Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use $\sqrt{7}$ = 2.6).

A. 656 cm²
B. 702 cm²
C. 763 cm²
D. 698 cm²

Let sides = 4x, 5x, 6x
👉 4x + 5x + 6x = 90
👉 15x = 90 → x = 6
$4x = 4\times 6 \\ 5x = 5\times 6 \\ 6x = 6\times 6$
So sides = 24, 30, 36

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

Where: $s = \frac{a+b+c}{2}$
$s = \frac{24+30+36}{2} \\ s = 45$
or directly half of 90 is 45.
Area of triangle =
$\sqrt{45(45-24)(45-30)(45-36)} \\ \sqrt{45\ \times\ 21\ \times\ 15\ \times\ 9}$

Simplify (Exam Trick 🔥): use $\sqrt{7} = 2.6$
Factor smartly: $\sqrt{45\ \times\ 21\ \times\ 15\ \times\ 9}$
$$= \sqrt{(9 \times 5)(3 \times 7)(3 \times 5)(9)}$$$$= \sqrt{9^2 \times 3^2 \times 5^2 \times 7}$$$$= 9 \times 3 \times 5 \times \sqrt{7} = 135\sqrt{7}$$
👉 Using given:$$\sqrt{7} = 2.6$$$$\text{Area of triangle PQR} = 135 \times 2.6 = 351 \text{ cm}^2$$
$Area\ of\ Quadrilateral\ ABCD = 2\times 351 = 702 cm^2$

✅ Answer: B. 702 cm²

❌ Why others wrong:
656, 702, 763 → calculation errors in square root or doubling, not using Heron’s formula.

What should come in place of the question mark (?) in the given series?
89 87 84 79 72 ?

A. 57
B. 59
C. 63
D. 61

Pattern:
The trick here is subtract Prime numbers increasing: 2, 3, 5, 7, 11…
89, 87, 84, 79, 72, ?
89 – 2 = 87
87 – 3 = 84
84 – 5 = 79
79 – 7 = 72
72 – 11 = 61
✅ Answer: D. 61

20% of a number is more than 20% of 620 by 210. The number is:

A. 1520
B. 1720
C. 1670
D. 1770

👉 20% common → remove it
Let number = x
0.2x = 0.2(620) + 210👉 0.2x = 124 + 210 = 334
👉 x = 334 / 0.2 = 1670
✅ Answer: C. 1670

Working of hydraulic lift and hydraulic brakes is based on:

A. Faraday’s law
B. Gay-Lussac’s law
C. Pascal’s law
D. Coulomb’s law

Concept: Hydraulic systems work on pressure transmission in fluids
✅ Answer: C. Pascal’s law

❌ Others:
– Coulomb → electrostatics
– Gay-Lussac → gases
– Faraday → electricity

P, Q, R, S, T, U and V sit around a circular table facing the centre. Only one person sits between U and P when counted from the right of U. Only one person sits between P and R. Only one person sits between U and Q. Only two people sit between V and R. Only one person sits between T and Q. How many people sit between T and V when counted from the left of T?

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

Key Points:
– “right of” means clockwise.
– “left of” means anti-clockwise
– Circular table like a clock: 1,2,3,4,5,6,7.
– There are total 7: P,Q,R,S,T,U,V.
– All we have to do is to fit them in position to solve.

Let’s begin.
1 = U
2 = V
3 = P
4 = T
5 = R
6 = Q
7 = S
✅ Now Check Conditions (Fast Trick Method):
1. U → P (1 person between, right side)
U → ? → P ✔️

2. P → R (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.
U → ? → P → ? → R ✔️

3. U → Q (1 person between): The question did not mention right or left, but the condition denotes it right of Q.
U → ? → P → ? → R → Q → ? → U ✔️ (The circle starts from U to U)

4. V → R (2 people between)
U → V → P → ? → R → Q → ? → U ✔️

5. T → Q (1 person between)
U → V → P → T → R → Q → ? → U ✔️

Now only S left and one sit let as well:
U → V → P → T → R → Q → S → U

The question asked:
👉 How many sit Between T and V (from left of T means anti-clockwise)
T → P → V → U → S → Q → R → T

👉 Answer D: 1

What is the name of the powerful non-nuclear bomb unveiled by Turkey at the 17th International Defence Industry Fair (IDEF) in July 2025?

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

Turkey’s non-nuclear bomb (2025 IDEF)
✅ Answer: C. Gazap

Anand has ₹1407 with him. He divides this amount between his two sons, Anil and Ashok, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Anil’s investment amounts to the same value after 15 years as Ashok’s investment does after 16 years. How much (in ₹) did Anand give to Ashok?

A. 737
B. 837
C. 520
D. 670

🔷 Given
~ Total money = ₹1407
~ Rate = 10% per annum (compound annually)
~ Time:
~~ Anil → 15 years
~~ Ashok → 16 years
Final amounts become equal

🔥 Core Concept (MOST IMPORTANT)
Compound Interest formula:
$A = P(1 + r)^{t}$
👉 Since final amounts are equal:$$P_{Anil}(1.1)^{15} = P_{Ashok}(1.1)^{16}$$
🔷 Step 1: Cancel Common Powers (Shortcut Trick)$$(1.1)^{15} \text{ cancels}$$$$P_{Anil} = P_{Ashok} \times 1.1$$
🔷 Step 2: Convert into Ratio
$$\frac{P_{Anil}}{P_{Ashok}} = 1.1 = \frac{11}{10}$$
👉 So ratio:$$Anil : Ashok = 11 : 10$$
🔷 Step 3: Total = 1407$$11x + 10x = 21x = 1407$$$$x = 67$$
🔷 Step 4: Find Ashok’s Share
$$Ashok = 10x = 10 \times 67 = \boxed{670}$$
🎯 Final Answer:
✅ Answer: D. 670

Which of the following Articles of the Indian Constitution directs the State to ensure equal pay for equal work for both men and women?

A. Article 42(b)
B. Article 15
C. Article 39(d)
D. Article 14

The correct answer is C: Article 39(d).

Which of the following letter-number clusters will replace the question mark “?” in the given series to make it logically complete?
VPG 7, ZTK 11, DXO 15, HBS 19, ?

A. LEU 23
B. MGX 23
C. LGY 24
D. LFW 23

The Key Pattern here is Addition of 4 each:
V→Z→D→H→L
P→T→X→B→F
G→K→O→S→W
7→11→15→19→23
Answer: LFW 23
✅ Answer: D

EGDH is related to FIFI in a certain way based on the English alphabetical order. In the same way, JMHL is related to KOJM. To which of the following is NPRS related, following the same logic?

A. ORTT
B. ORST
C. OSST
D. OOPT

The trick of the patten is the addition of +1, +2, +2, +1 per letter in the sequence.
EGDH → FIFI
E +1 is F
G +2 is I
D +2 is F
H +1 is I

JMHL → KOJM
J +1 is K
M +2 is O
H +2 is J
L +1 is M

Same way for NPRS:
N +1 is O
P +2 is R
R +2 is T
S +1 is T
NPRS → ORTT
✅ Answer: A

The average of 13 numbers is 8. If each number is multiplied by 7, then what will the new average be:

A. 7
B. 8
C. 56
D. 13

Trick:
If all numbers ×7 → average ×7
👉 8 × 7 = 56
✅ Answer: C

Administrators of the Andaman and Nicobar Islands and Puducherry are designated as ____.

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

Admins of UTs like Andaman & Puducherry
✅ Answer: B. Lieutenant Governor

If $(y-12) = 4\sqrt{5}$ , then find the value of $\sqrt{(y-3)} – \frac{1}{\sqrt{(y-3)}}$ .

A. 6
B. 4
C. 8
D. 9

Step 1: Start from the given:$$y – 12 = 4\sqrt{5}$$👉 So,$$y = 12 + 4\sqrt{5}$$
Step 2: What do we actually need?
We must find:$$\sqrt{y-3} – \frac{1}{\sqrt{y-3}}$$
👉 So we need y − 3

Step 3: Substitute y directly$$y – 3 = (12 + 4\sqrt{5}) – 3$$$$= 9 + 4\sqrt{5}$$
Now the REAL Concept Question
We need: $\sqrt{(y – 3)}$
$$\sqrt{9 + 4\sqrt{5}}$$
👉 This is not easy directly unless we recognize a pattern.
Look this:$$(\sqrt{4} + \sqrt{5})^2$$$$= (\sqrt{4})^2 + (\sqrt{5})^2 + 2(\sqrt{4})(\sqrt{5})$$$$= 4 + 5 + 2 \cdot 2 \cdot \sqrt{5}$$$$= 9 + 4\sqrt{5}$$
So if we reverse it back then it will be easy to solve. But the question is how do we know that it is 4 and 5.
Let’s understand!
We reached: $\sqrt{(y – 3)}$
$$\sqrt{9 + 4\sqrt{5}}$$
Now we assume logically (this is a standard method):$$\sqrt{9 + 4\sqrt{5}} = \sqrt{a} + \sqrt{b}$$
👉 Why this assumption?
Because:
$(\sqrt{a} + \sqrt{b})^2 = a^2 + b^2 + 2\sqrt{ab}$

And our expression looks exactly like this form if we remove exponent square on both sides:
$(\sqrt{a} + \sqrt{b}) = a + b + 2\sqrt{ab}$
So we put the value:$$9 + 4\sqrt{5} = a + b + 2\sqrt{ab}$$
Now assign the values: $a + b = 9$
👉 Compare root terms:$$2\sqrt{ab} = 4\sqrt{5}$$
Divide by 2:$$\sqrt{ab} = 2\sqrt{5}$$
Square both sides:$$ab = 20$$
Solve system:$$a + b = 9,\quad ab = 20$$👉 Numbers are:$$a = 4,\quad b = 5$$Hence we get our: $(\sqrt{4} + \sqrt{5})^2$
But: $(\sqrt{a} + \sqrt{b}) = 9 + 4\sqrt{5}$
So we put the values without exponent 2.
$(\sqrt{a} + \sqrt{b}) \\ (\sqrt{4} + \sqrt{5}) \\ (2 + \sqrt{5})$
Now it is simplified, let’s finish this.
$$(2+\sqrt{5}) – \frac{1}{2+\sqrt{5}}$$
Take LCM directly
Common denominator = $2+\sqrt{5}$$$= \frac{(2+\sqrt{5})^2 – 1}{2+\sqrt{5}}$$
Expand numerator:$$(2+\sqrt{5})^2 = 4 + 5 + 4\sqrt{5} = 9 + 4\sqrt{5}$$So:$$\text{Numerator} = 9 + 4\sqrt{5} – 1 = 8 + 4\sqrt{5}$$
Factor numerator$$8 + 4\sqrt{5} = 4(2+\sqrt{5})$$
Cancel$$\frac{4(2+\sqrt{5})}{2+\sqrt{5}} = 4$$
🎯 FINAL ANSWER: B. 4

At the 2025 ICC Champions Trophy held in Dubai, which country did India defeat to secure their seventh ICC title in men’s senior cricket?

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

India defeated:
✅ Answer: C. New Zealand

Which legislation forms the legal basis for the creation and operation of the Central Administrative Tribunal (CAT)?

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

In December 2025, the Finance Minister called on states to manage their debt within the limits prescribed under which fiscal framework?

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

Fiscal discipline framework:
✅ Answer: B. FRBM

Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only five people have exams between V and T. Only two people have exams between R and T. Q has the exam immediately after R. S has the exam immediately before P but after T.
How many people have exams between P and U?

A. One
B. Two
C. Three
D. Four

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: P,Q,R,S,T,U,V.
– All we have to do is to fit them in position to solve.

Let’s begin.
1 = V
2 = S
3 = P
4 = R
5 = Q
6 = U
7 = T
✅ Now Check Conditions (Fast Trick Method):
1. V → T (5 people between)
V → ? → ? → ? → ? → ? → T → V… ✔️ (The circle starts from V to V)

2. R → T (2 people between): (It did not say T and R, so we count from R to T)
V → ? → ? → R → ? → ? → T → V… ✔️

3. S before P but after T: (Did not force us to put S immediately after T, because not possible. But enforce us to put S immediately before P)
V → S → P → R → Q → ? → T → V… ✔️

4. We can assume safely that the last one is U.
V → S → P → R → Q → U → T → V… ✔️

The question asked:
👉 How many people have exams Between P and U
V → S → P → R → Q → U → T → V… ✔️

👉 Answer B: 2

Girish scored 572 marks in an examination and was 30 marks short of 28% of maximum marks. In the same examination, his friend scored 473 marks. What is the percentage of marks scored by his friend?

A. 22%
B. 23%
C. 21%
D. 24%

Trick:
572 = 28% – 30
👉 28% = 602
Max = 602 / 0.28 = 2150
Friend = 473
👉 % = (473/2150) ×100 ≈ 22%
✅ Answer: A

Two taps can fill a cistern in 4 hours and 38 hours respectively. A third tap can empty it in 38 hours. How long (in hours) will it take to fill one-fourth of the empty cistern, if all of them are opened together?

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

Visualize the situation:
One cistern: 1
Tap A fills in: 4 hours
Tap B fills in: 38 hours
Tap C empties in: 38 hours.
So technically the what Tap B fills, Tap C pours out.
One cistern + 4 + 38 -38 = One cistern + 4.

But the question asks how many hours will it take to fill only one-fourth:
One cistern: 4 hours
One-fourth of it:
$\frac{1}{4} \times 4 \\ \frac{4}{4}$
1 hour
✅ Answer: A. 1

If the median of a data is 61.54 less than its mode, then the median of the data exceeds its mean by ____. (Use the empirical formula to find the answer)

A. 32.03
B. 36.77
C. 30.77
D. 28.47

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

Given Condition
“Median is 61.54 less than Mode”$$\text{Mode} = \text{Median} + 61.54$$
Step 1: Substitute in formula$$\text{Median} + 61.54 = 3\text{Median} – 2\text{Mean}$$
Step 2: Rearrange$$61.54 = 2\text{Median} – 2\text{Mean}$$$$61.54 = 2(\text{Median} – \text{Mean})$$
Step 3: Final value$$\text{Median} – \text{Mean} = \frac{61.54}{2} = 30.77$$
🎯 FINAL ANSWER: C. 30.77​

What was the main purpose of the India–MERCOSUR Preferential Trade Agreement discussions held in New Delhi on 16 October 2025?

A. To establish a common currency
B. To coordinate defense policies
C. To standardize education systems
D. To promote trade and investment

Boost trade & investment
✅ Answer: D

Under the Union Budget 2025–26, the FDI limit in the insurance sector was increased from:

A. 26% to 49%
B. 51% to 100%
C. 74% to 100%
D. 49% to 74%

74% → 100%
✅ Answer: C

Refer to the following number and symbol series and answer the question that follows. Counting to be done from left to right only. All numbers are single-digit numbers only.
(Left) © 3 @ 8 5 1 £ 1 6 1 5 7 2 8 # € £ © € © 1 3 (Right)
How many such numbers are there each of which is immediately preceded by a symbol and also immediately followed by a symbol?

A. 1
B. 0
C. 2
D. 3

It asked us how many such numbers: it asks counting of it, not value.
So there is only one number that is between symbols.
© 3 @
👉 Only 1 number
✅ Answer: A

A train travelling at 60 km/hr crosses another train travelling in the opposite direction at 84 km/hr in 30 seconds. What is the combined length (in m) of both the trains?

A. 1000
B. 1300
C. 1200
D. 1100

Trick:
Relative speed = 60 + 84 = 144 km/h
👉 Convert → 144 × 5/18 = 40 m/s
Distance = speed × time
👉 40 × 30 = 1200 m
✅ Answer: C

Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?
FZN 4 XRF 6 PJX 9 HBP 13 ?

A. ZKW 21
B. LFR 17
C. ZTH 18
D. XHD 19

The fastest trick:
Focus only on number here, not pattern.
It increases like 2,3,4,5…
FZN 4 (4 + 2 = 6)
XRF 6 (6 + 3 = 9)
PJX 9 (9 + 4 = 13)
HBP 13 (13 + 5 = 18)

There is only one option with 18.
✅ Answer: C. ZTH 18