A sum of money was divided into 2 parts in the ratio 2:5. First part was invested for 2
years at the annual interest rate of 20% compounded annually. At what rate of simple
interest per annum the second part must be invested for 2 years, so that the interest
earned in both cases is the same?
A group of 630 children is arranged in rows for a group photograph. Each row contains
three fewer children than the row in front of it. What number of rows is not possible?
Suppose that $C$ represents the set of all countries,
$R$ represents the set of all countries that have at least one river flowing through it,
$M$ represents the set of all countries that have at least one mountain in it,
and $D$ represents the set of all countries that have at least one desert in it.
It is given that:
\[
R \cup M \cup D = C
\]
Which one of the following gives the set of all countries that have either a mountain or a river, but do not have a desert in it?
The notation $D^{c}$ represents the complement of the set $D$ with respect to the universal set $C$.
Consider the Boolean expression $ X = \overline{(A + B) \cdot C}$ over two Boolean variables $A$ and $B$. Which one of the following Boolean expressions is equivalent to the given Boolean expression $X$?
Given an unsigned 32-bit integer $x$, which of the following C/C++ expressions correctly toggles $m$ bits starting from position $p$ (with the least significant bit at position $0$)?
Assume: x is the input integer; p is the starting position of the bit range (0-based, LSB at position 0); m is the number of bits to toggle; and No overflow or invalid input conditions occur.
Which of the following correctly toggles $m$ bits of $x$ starting from position $p$?
A debugger is a tool used to test and debug programs. It allows programmers to pause execution at specific points (breakpoints), run code step-by-step, and inspect variables and registers to find logic or runtime errors.
Hence, the correct option is:
✅ Option 3: allows to set breakpoints, execute a segment of program, and display contents of registers.
Dynamic RAM (DRAM) stores each bit of data in a separate capacitor. Due to
leakage, the stored charge tends to dissipate over time and needs to be refreshed
periodically. Consider the following statements: P: DRAM requires refreshing because it uses capacitors to store bits.
Q: SRAM does not require refreshing because it uses flip-flops instead of
capacitors.
R: DRAM is faster than SRAM because it needs less frequent access.
S: DRAM is more suitable for main memory than SRAM due to its density.
In 8-bit two's complement arithmetic, compute the result of the following addition:
A = 10011001, B = 11010111. What is the resulting 8-bit binary value?
In the design of a control unit of a processor, two common approaches are used:
hardware control and microprogrammed control. Consider the following
statements:
Hardware control units are generally faster but more difficult to modify
than microprogrammed control units.
In a horizontal microprogrammed control unit, each control signal has a
separate bit in the control word.
Vertical microprogramming leads to longer control words but provides
greater parallelism.
Microprogrammed control units are typically easier to implement and
modify than hardware control units.
Statement 1 – True: Hardware control units are implemented using combinational logic circuits. They generate control signals directly through hardware, making them faster but difficult to modify since any change requires redesigning the hardware.
Statement 2 – True: In a horizontal microprogrammed control unit, each control signal is represented by a dedicated bit in the control word. This allows maximum parallelism but results in a wide (long) control word.
Statement 3 – False: In vertical microprogramming, control words use encoded fields to represent control signals. This makes the word shorter, not longer, but reduces parallelism since only a few signals can be activated at once.
Statement 4 – True:Microprogrammed control units are easier to implement and modify because control logic is stored in a control memory (microprograms). Modifications can be done by changing microinstructions instead of redesigning hardware.
Consider a system with a CPU having 6 registers and 32-bit instructions. The
maximum possible size of the main memory is 512 KB (1K = 210). Each instruction
takes two registers and one memory address as operands. Which one of the
following correctly gives the maximum possible distinct instructions that can be
there in the instruction set of the CPU?
Which of the following secondary storage devices has the fastest access time: Optical Drive,
Magnetic Tape Drive, Hard Disk Drive (HDD), Solid State Drive (SDD)?
Option (1) – True: Unicode was designed to be backward compatible with ASCII. The first 128 Unicode characters (U+0000 to U+007F) are identical to ASCII, ensuring compatibility.
Option (2) – False: ASCII uses 7 bits per character, while Unicode uses up to 16 bits or more (e.g., UTF-16, UTF-32 encodings).
Option (3) – False: Unicode and ASCII share the same first 128 characters; they are not completely different.
Option (4) – False: Unicode can represent far more characters than ASCII, not fewer.
✅ Correct Answer: (1) Unicode is backward compatible with ASCII and includes all ASCII characters in its encoding.
(4) — Interrupt-driven I/O frees the CPU for compute-heavy jobs; under very I/O-intensive loads, polling (programmed I/O) can outperform by avoiding high interrupt overhead.
(1) ✔ Correct — “It’s been raining since morning.” → Present perfect continuous tense, correct usage.
(2) ❌ Incorrect — “Understand” is a stative verb (expresses a state, not an action) and is not used in the continuous form. Correct form: “They understand the problem.”
(3) ✔ Correct — “It has clear ideas.” → Proper use of “has.”
(4) ✔ Correct — Grammatically fine.
✅ Incorrect sentence:They are understanding the problem.
Study the following sentence: The statue of Christ the Redeemer is located on Rio de
Janeiro, the largest city of Brazil. (Which of the following parts of the sentence is
grammatically incorrect)
After running around the city all day delivering invitations for the wedding, I
desperately needed to hit the sack. (Identify the meaning of the underlined phrase):
Which of the following statements correctly explains the use of articles in the following
sentence: After earning an MBA, Srinivas was able to approach a mathematical problem
from both a business and analytical perspective.
Even though in official statements, the Presidential office has warned against violating
the 25th protocol, the government's inaction against the Market group shows the
government's tacit approval of the movement.(Choose the antonym of the underlined
word):
Consider the matrix $$B=\begin{pmatrix}{-1} & {-1} & {2} \\ {0} & {-1} & {-1} \\ {0} & {0} & {-1}\end{pmatrix}$$. The sum of all the entries of the matrix $B^{19}$ is
The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is
Let A and B be two square matrices of same order satisfying $A^2+5A+5I =0$ and $B^2+3B+I=0$ repectively. Where I is the identity matrix. Then the inverse of the matrix $C= BA+2B+2A+4I$ is
The captains of five cricket teams, including India and Australia, are lined up randomly
next to one other for a group photo. What is the probability that the captains of India and
Australia will stand next to each other?
Treat India–Australia as one block. Then we have $4!$ ways to arrange the block with the other 3 captains, and $2$ orders inside the block (IA or AI). Favorable $=2\cdot4!=48$; total $=5!=120$.
There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and
for red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting
head is
If $\vec{a}, \vec{b}$ and $\vec{c} $ are three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ , $\vec{a}.\vec{c} = 2$ and $\vec{b}.\vec{c} = 1$. If $|\vec{b}| = 1$, then the value of $|\vec{a}| $ is
This is possible only if $\vec{c}$ is not perpendicular to $\vec{a}$, meaning $\vec{c}$ is not just $\vec{a} \times \vec{b}$ but also has a component along $\vec{a}$.
Use the identity:
$(\vec{a} \times \vec{b}) \cdot \vec{c}
= \det(\vec{a},\vec{b},\vec{c})$
But we need magnitudes.
Take dot product of $\vec{b}$ with $\vec{c}$:
If x, y and z are three cube roots of 27, then the determinant of the matrix $\begin{bmatrix}{x} & {y} & {z} \\ {y} & {z} & {x} \\ {z} & {x} & {y}\end{bmatrix}$ is
If $x, y, z$ are three cube roots of $27$, then the determinant of the matrix
\[
\begin{pmatrix}
x & y & z\\[4pt]
y & z & x\\[4pt]
z & x & y
\end{pmatrix}
\]
is:
The cube roots of $27 = 3^3$ are:
\[
x = 3,\qquad y = 3\omega,\qquad z = 3\omega^2,
\]
where $\omega$ is a cube root of unity satisfying
\[
\omega^3 = 1,\qquad 1+\omega+\omega^2 = 0.
\]
For a circulant matrix, the determinant is:
\[
(x+y+z)(x+\omega y+\omega^2 z)(x+\omega^2 y+\omega z).
\]
Now compute the first factor:
\[
x+y+z = 3(1+\omega+\omega^2) = 3\cdot 0 = 0.
\]
Therefore,
\[
\det = 0.
\]
Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be unit vectors such that the angle between them is ${\cos }^{-1}\Bigg{\{}\frac{1}{4}\Bigg{\}}$. If $\vec{b}=2\vec{c}+\lambda \vec{a}$,
where $\lambda$ > 0 and $\vec{b}=4$, then $\lambda$ is equal to
A tower subtends angles $\alpha, 2\alpha$ and $3\alpha$ respectively at points A, B and C which are lying on a horizontal line through the foot of the tower. Then $\frac{AB}{BC}$ is equal to
If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}+\hat{k}$, then a vector of magnitude $\sqrt{22}$ which is parallel to $2\vec{a}-\vec{b}+3\vec{c}$ is
Consider the sample space $\Omega={\{(x,y):x,y\in{\{1,2,3,4\}\}}}$ where each outcome is equally likely.
Let A = {x ≥ 2} and B = {y > x} be two events. Then which of the following is NOT true?
Let the line $\frac{x}{4}+\frac{y}{2}=1$ meets the x-axis and y-axis at A and B, respectively. M is the midpoint
of side AB, and M' is the image of the point M across the line x + y = 1. Let the point P lie on
the line x + y = 1 such that the $\Delta$ABP is an isosceles triangle with AP = BP. Then the
distance between M' and P is
Question: Which one of the following is NOT a correct statement?
The value of standard deviation changes by a change of scale.
The standard deviation is greater than or equal to the mean deviation (about mean).
The sum of squares of deviations is minimum when taken from the mean.
The variance is expressed in the same units as the units of observation.
Answer:Option 4
Why: Variance has squared units, not the same units as the data (e.g., if data are in cm, variance is in cm²). Standard deviation (the square root of variance) has the same units as the data.
Notes:
Change of scale: if each value is multiplied by \(k\), then \(\text{SD}\) becomes \(|k|\cdot \text{SD}\) and \(\text{Var}\) becomes \(k^2\cdot \text{Var}\).
\(\text{SD} \ge \text{Mean Deviation (about mean)}\) is a standard inequality.
\(\sum (x_i - a)^2\) is minimized at \(a = \bar{x}\) (the mean).
An equilateral triangle is inscribed in the parabola $y^2 = x$. One vertex of the triangle is at
the vertex of the parabola. The centroid of triangle is
The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° and 45°, respectively. What is the height of the multistoried building
and the distance between the two buildings?
The number of accidents per week in a town follows Poisson distribution with mean 3 (In Exam Given 2, which is incorrect).
If the probability that there are three accidents in two weeks time is $ke^{-6}$, then the
value of k is
Let $F_1, F_2$ be foci of hyperbola $\frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1$, a>0, b>0, and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a
point on $MF_1$ such that $MF_2\perp{{F}}_1{{F}}_2$, $MF_1\perp{{O}}{{H}}$, $|OH|=\lambda |OF_2|$ with $\lambda \in(2/5, 3/5)$, then the range of the eccentricity $e$ is
If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic roots whose roots $\frac{1}{\alpha^3+\alpha}$ and $\frac{1}{\beta^3+\beta}$ is
Given $x^{2} + ax + b = 0$ with roots $\alpha,\beta$,
we use
$\alpha + \beta = -a$ and $\alpha\beta = b$.
Required new roots are
$\dfrac{1}{\alpha^{3}+\alpha}$ and $\dfrac{1}{\beta^{3}+\beta}$.
Since
$\alpha^{3}+\alpha = \alpha(\alpha^{2}+1)$
and using $\alpha^{2}=-a\alpha-b$ (and same for $\beta$),
after simplification the sum and product of new roots become:
Let $\mathbb{R}\rightarrow\mathbb{R}$ be any function defined as $f(x)=\begin{cases}{{x}^{\alpha}\sin \frac{1}{{x}^{\beta}}} & {,x\ne0} \\ {0} & {,x=0}\end{cases}$, $\alpha , \beta \in \mathbb{R}$. Which of the following is true? ($\mathbb{R}$ denotes the set of all real numbers)
The circle $x^2 + y^2+ \alpha x+ \beta y+ \gamma=0$ is the image of the circle $x^2 + y^2- 6x- 10y+ 30=0$ across
the line 3x + y = 2. The value of $[\alpha+ \beta+ \gamma]$ is (where [.] represents the floor function.)
Let $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$, be two functions such that $h(x) = sgn(g(x))$. Then select
which of the following is not true?( $\mathbb{R}$ denotes the set of all real numbers, sgn stands for
signum function)
1) "The domain of $h(x)$ is the same as the domain of $g(x)$."
$\Rightarrow$ True, because $\operatorname{sgn}(g(x))$ is defined for every $x$ where $g(x)$ is defined.
2) "The domain of continuity of $h(x)$ equals the domain of continuity of $g(x) - \{x\in\mathbb{R} : g(x)=0\}$."
At points where $g(x)\neq 0$, $h(x)$ is locally constant ($1$ or $-1$), hence continuous there (provided $g$ itself is continuous).
At points where $g(x)=0$, $h(x)$ jumps from $-1$ to $1$, so it is discontinuous.
$\Rightarrow$
This statement is true.
3) "The domain of $h(x)$ is different from the domain of $g(x)$ at the same point."
Since for every $x$ in the domain of $g$, $h(x)=\operatorname{sgn}(g(x))$ is defined, the domains are exactly the same; they never differ.
$\Rightarrow$ This statement is false.
4) " $h(x)$ is discontinuous at $g(x)=0$."
At any $x_0$ where $g(x_0)=0$, the left and right limits of $h(x)$ are $-1$ and $1$, not equal to $h(x_0)=0$.
$\Rightarrow$ $h$ is discontinuous there, so this statement is true.
Therefore, the statement which is **not true** is:
$\boxed{\text{Option 3}}$
An airplane, when 4000m high from the ground, passes vertically above another airplane at
an instant when the angles of elevation of the two airplanes from the same point on the
ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes.
Suppose $t_1, t_2, ...t_5$ are in AP such that $\sum ^{18}_{l=0}{{t}}_{3l+1}=1197$ and ${{t}}_7+{{3}}t_{22}=174$. If $\sum ^9_{l=1}{{{t}}_l}^2=947b$, then the value of $b$ is
Since
$P(E|F) = \dfrac{P(E \cap F)}{P(F)}$,
the condition becomes:
$P(E)P(F) = P(E \cap F)$,
which is exactly the definition of independence of $E$ and $F$.
Now check each option:
1) "E and F are independent"
→ This is exactly equivalent to $P(E)=P(E|F)$ (TRUE).
3) $P(F) = P(F|E)$
→ Also true under independence (TRUE).
4) $E^c$ and $F$ are independent
→ Independence is preserved under complements (TRUE).
2) $2P(E^c)P(F^c) \ne P(E \cap F^c)$
→ This statement has no relation to $P(E)=P(E|F)$ and does NOT follow from independence (NOT equivalent).
Therefore, the option that is NOT equivalent is:
Option 2.
A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a
second point h meters above the first, the depression of the foot of the tower is 60°. What is
the horizontal distance of the tower from the point?
There are 40 female and 20 male students in a class. If the average heights of female and
male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet)
of all the students in the class equals
Read definition and all four choices carefully, and find the answer that provides the best
example of the given definition. Answer the question solely on the basis of the definition
given. Definition:
An informal gathering occurs when a group of people get together in a casual, relaxed
manner.
Which situation below is the best example of an informal gathering?
Four people (P,Q,R & S) are standing in a queue. Q is ahead of P. R is between P and S.
If S is at the end of the queue, who is at the front of the queue?
Statement I: The meteorological department predicts deficient rainfall during monsoon season.
→ This is related to weather/climate.
Statement II: The GDP growth estimates have been revised downwards by the government.
→ This is related to economic performance.
Now check each possibility:
1. Is Statement I the cause and Statement II the effect?
No.
A rainfall prediction cannot cause the government to revise GDP growth estimates directly.
GDP revisions depend on multiple economic indicators, not weather predictions.
So cause–effect relationship is not possible.
2. Are both statements effects of a common cause?
No.
Rainfall prediction is an effect of meteorological data.
GDP revision is an effect of economic and financial data.
These two sources of information are completely different → no common cause.
3. Are they effects of independent causes?
Yes.
Statement I is caused by climate analysis.
Statement II is caused by economic analysis.
Each comes from different, unrelated causes.
Correct Answer:
✅ Both the statements I and II are effects of independent causes.
A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips
back 20 feet before he again starts climbing in the beginning of the next hour. If he begins
his ascent at 8.00 am., at what time will he first touch a flag at 120 feet from the ground?
The monkey climbs 30 ft every hour and slips 20 ft after each climb.
Effective gain per hour = 30 - 20 = 10 ft.
So after 9 hours (till 5:00 pm): 9 × 10 = 90 ft.
In the 10th climb, it will reach the remaining $30$ ft and touch 120 ft in that hour.
✅ Final Answer: The monkey first touches the flag at 6:00 pm.
In a remote research outpost, five scientists (Dr. Anand, Dr. Beena, Dr. Chirag, Dr. Dinesh,
and Dr. Elango) are studying a rare phenomenon. They communicate through a secure,
text-based system. Over the course of an hour, the following exchanges occur:
Dr. Anand sends a message to Dr. Beena and Dr. Chirag.
Dr. Beena replies only to Dr. Anand.
Dr. Anand sends a reminder message to who did not reply.
Dr. Chirag sends a message to Dr. Dinesh and Dr. Elango.
While replying to Dr. Chirag, Dr. Dinesh accidentally sends a "Reply All"
Dr. Elango, having received Dr. Chirag's message, sends a message to Dr. Beena.
At the end of this hour, who has received the most messages directly from other scientists
within the group? (Consider only messages sent within the described hour and only
between the five scientists mentioned).
A two digit number is such that the product of its digits is 12. If 36 is added to the number, the digits
interchange their places. What is the number?
At an IIM entrepreneurship summit, two young founders - Karan and Deepak -
introduced their startup. In their quirky opening, they said: "The product of our ages is 240.
And just like in our startup strategy, twice Deepak's age is 4 years more than Karan's age."
How old was Deepak two years ago?
Average Cost (AC) is defined as the sum of Average Fixed Cost (AFC) and Average Variable Cost
(AVC), and dumping is defined as selling a product at a price less than AC but more than AVC. A
company in India, suddenly, found that the demand for its product "ZOOM" has fallen to 60% of the
output produced in that financial year. As a result, the company must sell 40% of the produced
output in a foreign market. If it decides to "dump" 40% of its output in a neighbouring country (by
reducing the price by 20%), what would be the objective of its 'dumping strategy', among the
following? (The company has set a profit margin of 10% of AC while fixing the price of its product
for sale in India).
(a) To minimize losses, (b) to maximize profits, (c) to contribute to the recovery of fixed
costs, (d) to contribute to the recovery of variable costs
A remote island has a unique social structure. Individuals are either 'Truth-tellers' (who always speak the truth) or 'Tricksters' (who always lie). You encounter three inhabitants: X, Y, and Z.
X says: “Y is a Trickster.”
Y says: “Exactly one of us (X, Y, Z) is a Truth-teller.”
Case 1: Assume X is T.
Then Y must be L.
Y’s statement must be false: “Exactly one of us is a Truth-teller” is false.
Truth-tellers so far: X (1).
If Z were L, then exactly one (X) would be T → Y’s statement would be true, contradiction.
So Z must be T.
Configuration: (X T, Y L, Z T) works.
Case 2: Assume X is L.
Then “Y is a Trickster” is false → Y is T.
Now Y’s statement must be true: exactly one of X, Y, Z is T.
We already have Y as T, so X and Z must both be L.
Configuration: (X L, Y T, Z L) works.
Reasoning:
From “Some men are great” and “Some men are wise,” we only know there exists at least one great man and at least one wise man (they may be the same or different).
Conclusion 1 (“All men are great or wise”) is not guaranteed—there could be men who are neither.
Conclusion 2 (“Some men are neither great nor wise”) is also not guaranteed—it's possible every man is in great or wise (or both).
"In order to be a teacher one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor". Which one of the following is not a valid conclusion regarding the above
argument?
Note: In NIMCET 2025 Original Exam given line was missing.
"Which one of the following is not a valid conclusion regarding the above argument?"
A, B, C, D, E, F and G are travelling in three different vehicles: Swift, Creta, and Nexon.
There are at least two passengers in each vehicle. Among them, only two are male. There
are two engineers, two doctors and three teachers.
C is a lady doctor and she does not travel with A and F, who are sisters.
B, a male engineer, travels with only G, a teacher, in a Swift.
D is a male doctor.
Two persons belonging to the same profession do not travel in the same vehicle.
A is not an engineer and travels in a Creta.
The pair of sisters A and F travels in the same vehicle
B is an engineer; doctors are C (lady) and D (male) ⇒ only one engineer left among A/E/F/G.
A is not an engineer and is a teacher; G is a teacher; we need 3 teachers total ⇒ E can be the 3rd teacher.
A and F sit together (in Creta), and no two same professions in one vehicle. Since A is a teacher, F cannot be a teacher; and doctors are already C & D.
Why:
From “All apples are fruits” and “All fruits are tasty,” it follows that all apples are tasty (I).
And from “All apples are tasty,” we can validly infer the particular statement some tasty things are apples (II), via valid conversion of a universal affirmative (“All A are B ⟹ Some B are A”).
A person walks 8 km north, turns right, walks 4 km, turns right again and walks 6 km.
Finally, he turns left and walks 3 km. How far is he from the starting point?
Consider a sequence formed by concatenating the positive integers in increasing order:
12345678910111213 ... Which among the following is the closest to the 2028th digit in
this infinite sequence?
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of
the top of the lighthouse is observed from the ships are 30° degree and 45° repectively.
If the lighthouse is 100 m high, the distance between the two ships is
A research team is studying the effects of three different fertilizers (X, Y, and Z) on the
growth of a specific plant species. They have four experimental plots with different
fertilizer combinations:
Plot 1: Fertilizer X only
Plot 2: Fertilizer Y only
Plot 3: Fertilizer X and Fertilizer Z only
Plot 4: Fertilizer Y and Fertilizer Z only
After a period of observation, they note the following:
Plants in plots with Fertilizer X showed significantly increased height compared to a control group (no fertilizer).
Plants in plots with Fertilizer Y showed a slightly increased leaf area compared to the control group.
Plants in Plot 3 (X and Z) showed no significant difference in height compared to the control group.
Plants in Plot 4 (Y and Z) showed significantly increased height compared to the control group.
Based on these observations, which of the following conclusions is best supported?
