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Question : What is the value of the positive square root of $(69+28\sqrt{5})$?
Option 1: $(7+2\sqrt{5})$
Option 2: $(7-2\sqrt{5})$
Option 3: $(2+7\sqrt{5})$
Option 4: $(2-7\sqrt{5})$
Correct Answer: $(7+2\sqrt{5})$
Solution : Given: $x = 69+28\sqrt{5}$ $⇒ x = 49+20+2×7×2\sqrt{5}$ $⇒ x = 7^2+(2\sqrt{5})^2+2×7×2\sqrt{5}$ $⇒ x = (7+2\sqrt{5})^2$ So, the positive square root of $x$ is $(7+2\sqrt{5})$. Hence, the correct answer is $(7+2\sqrt{5})$.
Question : Directions: In a certain code language, CANADA is written as XZMZWZ, and AFRICA is written as ZUIRXZ. How will DEPRESSION be written in that language?
Option 1: XVKIVGGPLM
Option 2: WVKIVHHRLM
Option 3: XVKIVGGRLM
Option 4: WVKIVGGPLM
Correct Answer: WVKIVHHRLM
Solution : Given: CANADA is written as XZMZWZ, and AFRICA is written as ZUIRXZ.
Write the opposite letters of CANADA, to obtain the required code – C→X, A→Z, N→M, A →Z, D→W, A→Z Thus, CANADA is coded as XZMZWZ. And in, AFRICA is written as ZUIRXZ –
Question : The Ganga Action Plan was directed by:
Option 1: Rajiv Gandhi
Option 2: Atal Bihari Vajpayee
Option 3: Manmohan Singh
Option 4: Indira Gandhi
Correct Answer: Rajiv Gandhi
Solution : The correct answer is Rajiv Gandhi.
The Ganga Action Plan was launched in 1985 by Prime Minister Rajiv Gandhi. It was the first river action plan and was launched under the aegis of the Ministry of Environment, Forestry, and Climate Change (MoEFCC). Now, it
Question : The simple interest on a sum for five years is two-fifths of the sum. The rate of interest per annum is:
Option 1: 1%
Option 2: 8%
Option 3: 6%
Option 4: 4%
Correct Answer: 8%
Solution : Time = 5 years Let the principal be $x$ Rate = $r$ So, simple interest = $\frac{2x}{5}$ Simple interest =$\frac{\text{Principal×Rate×Time}}{100}$ ⇒ $\frac{2x}{5}$ =$\frac{x×r×5}{100}$ ⇒ $r = \frac{2x×100}{5×5x}$ ⇒ $r = \frac{200x}{25x}$ $\therefore r = 8\%$ per annum Hence, the correct answer is 8%.
Question : The respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. What will be the angle of elevation of the top of the tower?
Option 1: 30°
Option 2: 60°
Option 3: 90°
Option 4: 45°
Correct Answer: 60°
Solution : It is given that the respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. So, AB : BC = $5\sqrt{3}:5$ In ΔABC, $\frac{AB}{BC}=\tan\theta$ ⇒ $\frac{5\sqrt{3}}{5}=\tan\theta$ ⇒ $\tan\theta=\sqrt{3}$ $\therefore \theta=60°$ Hence, the correct answer is 60°.
Question : A Navy captain is going away from a lighthouse at the speed of $4(\sqrt3–1)$ m/s. He observed that it took him 1 minute to change the angle of elevation of the top of the lighthouse from 60° to 45°. What is the height (in meters) of the lighthouse?
Option 1: $240\sqrt{3}$
Option 2: $480(\sqrt{3}–1)$
Option 3: $360\sqrt{3}$
Option 4: $280\sqrt{2}$
Correct Answer: $240\sqrt{3}$
Solution : Given: A Navy captain is going away from a lighthouse at the speed of $4(\sqrt3-1)$m/s. Let the base length be $B_{1}$ when the elevation is 60° and the base length be $B_{2}$ when the elevation is 45° and the height of the lighthouse be H.
Question : Which of the following is a natural fibre?
Option 1: Silk
Option 2: Rayon
Option 3: Nylon
Option 4: Polyester
Correct Answer: Silk
Solution : The correct option is Silk.
Fibres are formed by the repetition of carbohydrates, or other substances. They are classified into two types- natural fibres, and artificial fibres. Natural fibres are those that are derived from plant, or animal tissues or geological processes. A few
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) which may improve the sentence. Choose the correct alternative in case no improvement is needed your answer is (4).
There are many species of parakeets in India, the recognisable being the Rose-ringed parakeet.
(1) more recognisable
(2) more recognised
(3) most recognisable
(4) No improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The sentence can be improved using the third option.
Since the sentence is comparing the Rose-ringed parakeet to other species of parakeets in India, "most recognisable" is the correct choice, indicating that it is the most easily recognised among them. Most recognisable is used for
Question : Ravi buys salt at INR 16 per kg and sells it at INR 18 per kg. He also uses the weight of 900 gm instead of 1000 gm. What is Ravi’s actual profit percentage?
Option 1: $23 \%$
Option 2: $20 \%$
Option 3: $23 \frac{11}{18} \%$
Option 4: $25 \%$
Correct Answer: $25 \%$
Solution : The cost price of 1000 gm of salt = INR 16 Cost of 900 gm of salt $= \frac{16}{1000}\times900 = 14.4$ The selling price of 900 gm salt = INR 18 Profit = 18 – 14.4 = 3.6 So, the Profit percentage = $\frac{\text{Profit}}{\text{Cost
Question : Comprehension: In the following passage, some of the words have been deleted. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.
Although the (1)______in the Supreme Court arise out of the judgements or orders made by the Subordinate Courts including the High Courts, but of late the Supreme Court has started entertaining (2)______in which interest of the public at large is involved, and the Court can be moved by any (3)_______or group of persons either by filing a Writ Petition at the Filing Counter of the Court or by (4)________a letter to Hon'ble the Chief Justice of India highlighting the question of public importance for (5)_______this jurisdiction. Question: Select the most appropriate option to fill in the blank number 4.
Option 1: calculating
Option 2: addressing
Option 3: tagging
Option 4: summoning
Correct Answer: addressing
Solution : The correct choice is the second option.
In this context, addressing is a suitable term. The act of sending a letter, especially to a person in authority, often involves addressing the letter to that specific person.
Addressing here means sending or submitting a letter to
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