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Question : Fill in the blank with the most appropriate option.
It's a challenge, as you yourself said, and men find it hard to turn________challenges.
Option 1: up
Option 2: below
Option 3: down
Option 4: aside
Correct Answer: down
Solution : The correct choice is the third option.
Explanation:
The phrase turn down challenges is idiomatic and means to reject or refuse challenges. In the context of the sentence, the idea is that men find it difficult to decline or avoid challenges.
So, the correct
Question : Upon selling an article at $\frac{3}{7}$ of the marked price, a loss of 30% is incurred. What is the ratio between the marked price and the cost price of the article?
Option 1: 48 : 60
Option 2: 49 : 30
Option 3: 25 : 37
Option 4: 50 : 80
Correct Answer: 49 : 30
Solution : Let the cost price be Rs. 100 Selling price when sold at 30% loss = Rs. 70 Selling price = $\frac{3}{7}$ of Marked price ⇒ Marked price = $\frac{7}{3}$ of Selling price = 70 × ($\frac{7}{3})$ = $\frac{490}{3}$ Required ratio = $\frac{\frac{490}{3}}{100}=49:30$ Hence,
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
Neither the teacher nor the boys (is) in a mood to play.
(1) was
(2) are
(3) will
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The sentence can be improved using the second option.
In the case of neither... nor, the verb must agree to the subject closest to it. Here, the term "boys" is plural and should be followed by a plural verb. This helps in maintaining the
Question : If $\frac{\cos \theta}{1-\sin \theta}+\frac{\cos \theta}{1+\sin \theta}=4,0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\sec \theta+\operatorname{cosec} \theta+\cot \theta) ?$
Option 1: $1+2 \sqrt{3}$
Option 2: $\frac{1+2 \sqrt{3}}{3}$
Option 3: $\frac{2+\sqrt{3}}{3}$
Option 4: $2+\sqrt{3}$
Correct Answer: $2+\sqrt{3}$
Solution : Given, $\frac{\cos \theta}{1-\sin \theta}+\frac{\cos \theta}{1+\sin \theta}=4$ ⇒ $\frac{\cos\theta(1+\sin\theta)+\cos\theta(1-\sin\theta)}{(1+\sin\theta)(1-\sin\theta)}=4$ ⇒ $\frac{\cos\theta+\sin\theta\cos\theta+\cos\theta-\sin\theta\cos\theta}{(1+\sin\theta)(1-\sin\theta)}=4$ ⇒ $\frac{2\cos\theta}{1-\sin^2\theta}=4$ [As $\sin^2\theta+\cos^2\theta=1$] ⇒ $\frac{\cos\theta}{\cos^2\theta}=2$ ⇒ $\cos\theta=\frac{1}{2}$ ⇒ $\theta=60°$ Now, $\sec \theta+\operatorname{cosec} \theta+\cot \theta=\sec60°+\operatorname{cosec}60°+\cot60°$ $=2+\frac{2}{\sqrt3}+\frac1{\sqrt3}$ $=\frac{2\sqrt3+2+1}{\sqrt3}$ $=\frac{2\sqrt3+3}{\sqrt3}$ $=2+\sqrt3$ Hence, the correct answer is $2+\sqrt3$.
Question : a and b are two sides adjacent to the right angle of a right-angled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then p2 is equal to:
Option 1: $a^{2}+b^{2}$
Option 2: $\frac{1}{a^{2}}+\frac{1}{b^{2}}$
Option 3: $\frac{a^{2}b^{2}}{a^{2}+b^{2}}$
Option 4: $a^{2}-b^{2}$
Correct Answer: $\frac{a^{2}b^{2}}{a^{2}+b^{2}}$
Solution : In triangle ABC, The hypotenuse of the triangle, $AC=\sqrt{a^2+b^2}$ The area of triangle ABC, $\frac{1}{2}\times AB \times BC=\frac{1}{2}\times AC\times BD$ $⇒\frac{1}{2}ab=\frac{1}{2}p\sqrt{a^2+b^2}$ $⇒ab=p\sqrt{a^2+b^2}$ Squaring both sides, $⇒a^2b^2=p^2(a^2+b^2)$ $⇒p^2=\frac{a^{2}b^{2}}{a^{2}+b^{2}}$ Hence, the correct answer is $\frac{a^{2}b^{2}}{a^{2}+b^{2}}$.
Question : A canister holds 36 litres of a mixture of milk and water in a ratio of 3 : 1. 15 litres of milk is added to the canister. The new ratio of the mixture is:
Option 1: 12 : 5
Option 2: 14 : 3
Option 3: 7 : 4
Option 4: 9 : 4
Correct Answer: 14 : 3
Solution : Given: A canister holds 36 litres of a mixture of milk and water in a ratio of 3 : 1. Quantity of milk = $\frac{3}{4} × 36 = 27$ Quantity of water = $\frac{1}{4} × 36 = 9$ After adding 15 litres of
Question : A man buys 13 pens for a rupee. How many pens should he sell for a rupee to earn a profit of 30%?
Option 1: 8
Option 2: 10
Option 3: 5
Option 4: 15
Correct Answer: 10
Solution : A man buys 13 pens for a rupee. 1 rupee = 100 paise For a profit of 30%, he sells 13 pens in 100 + 30 = 130 paise So, in 100 paise, the number of pens he sells $=\frac{13}{130}×100=10$ Hence, the correct answer is
Question : Directions: In the following question a series is given, with one number missing. select the missing number from the given alternatives. 84, 42, 28, 21, ?
Option 1: 10.5
Option 2: 16.8
Option 3: 18.4
Option 4: 19.6
Correct Answer: 16.8
Solution : Given: 84, 42, 28, 21, ?
Let's apply the pattern – 84 ÷ (1 + $\frac{1}{1}$) = 42; 42 ÷ (1 + $\frac{1}{2}$) = 28; 28 ÷ (1 + $\frac{1}{3}$) = 21; 21 ÷ (1 + $\frac{1}{4}$) = 16.8
So, 16.8 is the missing term
Question : The value of $\tan1° \tan2° \tan3°...\tan89°$ is:
Option 1: $1$
Option 2: $0$
Option 3: $\sqrt{3}$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $1$
Solution : $\tan1° \tan2° \tan3°...\tan89°$ $= \tan1° \tan2° \tan3°...\tan45°...\tan(90-3)°\tan(90-2)°\tan(90-1)°$ $=\tan1° \tan2° \tan3°...\tan45°...\cot3°\cot2°\cot1°$ As we know, $\tan\theta=\frac{1}{\cot\theta}$ So, it will cancel out all the terms except $\tan45°$. $=\tan45°$ $= 1$ Hence, the correct answer is $1$.
Question : Directions: If P denotes ×, Q denotes ÷, R denotes +, and S denotes –, then what will come in place of (?) in the following equation? $\sqrt[4]{81}$ R 6 P 3 S 26 R 64 = ?
Option 1: 63
Option 2: 65
Option 3: 56
Option 4: 59
Correct Answer: 59
Solution : Given: $\sqrt[4]{81}$ R 6 P 3 S 26 R 64 = ?
After replacing the letters with the mathematical signs, we get: = $\sqrt[4]{81}$ + 6 × 3 – 26 + 64 = 3 + 6 × 3 – 26 + 64 = 3 +
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