List of practice Questions

The equation \( E = pc \), (where \( E \) and \( p \) are energy and momentum respectively) is valid: 
 

An electromagnetic wave propagating through vacuum, described by \( E = E_0 \sin(kx - \omega t) \), \( B = B_0 \sin(kx - \omega t) \), then: 
 

In our culture, the _________ of an individual is considered to be the reflection of one’s family.
 

Ivan Pavlov is known for explaining learning by __________.
 

The ink blot test is developed by psychologist __________.
 

Formula of Intelligence Quotient is given by __________.
 

Humanistic psychology school of thought is proposed by __________.
 

Internet addiction
Self-esteem – Determinant of happiness
Superstition – Hurdle in first aid in mental health
Atul participated in a tree plantation program to build self-esteem and self-confidence. So which type of technique is used by Atul to achieve emotional well-being?
Incubation
Mindfulness
Neuroticism
Plutchik’s wheel of emotions
Ramesh has been experiencing hallucinations for the past year. He talks in a disorganized manner and screams for no reason. These symptoms are symptoms of which psychological disorder?
To reduce the problem of acute water shortage caused by irregular rainfall, all the citizens of the village came together and built farm ponds in the fields. So what type of resilience do citizens of the village use to overcome natural disaster?
Differentiate \( y = x^x + (\cos x)^{\tan x} \) with respect to \( x \).

The probabilities of solving a question by \( A \) and \( B \) independently are \( \frac{1}{2} \) and \( \frac{1}{3} \) respectively. If both of them try to solve it independently, find the probability that:

 

 

Suppose that \( A = \{ 1, 2, 3 \} \), \( B = \{ 4, 5, 6, 7 \} \), and \( f = \{ (1, 4), (2, 5), (3, 6) \} \) be a function from \( A \) to \( B \). Then \( f \) is:

(e) The angle between the vectors \( 3\hat{i} - 2\hat{j} + \hat{k} \) and \( 2\hat{i} + \hat{j} + 3\hat{k} \) will be:
Find the shortest distance between the lines: \[ \vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}), \] \[ \vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}). \]
If \( A \) and \( B \) are independent events, where \( P(A) = \frac{3}{10} \), \( P(B) = \frac{6}{10} \), then find \( P(A \cup B) \) and \( P(A \cap B) \).
Find the shortest distance between two lines \( l_1 \) and \( l_2 \) whose vector equations are: \[ \mathbf{r} = \hat{i} + \hat{j} + \lambda (2\hat{i} - \hat{j} + \hat{k}) \] and \[ \mathbf{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu (3\hat{i} - 5\hat{j} + 2\hat{k}). \]
Prove that a relation \( R = \{(a, b) : (a-b) \) is a multiple of \( 5 \} \) is an equivalence relation in the set of integers \( \mathbb{Z} \).