If $p : q = 3 : 2$, then ($4p^3 – q^3$) : ($p^3 – 2q^3$) is____?

A. 100:11
B. 99:11
C. 11:100
D. 100:13

Given $p:q = 3:2$, let $p=3k$ and $q=2k$.
Then:$$4p^3 – q^3 = 4(27k^3)-8k^3=108k^3-8k^3=100k^3$$$$p^3 – 2q^3 = 27k^3 – 2(8k^3)=27k^3-16k^3=11k^3$$So the ratio is:$$100:11$$✅ Answer: A. 100 : 11

In triangle 𝑃𝑄𝑅, 𝑂 is the in-centre and ∠𝑄𝑂𝑅 = 132°. What is ∠𝑄𝑃𝑅?

A. 72°
B. 78°
C. 84°
D. 90°

Key Formula:
For a triangle with in-centre $O$,$$\angle QOR = 90^\circ + \frac{1}{2}\angle QPR$$Given:$$132^\circ = 90^\circ + \frac{1}{2}\angle QPR$$$$42^\circ = \frac{1}{2}\angle QPR$$$$\angle QPR = 84^\circ$$✅ Answer: C. 84°

Three machines P, Q and R can complete a job in 10 hours, 15 hours and 30 hours respectively. They work in rotation for one hour each, starting with P. After 6 hours, P stops working, and Q and R continue alternately, starting with Q. How many more hours will Q and R take to finish the job?

A. 10
B. 12
C. 14
D. 16

Rates per hour:
P = $\frac{1}{10}$
Q = $\frac{1}{15}$
R = $\frac{1}{30}$
In 3 hours of the cycle $P+Q+R$, work done is:$$\frac{1}{10}+\frac{1}{15}+\frac{1}{30} = \frac{3+2+1}{30} = \frac{6}{30} = \frac{1}{5}$$
In 6 hours, work done:$$2 \times \frac{1}{5} = \frac{2}{5}$$Remaining work:$$1-\frac{2}{5}=\frac{3}{5}$$Now Q and R work alternately. In 2 hours:$$\frac{1}{15}+\frac{1}{30}=\frac{1}{10}$$To complete $\frac{3}{5}$​:$$\frac{3}{5} \div \frac{1}{10} = 6$$So they need 6 such 2-hour blocks:$$6 \times 2 = 12 \text{ hours}$$✅ Answer: B. 12

Which of the following activities belongs to the tertiary sector?

A. Farming
B. Banking
C. Mining
D. Steel production

The tertiary sector is the service sector. It includes banking, transport, insurance, communication, education, and similar services.
So the correct choice is Banking.
✅ Answer: B. Banking

Who appoints the Governor of a State in India?

A. Prime Minister
B. President
C. Chief Justice of India
D. Speaker of Lok Sabha

In India, the President appoints the Governor of a State.
✅ Answer: B. President

A cube-shaped wooden block has side 9 m. The maximum number of cylinders of diameter 3 m and height 9 m that can be cut from it is formed. If the entire surface of each cylinder is painted at the rate of ₹10 per square metre, what is the total painting cost? (Take $\pi = \frac{22}{7}$)

A. ₹8,820
B. ₹8,910
C. ₹9,000
D. ₹9,180

For the cube of side $9$ m, cylinders of diameter $3$ m can fit as:$$\frac{9}{3} = 3$$So, on one face, $3 \times 3 = 9$ cylinders can be cut.
Now find the surface area of one cylinder:$$2\pi r(r+h)$$Here,$$r = 1.5,\quad h = 9$$So:$$2 \times \frac{22}{7} \times 1.5 \times (1.5+9) = 2 \times \frac{22}{7} \times 1.5 \times 10.5 = 99 \text{ m}^2$$
Cost to paint one cylinder:$$99 \times 10 = ₹990$$
Cost for 9 cylinders:$$9 \times 990 = ₹8910$$
✅ Answer: B. ₹8,910

Among the numbers 842, 617, 953, 726 and 489, what is the product of the first digit of the highest number and the second digit of the lowest number?

A. 64
B. 72
C. 81
D. 90

Highest = 953 → first digit = 9
Lowest = 489 → second digit = 8
👉 9 × 8 = 72
✅ Answer: B. 72

The sum of two numbers is 84. Their difference is one-sixth of their sum. What is their LCM?

A. 210
B. 245
C. 280
D. 315

Let the two numbers be $x$ and $y$.
Given:$$x+y=84$$Their difference is one-sixth of the sum:$$x-y=\frac{1}{6}\times 84=14$$So:$$x=\frac{84+14}{2}=49,\quad y=\frac{84-14}{2}=35$$
Now find LCM of 49 and 35:$$49=7^2,\quad 35=5 \times 7$$$$\text{LCM}=5 \times 7^2=245$$
Correct answer: B. 245

In a code language, MATH = 4137 and CLAM = 3468. What is the code for HAT?

A. 413
B. 137
C. 346
D. 468

MATH = 4137
CLAM = 3468
Common letter = M, A and 3, 4 appears in both
So position doesn’t matter. It is hard to find which is M or A out of 3 or 4. But options can make things easy for us.
Digit 1 and 7 are confirmed because of T and H. Only confusion is “which one is A between 3 or 4?”
Let’s check: HAT
413 = There is no 7 and both 4 and 3 are here – impossible, so incorrect.
137 = 1 and 7 is here . There is only one between 3 or 4. Seems correct.
346 = Both 7 and 1 isn’t here.
468 = Both 7 and 1 isn’t here.

✅ Answer: B. 137

What is the primary symmetry shown by adult starfish?

A. Bilateral symmetry
B. Radial symmetry
C. Asymmetrical body plan
D. Spiral symmetry

Adult starfish show radial symmetry, more specifically pentaradial symmetry.
✅ Answer: B. Radial symmetry

Which Harappan site is known for its fire altars?

A. Harappa
B. Mohenjodaro
C. Kalibangan
D. Lothal

The Harappan site famous for fire altars is Kalibangan.
✅ Answer: C. Kalibangan

In a code language,
A @ B means A is the son of B,
A # B means A is the sister of B,
A + B means A is the wife of B, and
A % B means A is the father of B.
How is Q related to P if 𝑄%𝑅@𝑆#𝑃?

A. Brother-in-law
B. Uncle
C. Son
D. Cousin

Trick:
@ means son of
# means sister of
+ means wife of
% means father of
Q is related to P: 𝑄%𝑅@𝑆#𝑃
– Q is father of R.
– R is son of S.
– S is sister of P.
So S and P are siblings. Since R is the son of S and Q is the father of R, Q is the spouse of S. Therefore, Q is the brother-in-law of P.
✅ Answer: A. Brother-in-law

$\frac{\sqrt[3]{2197}}{\sqrt[4]{16}} \times \frac{4}{13} \times 39$ = ?

A. 72
B. 78
C. 84
D. 96

Solution$$\sqrt[3]{2197}=13$$
because $13^3=2197$.$$\sqrt[4]{16}=2$$
because $2^4=16$.
Now evaluate:$$\frac{13}{2}\times \frac{4}{13}\times 39$$
First simplify:$$\frac{13}{2}\times \frac{4}{13}=2$$
Then:$$2 \times 39 = 78$$
✅ Answer: B. 78

A train 240 m long crosses a pole in 12 seconds. What is its speed?

A. 60 km/h
B. 72 km/h
C. 80 km/h
D. 84 km/h

Speed:$$\frac{240}{12}=20 \text{ m/s}$$Convert to km/h:$$20 \times \frac{18}{5}=72 \text{ km/h}$$✅ Answer: B. 72 km/h

Which gas is released when zinc reacts with dilute hydrochloric acid?

A. Oxygen
B. Carbon dioxide
C. Hydrogen
D. Nitrogen

Zinc reacts with dilute hydrochloric acid to release hydrogen gas.
✅ Answer: C. Hydrogen

Which is the smallest unit of an element that retains its chemical properties?

A. Molecule
B. Atom
C. Ion
D. Electron

The smallest unit of an element that retains its chemical properties is an atom.
✅ Answer: B. Atom

Find the next term in the series:
3, 8, 15, 24, 35, ?

A. 45
B. 46
C. 48
D. 50

Trick:
The trick here is to square first and then subtract 1 but the digit keeps increasing from left to right.
3 = $2^2 – 1 = 4 – 1$
8 = $3^2 – 1 = 9 – 1$
15 = $4^2 – 1 = 16 – 1$
24 = $5^2 – 1 = 25 – 1$
35 = $6^2 – 1 = 36 – 1$
? = $7^2 – 1 = 49 – 1$
👉 Answer C. 48

Which of the following is a metal?

A. Sulphur
B. Oxygen
C. Sodium
D. Chlorine

Among the options, Sodium is a metal.
✅ Answer: C. Sodium

Who composed the Ramayana in Tamil?

A. Vyasa
B. Valmiki
C. Kambar
D. Kalidasa

The original Ramayana was composed by Valmiki, which was in Sanskrit but Kambar composed it later in Tamil in 12th century A.D.
✅ Answer: C. Kambar

If 5𝑥 − 3 = 2𝑥 + 18, what is the value of 𝑥?

A. 5
B. 6
C. 7
D. 8

Simple Trick:
$5x – 3 = 2x + 18 \\ 5x – 2x = 18 + 3 \\ 3x = 21 \\ x = \frac{21}{3} \\ x = 7$
🎯 FINAL ANSWER: C. 7​

The ozone layer is found in the:

A. Troposphere
B. Stratosphere
C. Mesosphere
D. Thermosphere

✅ Answer: B. Stratosphere

Which country is known as the “Land of the Rising Sun”?

A. China
B. Japan
C. Korea
D. Thailand

Japan is known as the “Land of the Rising Sun”. This nickname stems from its location to the east of China, making it appear as if the sun rises from Japan, as well as the Japanese name “Nihon” or “Nippon,” which literally translates to “origin of the sun” or “sun’s origin”.
✅ Answer: B. Japan

Which cell organelle is the site of protein synthesis?

A. Mitochondria
B. Ribosome
C. Golgi body
D. Vacuole

✅ Answer: B. Ribosome

Which part of the human brain controls balance and coordination?

A. Cerebrum
B. Cerebellum
C. Medulla oblongata
D. Pons

The part of the brain responsible for balance and coordination is the cerebellum.
✅ Answer: B. Cerebellum

Which instrument is used to measure atmospheric pressure?

A. Hygrometer
B. Barometer
C. Anemometer
D. Altimeter

✅ Answer: B. Barometer