The area of a quadrilateral WXYZ is three times the area of triangle LMN. The sides of triangle LMN are in the ratio 3 : 5 : 7, and its perimeter is 60 cm.
Find the area of quadrilateral WXYZ. (use $\sqrt{3}$ = 1.73).

A. 103.8 cm²
B. 207.6 cm²
C. 248.6 cm²
D. 319.8 cm²

Let sides = 3x, 5x, 7x
👉 3x + 5x + 7x = 60
👉 15x = 60 → x = 4
$3x = 3\times 4 \\ 5x = 5\times 4 \\ 7x = 7\times 4$
So sides = 12, 20, 28

Using Heron’s Formula: $A = \sqrt{s(s-a)(s-b)(s-c)}$

Where: $s = \frac{a+b+c}{2}$
$s = \frac{12+20+28}{2} \\ s = 30$
Or directly half of 60 is 30.
Area of triangle =
$\sqrt{30(30-12)(30-20)(30-28)} \\ \sqrt{30\ \times\ 18\ \times\ 10\ \times\ 2}$

Simplify (Exam Trick 🔥): use $\sqrt{3} = 1.73$
Factor smartly: $\sqrt{30\ \times\ 18\ \times\ 10\ \times\ 2}$
$\sqrt{(6\ \times\ 5)(6\ \times\ 3)(5\ \times\ 2)(2)}$
$\sqrt{6^2\ \times\ 5^2\ \times\ 2^2\ \times\ 3} \\ 6\ \times\ 5\ \times\ 2\ \times\ \sqrt{3} \\ 60\ \times 1.73$
The exponent 2 cuts the square root and we have given the value of square root 3 already in question.
Area of triangle LMN = $60\ \times\ 1.73 = 103.8$
Area of Quadrilateral WXYZ = $2\ \times\ 103.8 = 207.6$

✅ Answer: B. 207.6 cm²

❌ Why others wrong:
calculation errors in square root or doubling or without using heron or no factorizing.

What should come in place of the question mark (?) in the given series?
75, 73, 70, 65, 58, ?

A. 47
B. 49
C. 51
D. 53

Pattern:
The trick here is subtract Prime numbers increasing: 2, 3, 5, 7, 11…
75, 73, 70, 65, 58, ?
75 – 2 = 73
73 – 3 = 70
70 – 5 = 65
65 – 7 = 58
58 – 11 = 47
✅ Answer: A. 47

25% of a number is 150 more than 25% of 800. Find the number.

A. 1400
B. 1600
C. 1800
D. 2000

25% of 800 = 200
Given:
25% of number is 150 more = 200 + 150 = 350
Since it was only 25% of the total value that means it was one-fourth. When we multiply it by 4 then we get the full value.
So the number is = 350 × 4 = 1400
✅ Answer: A. 1400

A medical lift in a hospital raises a patient chair using fluid pressure in a sealed system. Which law explains its working?

A. Newton’s first law
B. Pascal’s law
C. Archimedes’ principle
D. Boyle’s law

Correct answer: B. Pascal’s law
Solution:
In a closed fluid, pressure applied at one point is transmitted equally in all directions. That is exactly the principle behind hydraulic lifts and similar fluid-based machines.

Why the others are incorrect:
A. Newton’s first law is about inertia, not fluid pressure.
C. Archimedes’ principle explains buoyancy, not hydraulic systems.
D. Boyle’s law relates pressure and volume of gases, not force transmission in a liquid.

Six friends A, B, C, D, E and F sit around a circular table facing the centre. D sits immediately right of A. There is one person between A and B. There is one person between B and C. E sits immediately left of A. How many people sit between E and D when counted from the left of E?

A. 1
B. 2
C. 3
D. 4

Key Points:
– “right of” means clockwise.
– “left of” means anti-clockwise
– Circular table like a clock: 1,2,3,4,5,6.
– There are total 6: A,B,C,D,E,F.
– All we have to do is to fit them in position to solve.

Let’s begin.
1 = A
2 = D
3 = B
4 = F
5 = C
6 = E
✅ Now Check Conditions (Fast Trick Method):
1. A → D (1 person between, right side)
A → D ✔️

2. A → B (1 person between): The question did not mention right or left, but we know the obvious. Since it is a circle and based on conditions.
A → D → B ✔️

3. B → C (1 person between): The question did not mention right or left, but the condition denotes left of E.
A → D → B → ? → C → ? → A ✔️ (The circle starts from A to A)

4. E → A (left of A)
A → D → B → ? → C → E → A ✔️

Now only F left and one sit let as well:
A → D → B → F → C → E → A ✔️

The question asked:
👉 How many sit Between E and D (from left of E means anti-clockwise)
E → C → F → B → D →A → E ✔️

👉 Answer C: 3

Which weapon was reported in July 2025 as Türkiye’s most powerful non-nuclear aerial bomb unveiled at IDEF 2025?

A. Gazap
B. Nebula
C. Titan
D. Phantom-X

Correct answer: A. Gazap
Solution:
Türkiye unveiled GAZAP at IDEF 2025 as its most powerful conventional/non-nuclear aerial bomb.

Meera divides ₹2100 between two fixed deposits, X and Y. Both earn 10% per annum compounded annually. After 5 years, the amount in X becomes equal to the amount in Y after 6 years. How much did she invest in Y?

A. ₹900
B. ₹1000
C. ₹1100
D. ₹1200

Solution:
Let the amount invested in X be ₹x and in Y be ₹y.
Given:
x + y = 2100
Also,
x(1.1)⁵ = y(1.1)⁶
Divide both sides by (1.1)⁵:
x = 1.1y
Substitute into the total:
1.1y + y = 2100
2.1y = 2100
y = 2100/2.1
y = 1000
So, Meera invested ₹1000 in Y.

Which Article of the Indian Constitution directs the State to promote the educational and economic interests of the weaker sections, especially the Scheduled Castes and Scheduled Tribes?

A. Article 39(d)
B. Article 46
C. Article 42
D. Article 14

Correct answer: B. Article 46
Solution:
Article 46 states that the State shall promote with special care the educational and economic interests of the weaker sections of the people, especially the Scheduled Castes and Scheduled Tribes.

Why the others are incorrect:
A. Article 39(d) is about equal pay for equal work.
C. Article 42 is about just and humane conditions of work and maternity relief.
D. Article 14 guarantees equality before law.

Which letter-number cluster will replace the question mark?
FJQ 6, HLS 9, JNU 12, LPW 15, ?

A. NRY 18
B. NRX 18
C. NQY 18
D. MSY 18

The Key Pattern here is Addition of 2 each letters and 3 in each number:
F→H→J→L→N
J→L→N→P→R
Q→S→U→W→Y
6→9→12→15→18
Answer: NRY 18
✅ Answer: A

In a certain code, each letter is shifted alternately by +2 and -1. How is BRISK written?

A. DQKRM
B. DPKRM
C. DQKRN
D. EQKRM

Correct answer: A. DQKRM
Solution:
Apply the shifts letter by letter:
B → D (+2)
R → Q (-1)
I → K (+2)
S → R (-1)
K → M (+2)
So BRISK becomes DQKRM.

The average of 10 numbers is 9. If each number is multiplied by 4 and then 6 is subtracted from each result, what will be the new average?

A. 24
B. 30
C. 36
D. 42

Correct answer: B. 30
Solution:
If every number is multiplied by 4, the average also becomes 4 times as large:
9 × 4 = 36
Then 6 is subtracted from each number, so the average decreases by 6:
36 – 6 = 30
So the new average is 30.

Under Article 239, a Union Territory is administered by a ___.

A. Administrator
B. Governor
C. Chief Minister
D. Speaker

Correct answer: A. Administrator
Solution:
The official rule is that Union Territories are administered under Article 239, and the Government of India notes that such administrators may be called Administrator, Lieutenant Governor, or Chief Commissioner depending on the UT. The constitutional term asked here is Administrator.

Why the others are incorrect:
B. Governor is the head of a State, not the standard term for Union Territory administration.
C. Chief Minister heads an elected State government.
D. Speaker is the presiding officer of a legislature.

If $x + \frac{1}{x} = 6$, find the value of $x^2 + \frac{1}{x^2}$.

A. 34
B. 32
C. 36
D. 30

🔴 Step 0: What are we given?$$x + \frac{1}{x} = 6$$We need:$$x^2 + \frac{1}{x^2}$$
👉 Problem: we have powers 1, but we need powers 2
👉 So we must somehow convert power 1 → power 2
🧠 Step 1: WHY we square?
To go from:
$x → x^2$
$\frac{1}{x} → \frac{1}{x^2}$
👉 The only natural operation is square
Because:$$(x)^2 = x^2 \quad \text{and} \quad \left(\frac{1}{x}\right)^2 = \frac{1}{x^2}$$✔️ That’s why we square the whole equation.
🟢 Step 2: Apply squaring$$(x + \frac{1}{x})^2 = 6^2$$👉 Left side squared
👉 Right side also MUST be squared (rule of equations ⚖️)$$= 36$$
🧠 Step 3: Where did this identity come from?
Now we expand using basic formula:
👉 YES — this is from:$$(a + b)^2 = a^2 + b^2 + 2ab$$Apply here:
Let:
$a = x$
$b = \frac{1}{x}$
Then:
$(x + \frac{1}{x})^2 = x^2 + \frac{1}{x^2} + 2\cdot x \cdot \frac{1}{x}$

🧠 Step 4: Where did 2 come from?
From this part:$$2ab$$Now substitute:$$2 \cdot x \cdot \frac{1}{x}$$👉 $x$ cancels:$$= 2 \cdot 1 = 2$$✔️ That’s where the +2 comes from

🟡 Step 5: Final expanded form$$x^2 + \frac{1}{x^2} + 2 = 36$$
🧠 Step 6: Why we “shift” 2?
We want ONLY:$$x^2 + \frac{1}{x^2}$$So remove extra +2$$x^2 + \frac{1}{x^2} = 36 – 2$$$$= 34$$✅ Final Answer: A. 34

⚡ Ultra Short Exam Method
See:$$x + \frac{1}{x} = 6$$Direct formula:$$x^2 + \frac{1}{x^2} = (given)^2 – 2$$Put value:
$6^2 – 2 \\ 36 – 2 = 34$

Which team did the Indian Women’s Cricket Team defeat to win their maiden ODI World Cup in Nov 2025?

A. South Africa
B. England
C. New Zealand
D. Australia

India defeated:
✅ Answer: A. South Africa

Which Act provides the legal basis for the Central Administrative Tribunal?

A. The Service Matters Act, 1990
B. The Administrative Tribunals Act, 1985
C. The Judiciary Act, 1971
D. The Tribunals Reforms Act, 1980

CAT formed under:
✅ Answer: B. Administrative Tribunals Act, 1985

The fiscal discipline law that underpins India’s debt and deficit management is known as the:

A. GST
B. FRBM
C. Monetary Policy
D. NITI Aayog

Fiscal discipline framework:
✅ Answer: B. FRBM

Seven people W, X, Y, Z, A, B, and C are waiting for their food to serve on a round table facing to center. The waiter serves the food to W first then A. There are three people between W and A. C is in the middle of W and A with one person on both sides. B gets the food who is sitting after A. The waiter serves Z who is sitting before W. How many people waiter has not served yet?

A. 1
B. 2
C. 3
D. 4

Key Points:
– “after” goes clockwise.
– “before” goes anti-clockwise
– Circular table like a clock: 1,2,3,4,5,6,7.
– There are total 7: W,X,Y,Z,A,B,C.
– All we have to do is to find who did not get food. That is the trick here.

Let’s begin.
1 = W
2 = ? (X or Y)
3 = C
4 = ? (X or Y)
5 = A
6 = B
7 = Z

The question asked:
👉 How many people did not get food?
It is clear X and Y were not mentioned at all in question and the question tells only position of C. hence there are three people C,X,Y who did not get food.

👉 Answer C: 3

Arjun scored 452 marks in an examination and was 28 marks short of 30% of the maximum marks. His friend scored 400 marks. What percentage of the maximum marks did his friend score?

A. 24%
B. 25%
C. 26%
D. 27%

Correct answer: B. 25%
Solution:
If 452 is 28 short of 30%, then 30% of the maximum marks is:$$452+28=480$$
So the maximum marks are:$$\frac{480\times 100}{30}=1600$$
Friend’s percentage:$$\frac{400}{1600}\times 100=25\%$$

A pipe fills a tank in 6 hours, another pipe fills it in 12 hours, and a drain empties it in 8 hours. If all are opened together, how long will it take to fill half the tank?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours

Correct answer: B. 4 hours
Solution:
Net rate per hour:$$\frac{1}{6}+\frac{1}{12}-\frac{1}{8} = \frac{4}{24}+\frac{2}{24}-\frac{3}{24} = \frac{3}{24} = \frac{1}{8}$$
So the tank fills at $\frac{1}{8}$​ per hour.
To fill half the tank:$$\frac{1/2}{1/8}=4 \text{ hours}$$

If the mode of a data set is 74.8 and the median is 58.4, then by how much does the median exceed the mean? (Use the empirical relation.)

A. 7.2
B. 8.2
C. 9.2
D. 10.2

🧠 Empirical Formula Trick (Do in 20–30 sec)
We use the standard relation:
$\text{Mode} = 3\text{Median} – 2\text{Mean}$

Correct answer: B. 8.2
Solution:
Using the empirical formula:$$\text{Mode} = 3(\text{Median}) – 2(\text{Mean})$$$$74.8 = 3(58.4) – 2(\text{Mean})$$$$74.8 = 175.2 – 2(\text{Mean})$$$$2(\text{Mean}) = 100.4$$$$\text{Mean} = 50.2$$So,$$\text{Median} – \text{Mean} = 58.4 – 50.2 = 8.2$$

Which country handed over the BRICS presidency to India for 2026?

A. Brazil
B. Russia
C. China
D. South Africa

South Africa
✅ Answer: D

Which ISRO mission involves uncrewed test flights planned for 2026?

A. SAKSHAM
B. Gaganyaan
C. ANIRUDH
D. Aakashyaan

Gaganyaan
✅ Answer: B

Which country has developed the “second living drug” Qartemi for blood cancer?

A. India
B. China
C. South Korea
D. Israel

👉 India (approved by CDSCO).
✅ Answer: A

Two trains are moving in opposite directions at 72 km/h and 54 km/h. They cross each other in 24 seconds. What is the combined length of both trains?

A. 780 m
B. 840 m
C. 900 m
D. 960 m

Correct answer: B. 840 m
Solution:
Relative speed:$$72+54=126 \text{ km/h}$$
Convert to m/s: (The factor 5/18 derived from 1000/3600)$$126\times \frac{5}{18}=35 \text{ m/s}$$
Distance covered in 24 seconds:$$35\times 24=840 \text{ m}$$

Which letter-number cluster will replace the question mark in the series?
ADL 5, CFN 8, EHP 11, GJR 14, ?

A. ILT 17
B. IMT 17
C. ILS 17
D. ILT 18

The fastest trick:
Correct answer: A. ILT 17
Solution:
Look at each part separately:
First letters: A, C, E, G, I
Second letters: D, F, H, J, L
Third letters: L, N, P, R, T
Numbers: 5, 8, 11, 14, 17
So the next term is ILT 17.