Which of the following is a subspace of $M_n(\mathbb{R})$, the vector space of all $n \times n$ real matrices

C) The set of all matrices with $\text{trace } A = 0$

Let A be a $5 \times 5$ real matrix. Which of the following is true?

D) If A is a skew-symmetric matrix, then $\det A = 0$

Which of the following is the Jordan form of a $3 \times 3$ matrix?

B) $\begin{pmatrix} 2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \end{pmatrix}$

Let $f : \mathbb{R} \to \mathbb{R}$ be defined as :

B) f is continuous on $\mathbb{R} \setminus \mathbb{Q}$

Which of the following functions is uniformly continuous on (0,1)?

C) $f(x) = x \sin\left(\frac{1}{x}\right)$

Let $f : \mathbb{R} \to \mathbb{R}$ be a thrice differentiable function such that $f(a) = f'(a) = f(b) = f'(b) = 0$ where $a, b \in \mathbb{R}, a < b$. Then choose the correct statement.

C) $f'''(c) = 0$ for some $c \in (a, b)$

Consider the sequences of functions $(f_n)$ and $(g_n)$ defined by $f_n(x) = \frac{1}{1+nx}, x \in (0,1)$, $g_n(x) = \frac{x}{1+nx}, x \in (0,1)$. Choose the correct statement from the following:

A) $g_n$ converges uniformly on (0,1)

Let $f : [0,1] \to [0,1]$ be defined as: $f(x) = \begin{cases} 0 & \text{if } x \in \mathbb{Q} \\ x & \text{if } x \in \mathbb{R} \setminus \mathbb{Q} \end{cases}$. Which of the following statements is true?

B) The upper Riemann integral of f is $\frac{1}{2}$

Which of the following sets has nonzero Lebesgue measure?

D) $(\mathbb{R} \setminus \mathbb{Q}) \cap [0,1]$

Consider the function $f:\mathbb{R}^2 \to \mathbb{R}$ defined by $f(x) = \frac{x^2 y^2}{x^2 + y^4}$ if $x \neq 0$, $0$ if $x = 0$. Choose the correct statement from the following:

C) f has directional derivatives at (0,0) in all directions

Let $f(x) = x, 0 < x < \pi$. Which of the following is true?

C) $f(x) = \pi - 2 \sum_{n=1}^{\infty} \frac{\sin nx}{n}, 0 < x < 2\pi$

Let $f:\mathbb{R}^2 \to \mathbb{R}^2$ be defined by $f(x,y) = (x+y, x-y)$, choose the correct statement from the following:

B) $Df(0,0)$ exists and is invertible

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100 questions with answersProvisional keyKerala Higher Secondary Education

Higher Secondary School Teacher Mathematics - Kerala Higher Secondary Education question paper 2022

Kerala Higher Secondary Education

Date of test: 13-08-2022
Question paper code: 66/2022/OL
Category No.: 484/2019
Questions: 100
Answer key: Provisional Answer Key
Exam mode: Online (computer based)

Provisional key. Kerala PSC can change answers after reviewing complaints; the final key decides the marks.

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Source: Kerala PSC (keralapsc.gov.in) · official document· Last updated 25 Sept 2026· How we check content

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All 100 questions with answers

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1.
Which of the following is a subspace of $M_n(\mathbb{R})$ , the vector space of all $n \times n$ real matrices
Show answer and explanation
Answer: C —
The set of all matrices with $\text{trace } A = 0$
The set of matrices with trace zero forms a subspace since the trace function is a linear map.
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2.
Let A be a $5 \times 3$ matrix and B be a $3 \times 7$ matrix then the rank of AB can be:
Show answer and explanation
Answer: B —
3
The rank of the product AB cannot exceed the rank of either factor, so $\text{rank}(AB) \le \min(\text{rank}(A), \text{rank}(B)) = \min(3, 3) = 3$ .
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3.
The number of linearly independent eigen vectors of the matrix $\begin{pmatrix} 2 & 2 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 1 & 4 \end{pmatrix}$ is
Show answer and explanation
Answer: D —
4
The eigenvalues can be found from the characteristic polynomial. Computing for this matrix yields 4 distinct or independent eigenvectors.
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4.
Let A be a $5 \times 5$ real matrix. Which of the following is true?
Show answer and explanation
Answer: D —
If A is a skew-symmetric matrix, then $\det A = 0$
For an odd-order ( $n = 5$ ) skew-symmetric matrix, the determinant is always zero.
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5.
Which of the following is the Jordan form of a $3 \times 3$ matrix?
Show answer and explanation
Answer: B —
$\begin{pmatrix} 2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \end{pmatrix}$
Option B represents a valid Jordan canonical form matrix with blocks along the diagonal.
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6.
Let $T : P_3(\mathbb{R}) \to M_{2 \times 2}(\mathbb{R})$ be defined by $T(f(x)) = \begin{pmatrix} f(1) & f(-1) \\ f(2) & f(-2) \end{pmatrix}$ . Then which of the following statements is true?
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Answer: B —
T is both one-one and onto
Since the dimension of both spaces is 4, and T is injective (one-one), by the rank-nullity theorem it is also surjective (onto).
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7.
Let $V = M_2(\mathbb{R})$ , $A^T$ denotes the transpose of the matrix A and I be the identity matrix in V. Define an inner product on V as $\langle A, B \rangle = \text{trace}(B^T A)$ . Then the dimension of the orthogonal complement of the set \{I\} is:
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Answer: C —
3
The space V has dimension 4. The orthogonal complement of a 1-dimensional subspace spanned by {I} has dimension $4 - 1 = 3$ .
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8.
The series $1 - \frac{1}{2} + \frac{1}{4 \cdot 2!} + \frac{1}{8 \cdot 3!} + \frac{1}{16 \cdot 4!} + \dots$ converges to:
Show answer and explanation
Answer: D —
$e^{-\frac{1}{2}}$
The series can be expressed as $\sum_{n=0}^{\infty} \frac{(-1/2)^n}{n!} = e^{-1/2}$ (Note: Question was cancelled in final key, but original provisional key option was D).
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9.
Let $f : \mathbb{R} \to \mathbb{R}$ be defined as :
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Answer: B —
f is continuous on $\mathbb{R} \setminus \mathbb{Q}$
Standard Dirichlet-like function behavior where continuity holds on the irrational numbers.
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10.
Which of the following functions is uniformly continuous on (0,1)?
Show answer and explanation
Answer: C —
$f(x) = x \sin\left(\frac{1}{x}\right)$
$f(x) = x\sin(1/x)$ can be continuously extended to $[0, 1]$ by defining $f(0)=0$ , hence it is uniformly continuous on $(0, 1)$ .
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11.
Let $f : [0,1] \to [0,1]$ be a continuous function. Then which of the following statements is true?
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Answer: A —
f has a fixed point
By Brouwer's Fixed Point Theorem, every continuous function from a closed interval to itself has at least one fixed point.
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12.
Let $f : \mathbb{R} \to \mathbb{R}$ be a thrice differentiable function such that $f(a) = f'(a) = f(b) = f'(b) = 0$ where $a, b \in \mathbb{R}, a < b$ . Then choose the correct statement.
Show answer and explanation
Answer: C —
$f'''(c) = 0$ for some $c \in (a, b)$
Using Rolle's Theorem repeatedly on $f, f', f''$ , we obtain that $f'''(c) = 0$ for some $c \in (a, b)$ .
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13.
Consider the sequences of functions $(f_n)$ and $(g_n)$ defined by $f_n(x) = \frac{1}{1+nx}, x \in (0,1)$ , $g_n(x) = \frac{x}{1+nx}, x \in (0,1)$ . Choose the correct statement from the following:
Show answer and explanation
Answer: A —
$g_n$ converges uniformly on (0,1)
Limit of $g_n(x)$ is 0 and the supremum norm $\sup |g_n(x) - 0| \to 0$ , showing uniform convergence.
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14.
Let $f : [0,1] \to [0,1]$ be defined as: $f(x) = \begin{cases} 0 & \text{if } x \in \mathbb{Q} \\ x & \text{if } x \in \mathbb{R} \setminus \mathbb{Q} \end{cases}$ . Which of the following statements is true?
Show answer and explanation
Answer: B —
The upper Riemann integral of f is $\frac{1}{2}$
The lower Riemann integral is 0 and the upper Riemann integral is $\int_0^1 x dx = \frac{1}{2}$ .
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15.
Which of the following sets has nonzero Lebesgue measure?
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Answer: D —
$(\mathbb{R} \setminus \mathbb{Q}) \cap [0,1]$
The set of irrationals in $[0,1]$ has Lebesgue measure 1, which is nonzero.
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16.
Consider the function $f:\mathbb{R}^2 \to \mathbb{R}$ defined by $f(x) = \frac{x^2 y^2}{x^2 + y^4}$ if $x \neq 0$ , $0$ if $x = 0$ . Choose the correct statement from the following:
Show answer and explanation
Answer: C —
f has directional derivatives at (0,0) in all directions
All directional derivatives exist at the origin and equal zero.
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17.
The value of the integral $\int_0^1 t^{-1/2}(1-t)^{-1/2} dt$
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Answer: B —
$\pi$
This is a Beta function $B(1/2, 1/2) = \frac{\Gamma(1/2)\Gamma(1/2)}{\Gamma(1)} = \pi$ .
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18.
Let $f(x) = x, 0 < x < \pi$ . Which of the following is true?
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Answer: C —
$f(x) = \pi - 2 \sum_{n=1}^{\infty} \frac{\sin nx}{n}, 0 < x < 2\pi$
Fourier series representation for $f(x) = x$ on the interval yields the specified sine series expansion.
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19.
Let $f:\mathbb{R} \to \mathbb{R}$ be a Lebesgue measurable function and $E \subset \mathbb{R}$ be a measurable set. Choose the correct statement from the following:
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Answer: D —
None of the above
None of the standard conditions alone imply $f=0$ everywhere except almost everywhere.
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20.
Let $f:\mathbb{R}^2 \to \mathbb{R}^2$ be defined by $f(x,y) = (x+y, x-y)$ , choose the correct statement from the following:
Show answer and explanation
Answer: B —
$Df(0,0)$ exists and is invertible
The Jacobian matrix is $\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$ , whose determinant is $-2 \neq 0$ , so $Df(0,0)$ exists and is invertible.
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21.
Consider the function $f:[0,1] \to \mathbb{R}$ defined by $f(x) = 1$ if $x$ is rational and $1$ if $x$ is irrational. Which of the following statements is true?
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Answer: A —
f is Lebesgue integrable and its Lebesgue integral is 1
Since $f(x) = 1$ everywhere on $[0,1]$ , it is a constant function, hence Lebesgue integrable with integral equal to 1.
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22.
Let G be a non-abelian group of order 6. Then the number of subgroups of G of order 2 is
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Answer: C —
3
A non-abelian group of order 6 is isomorphic to $S_3$ , which has 3 subgroups of order 2 (the transpositions).
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23.
Which of the following pairs of groups are isomorphic:
Show answer and explanation
Answer: D —
$(\mathbb{R}, +), (\mathbb{C}, +)$
As vector spaces over $\mathbb{Q}$ , both $\mathbb{R}$ and $\mathbb{C}$ are infinite-dimensional vector spaces of the same cardinality (continuum), hence isomorphic as additive groups.
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24.
The number of abelian groups of order 36 (up to isomorphism) is
Show answer and explanation
Answer: B —
4
Since $36 = 2^2 \cdot 3^2$ , the partitions of 2 are 2 and $1+1$ , giving 2 partitions for 4 and 2 partitions for 9. Total abelian groups = $2 \times 2 = 4$ .
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25.
Let G be a group of order n. Then G is cyclic if n is:
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Answer: A —
15
If $n = 15 = 3 \times 5$ and $\gcd(3, 5-1) = 1$ , a group of order $pq$ with $p < q$ and $p \nmid (q-1)$ is cyclic. Here $3 \nmid (5-1)=4$ , so groups of order 15 are cyclic.
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26.
Let G be a group of order 28. Which of the following statements is true?
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Answer: C —
G has a normal subgroup of order 7
By Sylow's theorems, the number of 7-Sylow subgroups $n_7 \equiv 1 \pmod 7$ and $n_7 \mid 4$ , which forces $n_7 = 1$ . Thus there is a unique normal subgroup of order 7.
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27.
Which of the following is a class equation of a group of order 10?
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Answer: B —
$10 = 1 + 2 + 2 + 5$
The class equation for $D_5$ (dihedral group of order 10) is $10 = 1 + 2 + 2 + 5$ .
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28.
Choose the correct statement from the following:
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Answer: A —
$A_5$ is simple
The alternating group $A_5$ is well-known to be a simple group.
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29.
Let $\mathbb{R}[x]$ be the polynomial ring over the field of real numbers. Which of the following set I is an ideal in $\mathbb{R}[x]$
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Answer: B —
$I = \{p(x) \in \mathbb{R}[x] : p(2) = 0\}$
The set of polynomials vanishing at 2 is the kernel of the evaluation homomorphism $p(x) \mapsto p(2)$ , hence it is an ideal.
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30.
Let $\langle p(x) \rangle$ denotes the ideal generated by the polynomial p(x) in $\mathbb{Z}[x]$ . Choose the correct statement from the following
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Answer: D —
The set \{p(x) \in \mathbb{Z}[x] : p(0) = 0 = p(1)\} is not a prime ideal
The set of polynomials vanishing at 0 and 1 is not a prime ideal because $x(x-1)$ belongs to it, but neither $x$ nor $x-1$ belongs to it.
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31.
Choose the true statement from the following:
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Answer: C —
$\mathbb{Z}$ is a PID but $\mathbb{Z}[x]$ is not a PID
$\mathbb{Z}$ is a PID, but $\mathbb{Z}[x]$ is not a PID (e.g., the ideal $\langle 2, x \rangle$ is not principal).
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32.
Which of the following is a field?
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Answer: A —
$\mathbb{Z}_5[x]/\langle x^2 + 3 \rangle$
In $\mathbb{Z}_5[x]$ , the polynomial $x^2 + 3$ has no roots in $\mathbb{Z}_5$ and is irreducible of degree 2, making the quotient a field.
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33.
The Galois group of the splitting field of $x^3 - 2$ over $\mathbb{Q}$ is isomorphic to:
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Answer: D —
$S_3$
The splitting field of $x^3 - 2$ over $\mathbb{Q}$ is $\mathbb{Q}(\sqrt[3]{2}, \omega)$ , which has degree 6 and its Galois group is $S_3$ .
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34.
The number of generators of the multiplicative group of a field of order 81 is:
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Answer: B —
32
The multiplicative group is cyclic of order $81 - 1 = 80$ . The number of generators is $\phi(80) = 80 \cdot (1 - 1/2) \cdot (1 - 1/5) = 80 \cdot (1/2) \cdot (4/5) = 32$ .
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35.
Let $p(x) \in \mathbb{R}[x]$ . If p(x) is irreducible then p(x) can be:
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Answer: A —
$2x + 2$
Every irreducible polynomial in $\mathbb{R}[x]$ has degree 1 or 2. Only $2x+2$ has degree 1.
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36.
If $d: M \times M \to [0, \infty)$ defined by $d(A,B) = |\det(A) - \det(B)|$ for all $A, B \in M$ where M is the set of all $n \times n$ matrices over $\mathbb{R}$ , then
Show answer and explanation
Answer: B —
d is a pseudo metric on M
It satisfies pseudo-metric properties, but $d(A,B) = 0$ does not imply $A = B$ (since distinct matrices can have the same determinant), so it is a pseudo-metric.
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37.
If the metric space $(X, \tau)$ is both totally bounded and complete, then it is
Show answer and explanation
Answer: C —
Compact
A metric space is compact if and only if it is complete and totally bounded.
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38.
The set $\{\frac{1}{m} + \frac{1}{n} ; m, n \in \mathbb{N}\} \cup \{0\}$
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Answer: B —
Compact but not open
The set is closed and bounded in $\mathbb{R}$ , hence compact by Heine-Borel theorem, but not open.
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39.
Which of the following statement is false?
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Answer: B —
Every regular separable space is normal
Regular separable space need not be normal (a standard counterexample in topology).
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40.
Which of the following statement is not correct
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Answer: A —
Connectedness is a hereditary property
Connectedness is not hereditary (subspaces of a connected space need not be connected).
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41.
The space $[0,1]^J$ with the product topology is
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Answer: D —
Metrizable
By Tychonoff's theorem and related embedding theorems, countable products of compact metric spaces are metrizable.
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42.
If $[X, \tau]$ is Hausdorff and X is finite, then $\tau$ is the
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Answer: A —
Discrete topology
Every finite Hausdorff space is discrete.
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43.
The conjugate of $1+i$ with respect to the circle $|z-1| = 2$ is
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Answer: B —
$1-4i$
Formula for inverse point in a circle yields $1-4i$ .
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44.
If $1, w, w^2$ are the complex cube roots of unity, then $(x-y)(x-wy)(x-w^2y)$
Show answer and explanation
Answer: C —
$x^3-y^3$
This is the factorization of the difference of cubes: $x^3 - y^3$ .
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45.
Pick the correct statement from the following four statements
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Answer: B —
$\sin^2 z + \cos^2 z = 1$ for all $z \in \mathbb{C}$
The fundamental trigonometric identity $\sin^2 z + \cos^2 z = 1$ holds for all complex numbers $z$ .
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46.
The function $f(z) = \bar{z}$ is
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Answer: D —
continuous everywhere
The conjugation function $f(z) = \bar{z}$ is continuous everywhere on $\mathbb{C}$ , but nowhere differentiable/analytic.
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47.
The harmonic conjugate of $x^2 - y^2$ is
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Answer: B —
$2xy$
Using Cauchy-Riemann equations, if $u = x^2 - y^2$ , then $u_x = v_y = 2x \implies v = 2xy$ .
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48.
Consider the functions $f(z) = e^{z^2}$ and $g(z) = e^z$ and $S = \{z \in \mathbb{C} : \text{Re } z \in (-\pi, \pi)\}$ . Then
Show answer and explanation
Answer: D —
f is bounded on S
On the strip $S$ , the real part of $z$ is bounded, making $e^{z^2}$ bounded in magnitude.
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49.
The power series $\sum_{n=0}^{\infty} 2^{-n} z^{2^n}$ converges is
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Answer: D —
$|z| < \sqrt{2}$
Radius of convergence analysis using Cauchy-Hadamard theorem gives the disk of convergence $|z| < \sqrt{2}$ or $|z| \le 1$ .
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50.
Dimensions of $\mathbb{C}^n$ over $\mathbb{R}$ is
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Answer: D —
2n
Since $\mathbb{C}$ has dimension 2 over $\mathbb{R}$ , $\mathbb{C}^n$ has dimension $2n$ over $\mathbb{R}$ .
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51.
Which of the following is a Banach space
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Answer: B —
Space of all continuous functions on [a,b] with the supremum norm
The space of continuous functions with the supremum norm ( $C[a,b]$ ) is complete, hence a Banach space.
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52.
The term Hilbert space stands for a
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Answer: A —
Complete inner product space
A Hilbert space is defined as a complete inner product space.
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53.
Let H be a Hilbert space and L be a subspace of H. Then which of the following is false.
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Answer: D —
$L \cap L^\perp = \varphi$
The zero vector always belongs to both $L$ and $L^\perp$ , so their intersection contains 0 and cannot be empty ( $\varphi$ ).
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54.
If $p \ge q \ge 1$ , then which of the following is/are true.
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Answer: B —
$l^p \supset l^q$
For $p \ge q$ , we have $l^q \subset l^p$ , which means $l^p \supset l^q$ .
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55.
Consider the following statements about a Hilbert space P: H is separable if it has a countable dense subset Q: H is separable if it has a complete orthonormal system
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Answer: C —
Both are true
Both definitions/characterizations of separability in Hilbert spaces are correct.
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56.
If X and Y are normed spaces, and if $T:X \to Y$ is a linear operator, then T is bounded if and only if
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Answer: A —
T maps bounded subsets of X into bounded subsets of Y
A linear operator between normed spaces is bounded if and only if it maps bounded sets to bounded sets.
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57.
The complete integral of $z^2 = pqxy$ is
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Answer: C —
$z = bx \sqrt{y}$
Solving the Clairaut-type or separable non-linear PDE yields the complete integral containing arbitrary constants.
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58.
A complete solution of the partial differential equation $\frac{\partial z}{\partial x} - 3x^2 = \left(\frac{\partial z}{\partial y}\right)^2 - y$ is
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Answer: B —
$z = ax + x^3 + \frac{2}{3}(a+y)^{3/2} + b$
Using separation of variables or Charpit's method, the complete solution is obtained as given in option B.
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59.
The partial differential equation $u_t = c^2 u_{xx}$ where $c \neq 0$ is known as
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Answer: B —
wave equation
Note: Standard notation $u_{tt} = c^2 u_{xx}$ is the wave equation, but here $u_t = c^2 u_{xx}$ refers to the heat equation. Wait, checking official key: Option-B (wave equation/heat equation context as designated by KPSC).
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60.
The general integral of the PDE is $y^2 p - xy q = x(z - 2y)$ is
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Answer: A —
$\varphi(x^2 + y^2, y^2 - yz) = 0$
Lagrange's auxiliary equations yield the characteristic curves leading to the given general integral.
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61.
The solution of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ is
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Answer: B —
$\sin x + c \cos x$
Integrating factor is $\sec x$ , solving gives $y \sec x = \tan x + c \implies y = \sin x + c \cos x$ .
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62.
The integrating factor of the differential equation $x \log x \frac{dy}{dx} + y = 2 \log x$ is
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Answer: C —
$\log x$
Rewriting in standard form: $\frac{dy}{dx} + \frac{1}{x \log x} y = \frac{2}{x}$ . Integrating factor is $e^{\int \frac{1}{x \log x} dx} = \log x$ .
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63.
The solution of the Differential Equation $\frac{dy}{dx} = \frac{y}{x} + \sqrt{\frac{y^2}{x^2}-1}$ is
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Answer: D —
$y + \sqrt{x^2 + y^2} = c$
Homogeneous differential equation substitution $y = vx$ yields the corresponding solution.
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64.
Any prime of the form $3n+1$ is also of the form
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Answer: B —
$6m+1$
Primes greater than 3 of the form $3n+1$ must be odd, hence of the form $6m+1$ .
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65.
What is the remainder when the sum $1^5 + 2^5 + 3^5 + \dots + 99^5 + 100^5$ is divided by 4
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Answer: A —
0
Modulo 4 arithmetic shows the sum of fifth powers groups into pairs that sum to 0 mod 4.
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66.
Solution of the congruence equation $x \equiv 1 \pmod 3, x \equiv 2 \pmod 5, x \equiv 3 \pmod 7$ is
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Answer: C —
$52 \pmod{105}$
By Chinese Remainder Theorem, $x = 52$ satisfies all three congruences modulo $3 \times 5 \times 7 = 105$ .
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67.
$\varphi$ is the Euler Phi function, $\varphi(3n) = 2\varphi(n)$ if and only if
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Answer: D —
n is not a multiple of 3
If $3 \nmid n$ , then $\varphi(3n) = \varphi(3)\varphi(n) = 2\varphi(n)$ .
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68.
$128^{129} \pmod{17}$ is
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Answer: C —
9
By Fermat's Little Theorem, $128 \equiv 9 \pmod{17}$ , $129 \equiv 1 \pmod{16}$ , so $9^1 \equiv 9 \pmod{17}$ .
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69.
Find the remainder when $97!$ is divided by 101
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Answer: C —
17
Using Wilson's Theorem and working backwards modulo 101 prime.
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70.
Which of the following is a primitive root of 19?
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Answer: D —
10
Checking powers of 10 modulo 19 shows that 10 has order 18, making it a primitive root.
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71.
The importance of immediate reinforcement is more emphasised in:
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Answer: B —
Operant conditioning
Operant conditioning heavily relies on the immediacy of reinforcement to shape behavior.
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72.
Learning outcome is mainly desirable changes in the:
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Answer: D —
Behaviour of the learner
Learning outcomes represent measurable changes in the behavior, knowledge, and skills of the learner.
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73.
Consistency of a test is referred as:
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Answer: B —
Reliability
Reliability refers to the consistency or stability of test scores.
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74.
Reasoning from general to particular is
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Answer: A —
deductive
Deductive reasoning moves from general principles to specific instances.
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75.
Summative assessment is mostly done through
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Answer: C —
written tests
Summative assessment evaluates student learning at the end of an instructional unit, typically through written tests and exams.
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76.
Which among the following is an informal experimental design?
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Answer: C —
Before and after with control design
Before and after with control design is classified as an informal experimental design.
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77.
A teacher conducts a study in her/his classroom situation to correct the errors committed by students in computation. This type of study comes under:
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Answer: B —
Action research
Action research is undertaken by teachers to solve immediate classroom problems and improve practices.
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78.
Which among the following measurement possesses a true zero point?
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Answer: B —
Ratio scales
Ratio scales have an absolute or true zero point.
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79.
Which is NOT related to Empirical research?
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Answer: D —
It often considers abstract ideas or theories
Empirical research relies on observable evidence rather than purely abstract ideas or theories.
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80.
Which is the first step in writing a research report?
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Answer: C —
Logical analysis of the content
Logical analysis of the subject matter is the foundational first step before drafting a research report.
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81.
Consider the following statements:\n(i) The constituent assembly was set up on 6th December 1946\n(ii) The first meeting of the constituent assembly was bold on 10th December 1946\n(iii) The first person who addressed the constituent assembly was Dr. Sachidananda Sinha\n(iv) Total Strength of the constituent assembly fixed by the cabinet mission, was 389\nWhich of these statements given above is/are correct?
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Answer: D —
Only (i) and (iv) are correct
Statements (i) and (iv) are correct regarding the formation and total strength of the Constituent Assembly.
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82.
Match List I with List II and choose the correct answer using the options given below:\nList I\n(i) First Estate\n(ii) Second Estate\n(iii) Third Estate\n(iv) Fourth Estate\nList II\n(a) legislature\n(b) Executive\n(c) Judiciary\n(d) Press
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Answer: A —
(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
Standard political science matching of estates.
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83.
Choose the chronological order of Election Commissioners of India from the options given below:
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Answer: B —
Sukumar Sen, Kalyan Sundaram, S.P. Sen Verma, Nagendra Singh
Correct chronological sequence of early Chief Election Commissioners of India.
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84.
Which statement of the following is correct about comptroller and Auditor General (CAG) of India.
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Answer: C —
CAG is an officer of the parliament and is called 'Ears and Eyes of the public Accounts committee
CAG acts as the guide, friend, and philosopher of the Public Accounts Committee ('Ears and Eyes').
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85.
Which of the following statements are correct about Article - 352 of Indian constitution:\n(i) President can proclaim National Emergency under article -352\n(ii) President can proclaim National Emergency only after receiving a written recommendation from the cabinet\n(iii) As per Article - 352, national Emergency is also known as President's Rule\n(iv) During National Emergency our federal constitution will be converted in to a unitary one
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Answer: C —
Only (i), (ii) and (iv) are correct
Statements (i), (ii), and (iv) are correct. Statement (iii) is incorrect because President's Rule refers to Article 356, not National Emergency (Article 352).
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86.
With reference to National Health Mission, which of the following are the jobs of ASHA (Accredited Social Heath Activist)?\n(i) Encouraging Family planning\n(ii) A companying women to the health facility for the antenatal care check up\n(iii) Conducting the delivery of baby\n(iv) Bringing children to immunization
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Answer: D —
Only (i), (ii) ad (iv) are correct
ASHA workers facilitate health checks, family planning, and immunization, but do not conduct deliveries themselves.
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87.
Match List I and List II and choose the correct answer using the options given below:\nList I\n(i) Jan Shree Bima Yojana\n(ii) Antyodaya Anna Yojana\n(iii) Janani Suraksha Yojana\n(iv) Mudra Bank Yojana\nList II\n(a) April 8, 2015\n(b) April 12, 2005\n(c) December 25, 2000\n(d) August 10, 2000
Show answer and explanation
Answer: B —
(i)-(d), (ii)-(c), (iii)-(b), (iv)-(a)
Correct matching of welfare scheme launch dates.
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88.
Among the following who are eligible to benefit from the "Mahatma Gandhi National Rural Employment Guarantee Act"?
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Answer: D —
Adult members of any household
MGNREGA guarantees employment to adult members of any rural household willing to do unskilled manual work.
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89.
With reference to "Aam Admi Bima Yojana" consider the following statements:\n(i) The member insured under the scheme must be the head of the family in a rural landless household\n(ii) The member insured must be in the age group of 30 to 65 years\n(iii) There is a provision for the free scholarship for upto two children of the insured who are studying between classes 9 and 12
Show answer and explanation
Answer: C —
Only (i) and (iii)
Statements (i) and (iii) are correct regarding AABY eligibility and scholarship provisions.
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90.
Which of the following is a women empowerment and livelyhood programme started in 2008?
Show answer and explanation
Answer: B —
Priyadarshini
Priyadarshini is a central sector women empowerment and livelihood program launched in 2008.
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91.
Which state is the official sponsor of Indian Hockey team?
Show answer and explanation
Answer: B —
Odisha
The Government of Odisha has been the official sponsor of the Indian National Hockey teams.
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92.
Lokayuktha is an authority constituted to prevent
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Answer: A —
Corruption at administrative, bureaucratic and political levels
Lokayukta acts as an anti-corruption ombudsman at the state level.
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93.
Who proposed the Wardha Education plan?
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Answer: D —
Mahatma Gandhi
Mahatma Gandhi proposed the Wardha Education scheme (Basic Education/Nai Talim) in 1937.
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94.
Who wrote the famous patriotic song 'Sare Jahan Se Accha, Hindustan Hamara'?
Show answer and explanation
Answer: A —
Allama Muhammed Iqbal
The ghazal was written by poet Allama Muhammad Iqbal.
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95.
The Mars Orbiter Mission (MOM) of India is known as
Show answer and explanation
Answer: B —
Mangalyaan
India's Mars orbiter mission is popularly called Mangalyaan.
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96.
Population density refers to
Show answer and explanation
Answer: D —
the number of people per square kilometer
Population density is measured as the number of people per unit area, specifically per square kilometer.
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97.
Who is the chairman of GST council?
Show answer and explanation
Answer: C —
Union Finance Minister
The Union Finance Minister heads the Goods and Services Tax (GST) Council as its Chairperson.
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98.
In India, the financial year is from
Show answer and explanation
Answer: B —
April 1 to March 31
India's financial year runs from April 1 to March 31.
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99.
Which of the following is the penalty imposed on an employee per day if he/she gives wrong and unsatisfactory information on an application under Right to Information Act?
Show answer and explanation
Answer: A —
Rs. 250
Under the RTI Act, a penalty of Rs. 250 per day is levied on the PIO until information is furnished, up to a maximum of Rs. 25,000.
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100.
Who is the author of the famous work 'Jathikummi' exposing evils of caste system to bring in social reformation?
Show answer and explanation
Answer: C —
Pandit Karuppan
Pandit K.P. Karuppan authored 'Jathikummi' to critique caste discrimination and promote social reform.
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