��(−2, 1,4 ) is given by: 

Given,

The average income of 50 persons = Rs. 5200 

The average income of another 45 persons = Rs. 5000

As we know,

Required average

Sum of total income of 50 persons = 50 × 5200 = Rs. 260000

Sum of total income of 45 persons = 45 × 5000 = Rs. 225000

Required average of income

Therefore, the average income of the whole group = Rs. 5,105.26 = Rs. 5,105

Given:

Now we know:

Similarly,

∴ From above we conclude

Now also we know,

Similarly,

To find the Eigen values it satisfy the condition, 

By solving the above equation, we get,

Lets consider  term in the given expansion contains x and y to one and the same power.

Now we have,

Now, if x and y have the same power, then

Thus, the required term is the 10^th term.

Let

Let the line joining and be divided by the -plane at point in the ratio .

We know that:

Since P lies on the YZ -plane, the x -coordinate of P will be zero.

Thus, YZ-plane divides AB externally in the ratio 2 : 3.