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Question : In $\triangle ABC$, right angled at B, if $\tan A=\frac{1}{2}$, then the value of $\frac{\sin A(\cos C+\cos A)}{\cos C(\sin C-\sin A)}$ is:
Option 1: $2$
Option 2: $1$
Option 3: $3$
Option 4: $2\sqrt5$
Correct Answer: $3$
Solution : $\tan A=\frac{1}{2}$ $⇒\frac{BC}{AB}=\frac{1}{2}$ Let $BC=x$ units, then $AB=2x$ units Using Pythagoras theorem, $⇒AC^2=AB^2+BC^2$ $⇒AC^2=x^2+(2x)^2$ $⇒AC^2=5x^2$ $⇒AC =x\sqrt5 $ units Now, we have $\triangle ABC$ right-angled at B, with $\tan A=\frac{1}{2}$, and we've found that $BC=x$, $AB=2x$, and $AC=x\sqrt{5}$. $⇒\sin A = \frac{BC}{AC} = \frac{x}{x\sqrt{5}} =
Question : What is the difference between a single discount of 35% on INR 700 and two successive discounts of 18% and 12% on the same amount (correct to two places of decimals)?
Option 1: INR 51.20
Option 2: INR 50.12
Option 3: INR 52.10
Option 4: INR 49.80
Correct Answer: INR 50.12
Solution : First discount = 35% of 700 Successive discounts = 18% and 12% Effective discount = $18+12-\frac{18×12}{100}= 30-2.16 = 27.84$% Second discount = 27.84% of 700 Required difference = (35 – 27.84)% of 700 = 7.16% of 700 = 0.0716 × 700 = 50.12 Hence,
Question : Directions: In the following question, select the related word from the given alternatives. Intelligent : Dumb :: Inflate : ?
Option 1: Raise
Option 2: Deflate
Option 3: Degrade
Option 4: Aerated
Correct Answer: Deflate
Solution : Given: Intelligent : Dumb :: Inflate : ?
Intelligent and dumb are antonyms. Similarly, inflate and deflate are antonyms.
Hence, the second option is correct.
Question : Directions: Study the following bar graph carefully and answer the question.
Total enrolments in both State University and Central University during the years 1980, 1990, and 2000 are:
Option 1: 80,000
Option 2: 66,000
Option 3: 70,000
Option 4: 76,000
Correct Answer: 70,000
Solution : As per the given graph: The number of students enrolled at State and Central Universities in 1980 = 8000 + 10000 = 18000 The number of students enrolled at State and Central Universities in 1990 = 14000 + 12000 = 26000 The number of students
Question : The wind vane instrument measures the _______.
Option 1: relative humidity
Option 2: temperature
Option 3: wind velocity
Option 4: wind direction
Correct Answer: wind direction
Solution : The correct answer is wind direction.
The wind vane instrument measures the direction of the wind. It is a simple and common meteorological tool used to determine the wind's compass direction. The instrument typically consists of a vane or arrow that aligns itself
Question : The President of which of the following countries was invited as the Chief Guest for the Republic Day parade on 26 January 2020?
Option 1: New Zealand
Option 2: Australia
Option 3: Brazil
Option 4: Indonesia
Correct Answer: Brazil
Solution : The correct option is Brazil.
The President of Brazil, Jair Bolsonaro, was invited as the Chief Guest for the Republic Day parade on January 26, 2020. His invitation reflected various geopolitical considerations and aimed to strengthen India's ties with Brazil in areas like trade,
Question : In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of the chord PQ is:
Option 1: $2\sqrt{13}\;\mathrm{cm}$
Option 2: $5\sqrt{3}\;\mathrm{cm}$
Option 3: $4\sqrt{6}\;\mathrm{cm}$
Option 4: $6\sqrt{5}\;\mathrm{cm}$
Correct Answer: $4\sqrt{6}\;\mathrm{cm}$
Solution :
We have, $\mathrm{AX:BX = 3:2}$ and the radius of the circle is $5\;\mathrm{cm}$. $\mathrm{AX=\frac{3}{5} \times 10 = 6}\;\mathrm{cm}$ $\mathrm{BX=\frac{2}{5} \times 10 = 4}\;\mathrm{cm}$ We know the theorem states that the two chords of a circle intersect within the circle, the product of the segments of
Question : Which of the following fundamental rights implies the prohibition of traffic in human beings, begar and other forms of forced labour?
Option 1: Right against Exploitation
Option 2: Cultural and Educational Rights
Option 3: Right to Constitutional Remedies
Option 4: Right to Freedom of Religion
Correct Answer: Right against Exploitation
Solution : The correct answer is Right against Exploitation.
The Right against Exploitation (Articles 23–24) in the Indian Constitution safeguards against human trafficking, beggars, and forced labour. It explicitly prohibits children's employment in hazardous conditions under the age of 14. Article 23(1) states the
Question : Which measure(s) is the Reserve Bank most likely to take to combat inflation in the economy?
A) Increase repo rate
B) Increase money supply
C) Decrease cash reserve ratio
Option 1: Only A
Option 2: Both B and C
Option 3: Only B
Option 4: Both A and C
Correct Answer: Only A
Solution : The correct answer is Only A.
The repo rate is the interest rate that the central bank of a nation—in India, the RBI—uses to lend money to commercial banks in times of financial crisis. To control inflation and deflation, the Bank of India (RBI)
Question : Which of the following is protected under Wildlife(Protection) Act,1972
Option 1: Porcupine
Option 2: Gerbil
Option 3: Bandicoot rat
Option 4: Squirrel
Correct Answer: Porcupine
Solution : The correct option is Porcupine.
Among the options given, the "porcupine" is protected in India under the Wildlife (Protection) Act of 1972. The porcupine is a Schedule II species under the Act, which means it is legally protected and killing or catching them without valid
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