For two complex numbers p and q, if Arg(p)-Arg(q)=π/2 as well as |pq|=1, what is the value of p̅q ?

There are 4 consecutive odd numbers (x₁, x₂, x₃ and x₄) and three consecutive even numbers (y₁, y₂ and y₃). The average of the odd numbers is 6 less than the average of the even numbers. If the sum of the three even numbers is 16 less than the sum of the four odd numbers, what is the average of x₁, x₂, x₃ and x₄?

A

30

B

38

C

32

D

34

In a set of three numbers, the average of first two numbers is 2. The average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers ?

A

3

B

6

C

9

D

24

In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?

A

2

B

2.5

C

3

D

3.5

The magnitude and phase of the complex Fourier series coefficient a_k of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.

A

$$x\left( t \right) \in R$$

B

$$x\left( t \right) \in P$$

C

$$x\left( t \right) \in \left( {C - R} \right)$$

D

The information given is not sufficient to draw any conclusion about x(t)

Consider the given question and decide which of the following statements is sufficient to answer the question. All natural numbers are whole numbers?
(I) All natural numbers plus 0 are called whole numbers (II) Whole numbers are different from natural numbers

A

Neither (I) nor (II) is sufficient to answer the question

B

(II) alone is sufficient while (I) alone is not sufficient to answer the question

C

(I) alone is sufficient while (II) alone is not sufficient to answer the question

D

Both (I) and (II) are sufficient to answer the question

A point z has been plotted in the complex plane, as shown in figure below.

The plot for point $$\frac{1}{{\text{z}}}$$ is

A

B

C

D

Sum of 4 consecutive even numbers is greater than three consecutive odd numbers by 81 . If the sum of the least odd and even numbers is 59 then find the sum of largest of odd and even numbers is 59 then find the sum of largest odd and even numbers.

A

69

B

53`

C

65

D

72

Of three positive numbers, the ratio of the first and second numbers is 3:4 & that of the second and third numbers is 5:6. The product of the second and third numbers is 4320. What is the sum of three numbers?

A

167

B

177

C

187

D

197

Read the passage carefully and select the best answer to each question out of the given four alternatives. By practicing mindfulness and other principles, we become more aware of and present to our fears and others fears, bearing witness as a way of healing andempowering. We see the spiritual path as intertwined with the path of social action, with contemplation and action parts of the same whole, each nourishing andguiding the other. Acknowledging that our well-being depends on others makes caring for others well-being a moral responsibility.
Through a “mindful citizen” exercise, we create a story articulating who we are as individuals who are also part of communities. This exercise helps us move beyond cynicism, complacency, and despair, instead infusing us with a sense of purpose. We embrace our gifts, resolving to do our part to promote a sense of common humanity as a means toward social justice.
With this exercise, I believe we can help students bridge their divides and replace anger and distrust with compassionate connections – just as I witnessed betweenShirley and Tiffany.
Shirley returned to class after a brief hiatus, keeping a cool distance from Tiffany. But over the weeks spent together they gradually came to know each other. They practiced seeing and listening, sharing stories so different that they felt bewildered as to how they could overcome the gap. But they found that acknowledging their
differences led them to discover a place of deep connection in commonalities, such as being raised by grandmothers, and even wounds, including childhood trauma,that they never imagined existed.
In assessments of these classes, students say that these small groups become “healing communities,” where we overcome victimization and claim agency. Healingoccurs as we transcend an “us vs. them” mentality, crossing borders and forging connections. These communities show a way of reducing intergroup prejudice andfostering inclusion based in psychology research and pedagogical practice. What makes the others well-being a moral responsibility for us?

A

By way of our concerned nature.

B

As our own well-being depends on others well-being.

C

It depends on one\u2019s upbringing.

D

It is mentioned as a fundamental duty in our Indian Constitution.

The average of eight numbers in 14. The average of six of these numbers 16. The average of the remaining two numbers is 16. The average of the remaining two numbers is-

A

4

B

8

C

16

D

Data inadequate