Statistics & Demography Solved MCQs for JKSSB & JKPSC — 647 Questions

Q1

General Knowledge with special ref to J&K UTDemography

The population growth rate means:

Q2

Statistics & MathematicsStatistics

Secondary data is primarily sourced from:

Q3

Statistics & MathematicsStatistics

What is an example of a primary data collection method?

Q4

Statistics & MathematicsStatistics

Consider the following statements regarding questionnaire preparation:

- a. Questionnaires collect data by asking people to respond to different sets of questions.
- b. The validity and reliability of the data you collect depend on the design of questions.
- c. Collect the data without a pilot test of all questionnaires.
- d. When designing your questionnaire, you should consider the wording of individual questions prior to the order in which they appear.

Which of the following statements is/are correct?

Q5

Statistics & MathematicsStatistics

Which of the following statements regarding tabulation is FALSE?

Q6

Statistics & MathematicsStatistics

Eight randomly selected college students slept for the following hours previous night: 4, 8, 7, 5, 3, 7, 7, 3.

Arrange the following values in decreasing order:
- a. Mean of sleeping hours of the students
- b. Median of sleeping hours of the students
- c. Mode of sleeping hours of the students
- d. Number of random Sample

Q7

Statistics & MathematicsProbability

Consider the following statements regarding probabilities:

- P: Probabilities can never add up to more than one.
- Q: Probabilities of mutually exclusive events always add up to one.
- R: Probabilities can never be zero.
- S: Probabilities are always positive.

Which of the following statements is/are correct?

💡Correct Answer: Option A (Pand S)

P is correct (probabilities in a sample space sum to 1). S is considered correct in standard exam keys assuming probability is non-negative (

P(E) \ge 0

). Statement Q is false because mutually exclusive events only sum to 1 if they are also exhaustive. Statement R is false because impossible events have a probability of 0.

Q8

Statistics & MathematicsStatistics

In a class of 100 students, every student must pick exactly one sport to play:
- 28 students pick Football.
- 27 students pick Kho-Kho.
- 33 students pick Volleyball.
- 12 students pick Cricket.
- Total girls = 40. Total boys = 60.
- 13 girls play Kho-Kho.
- 13 boys play Volleyball.
- 10 boys play Cricket (written as 23 boys play Cricket due to a typo in the question).

Match the following:
- a. Boys who play Kho-Kho: 1. 2
- b. Girls who play cricket: 2. 10
- c. Boys who play cricket: 3. 14
- d. Total number of boys: 5. 60

Which of the pairs given above is/are correctly matched?

Q9

Statistics & MathematicsStatistics

An economist estimated that a commodity Y had a price index of 10, calculated for 1993 with a base year of 1990, and a quantity index of 0.5 when calculated for 1990 with a base year of 1993. What is the Fisher Ideal Value Index for 1993 with the base year taken to be 1990?

💡Correct Answer: Option C (20)

Price Index for 1993 with base 1990 (

P_{01}

) = 10. Quantity Index for 1990 with base 1993 (

Q_{10}

) = 0.5. Quantity Index for 1993 with base 1990 (

Q_{01}

) = 1 /

Q_{10}

= 1 / 0.5 = 2. Value Index =

P_{01}

$Q_{01}$ = 10 2 = 20.

Q10

Statistics & MathematicsStatistics

One of the key features of the census is:

Q11

Statistics & MathematicsStatistics

Consider the following statements regarding Measures of Mortality:

- a. Gross Reproduction Rate: 5. Measures the number of daughters over a lifetime.
- b. Age-Specific Fertility Rate: 3. Has modal value between 20 and 25
- c. Net Reproduction Rate: 2. Affected by mortality rates
- d. Maternal Mortality Rate: 4. Is measured per 1000 live births.

Which of the pairs given above is/are correctly matched?

Q12

Statistics & MathematicsSimple Interest

The interest on Rs. 54,000 loan for nine months at 8% interest per year is:

Q13

Statistics & MathematicsLinear Equations

Tom and Jerry went to a restaurant for dinner. Tom ordered 2 hamburgers and 1 soft drink, totalling Rs. 70. Jerry ordered 1 hamburger and 2 soft drinks, totalling Rs. 50. What is the cost of one hamburger and one soft drink?

Q14

Statistics & MathematicsPermutations and Combinations

Consider the following statements:

- a. The number of ways to arrange the letters of the word "PEPPER" is 60.
- b. In a group of 20 people, the number of ways to select a committee of 3 members where the order doesn't matter is $\binom{20}{3}$ .
- c. The expansion of $(2+x)^3$ using binomial theorem is $8+6x+12x^2+x^3$ .
- d. The number of ways 3 boys and 3 girls can sit in a row is 360.

Which of the following statements is/are correct?

💡Correct Answer: Option C (a and b)

Statement a is correct (PEPPER has 6 letters: 3 P's, 2 E's, 1 R. Arrangements =

6! / (3! 2!) = 60

). Statement b is correct (order does not matter, so combination

\binom{20}{3}

is used). Statement c is incorrect (expansion is

8 + 12x + 6x^2 + x^3

). Statement d is incorrect (6 people in a row can sit in

6! = 720

ways). Thus, a and b are correct.

Q15

Statistics & MathematicsCalculus

Consider the following statements:

- a. The limit of $\frac{x^2-1}{x-1}$ as x approaches 1 is 0.
- b. If $f(x)=\frac{1}{x}$ then the derivative of $f(x)$ with respect to x is $\frac{1}{x^2}$ .
- c. The limit of $\frac{e^x-1}{x}$ as x approaches 0 is 1.
- d. The limit definition of a derivative for a function $f(x)$ is $\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$ .

Which of the following statements is/are correct?

💡Correct Answer: Option D (cand d)

Statement c is correct (standard exponential limit = 1). Statement d is correct (definition of derivative). Statement a is incorrect (limit is 2). Statement b is incorrect (derivative of

1/x

is

-1/x^2

, not

1/x^2

). Thus, c and d are correct.

Q16

Statistics & MathematicsSet Theory

Let $A=\{x: x\in \mathbb{R}, |x|<1\}$ and $B=\{x: x\in \mathbb{R}, |x-1|\ge1\}$ . If $A \cup B = \mathbb{R} \setminus D$ , then the set D is:

💡Correct Answer: Option A ($\{x\in \mathbb{R}: 1\le x<2\}$)

A = (-1, 1)

.

|x-1| \ge 1 \implies x-1 \ge 1

or

x-1 \le -1 \implies x \ge 2

or

x \le 0

. Thus

B = (-\infty, 0] \cup [2, \infty)

.

A \cup B = (-\infty, 1) \cup [2, \infty)

. The complement is

D = \mathbb{R} \setminus (A \cup B) = [1, 2) = \{x\in \mathbb{R}: 1 \le x < 2\}

.

Q17

Statistics & MathematicsRelations and Functions

Consider the following relations/functions and their properties:

- a. $F=\{(x,y)\in \mathbb{R}\times \mathbb{R}: x^2+y=2\}$
- b. $F=\{(x,y)\in \mathbb{R}\times \mathbb{R}: x^2+y^2=25\}$
- c. $F=\{(x,y)\in \mathbb{R}\times \mathbb{R}: y=2x+1\}$
- d. $F=\{(x,y)\in \mathbb{R}\times \mathbb{R}: y=x^2\}$

Matches:
- 1. $F \circ F = \{(x,z)\in \mathbb{R}\times \mathbb{R}: z=4x+3\}$
- 2. F is increasing on $(0,\infty)$ but not on $\mathbb{R}
- 3$. F is one-one but not onto
- 4. Range of $F = [-2,\infty)$ (assuming $y=x^2-2$ in the paper's original intended equation)
- 5. F is not a function

Which of the pairs given above is/are correctly matched?

💡Correct Answer: Option D (a-4, b-5, c-1, d-2)

F in (b) is a circle equation, which is not a function (b-5). F in (c) has

F(F(x)) = 2(2x+1)+1 = 4x+3

(c-1). F in (d) is

y=x^2

, which is increasing on positive real numbers but not on the whole real line (d-2). This makes D (a-4, b-5, c-1, d-2) the correct match.

Q18

Statistics & MathematicsMatrices and Determinants

Consider the following matrices and their determinants:

- a. Square matrix has two identical rows
- b. $3\times3$ Identity matrix
- c. $3\times3$ diagonal matrix with diagonal entries 1, 2 and 3
- d. P and Q are two $3\times3$ matrices with $\det(P)=2$ and $\det(Q)=4$ . Determinant of $P Q^T$ is:

Matches:
- 1. Determinant = 1
- 2. Determinant = 4
- 3. Determinant = 0
- 4. Determinant = 6
- 5. Determinant = 8

Which of the pairs given above is/are correctly matched?

💡Correct Answer: Option A (a-3, b-1, c-4, d-5)

Determinant properties: Identical rows result in determinant 0 (a-3). Identity matrix determinant is 1 (b-1). Diagonal matrix determinant is the product of diagonals = 123 = 6 (c-4).

\det(PQ^T) = \det(P)\det(Q) = 2*4 = 8

(d-5). Correct match: a-3, b-1, c-4, d-5.

Q19

Statistics & MathematicsProbability

Arrange the following events in increasing order of probability:

- a. Picking a diamond from a well-shuffled deck of 52 playing cards.
- b. Drawing a King from a standard deck of 52 cards.
- c. Rolling a number between 1 and 6 on a fair six-sided die.
- d. Getting heads on a fair coin toss.

💡Correct Answer: Option C (b, a, d, c)

Calculating probabilities:

P(b) = 4/52 \approx 0.077

.

P(a) = 13/52 = 0.25

.

P(d) = 0.5

.

P(c) = 4/6 \approx 0.67

(strictly between 1 and 6 is {2,3,4,5}). Increasing order: b, a, d, c.

Q20

Statistics & MathematicsVectors

The area of the triangle determined by the three points A(1,2,3), B(3,2,1) and C(2,4,5) is:

💡Correct Answer: Option D ($\sqrt{29}$)

Using vectors:

\vec{AB} = B - A = (2, 0, -2)

and

\vec{AC} = C - A = (1, 2, 2)

. Cross product

\vec{AB} \times \vec{AC} = (4, -6, 4)

. Magnitude

= \sqrt{4^2 + (-6)^2 + 4^2} = \sqrt{68} = 2\sqrt{17}

. Area

= 1/2 * 2\sqrt{17} = \sqrt{17}

. Note:

\sqrt{17}

is the mathematically correct answer, but due to a question error, the official JKSSB answer key marked it as option D (

\sqrt{29}

).

Q21

Statistics & MathematicsVectors

The unit vector having the opposite direction of the vector (1,-1) is:

💡Correct Answer: Option B ($\frac{-1}{\sqrt{2}}(1,-1)$)

Vector

\vec{v} = (1, -1)

. Magnitude

= \sqrt{1^2 + (-1)^2} = \sqrt{2}

. The unit vector in the same direction is

\frac{1}{\sqrt{2}}(1, -1)

. The unit vector in the opposite direction is obtained by multiplying with -1, which is

\frac{-1}{\sqrt{2}}(1, -1)

.

Q22