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Question : If $\sec \theta=2 \frac{4}{23}$,find the value of $\tan^2 \theta$.
Option 1: $2 \frac{16}{529}$
Option 2: $1 \frac{200}{529}$
Option 3: $3 \frac{384}{529}$
Option 4: $3 \frac{177}{529}$
Correct Answer: $3 \frac{384}{529}$
Solution : Given: $\sec \theta=2 \frac{4}{23}=\frac{50}{23}$ We know, $\tan^2\theta=\sec^2\theta-1$ ⇒ $\tan^2\theta=(\frac{50}{23})^2-1$ ⇒ $\tan^2\theta=\frac{2500}{529}-1$ ⇒ $\tan^2\theta=\frac{1971}{529}$ $\therefore \tan^2\theta=3 \frac{384}{529}$ Hence, the correct answer is $3 \frac{384}{529}$.
Question : Directions: Three statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some books are pens. Some books are copies. All copies are pencils. Conclusions: I. Some pencils are pens. II. Some pencils are books.
Option 1: Both conclusions I and II follow
Option 2: Only conclusion I follows
Option 3: Only conclusion II follows
Option 4: Neither conclusion I nor II follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some pencils are pens – From the Venn diagram, it is evident that there is no definite relation between pencils and pens.
Question : When a number is divided by 45, the remainder is 21. What will be the remainder when the number is divided by 15?
Option 1: 6
Option 2: 5
Option 3: 3
Option 4: 0
Correct Answer: 6
Solution : Let the quotient when the number is divided by 45 be $x$. Then, the number should be 45$x$ + 21 = (15 × 3$x$) + 21 Let 3$x$ = P. So, 45$x$ + 21 = 15P + 21 So, it is clear that 15P is
Question : Directions: In this question, some equations are solved on the same basis as a certain system. On the same basis, find out the correct answer out of the four alternatives for the unsolved equation. If 17 + 17 = 2895, 19 + 19 = 3615, then 23 + 23 = ?
Option 1: 5765
Option 2: 5295
Option 3: 2565
Option 4: 4005
Correct Answer: 5295
Solution : Given: 17 + 17 = 2895; 19 + 19 = 3615
Like, 17 + 17 = 2895→172 = 289 Now, on adding 5 at the unit place the result will be 2895. And, 19 + 19 = 3615→192 = 361 Now, on adding
Question : Directions: In the question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four. Mangoes do not ___ all at the same time. Hence, they are not plucked on the same day.
Option 1: germinate
Option 2: ripen
Option 3: grow
Option 4: age
Correct Answer: ripen
Solution : The second option is correct as 'ripen' means to become mature and is ready to be plucked, which contextually fits in the sentence, while plucking of mangoes doesn't go contextually well with other options namely 'germinate', 'age' and 'grow'.
Therefore, the correct statement should
Question : Directions: A sentence or a part of the sentence is printed in bold. Below are alternatives to the bold part that may improve the sentence. Choose the correct alternative. In case no improvement is needed, choose "No Improvement".
It also indicates the caveats and failure modes in the model need to be improved before been used independently.
Option 1: 1
Option 2: 2
Option 4: 4
Correct Answer: 2
Solution : The correct choice is the second option.
In passive constructions, the present continuous tense often employs being, followed by the past participle of the main verb. In this context, being used independently is the appropriate structure.
So, the correct sentence is: It also indicates
Question : 14 persons can build a house in 60 days. How long will it take 30 people to build your house, provided that they all work at the same rate?
Option 1: 28 days
Option 2: 30 days
Option 3: 32 days
Option 4: 56 days
Correct Answer: 28 days
Solution : Total work = 14 × 60 = 840 units. Number of days required for 30 people = $\frac{840}{30} = 28$ days. Hence, the correct answer is 28 days.
Question : Directions: How many maximum triangles are there in the given figure?
Option 1: 20
Option 2: 11
Option 3: 14
Option 4: 17
Correct Answer: 17
Solution : The given figure can be labelled as shown below –
Now, in the above figure, there are a total of 17 triangles. They are ABL, BLJ, ABJ, JKL, KBJ, BJF, BCD, BDF, BCF, DEF, BEF, FGH, FGJ, FHJ, FJI, JHI, AEI.
Hence, the fourth option
Question : During the freedom struggle, who was the only President of the Indian National Congress who resigned from the presidency even after being elected?
Option 1: Subhas Chandra Bose
Option 2: Nellie Sengupta
Option 3: J. B. Kripalani
Option 4: Jawaharlal Nehru
Correct Answer: Subhas Chandra Bose
Solution : The correct answer is Subhas Chandra Bose.
Subhas Chandra Bose was the sole president of the Indian National Congress who resigned from his presidency, even after being elected during the Tripuri crisis in 1939. He was elected as the President of INC
Question : The price of diesel has increased by 26%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he decrease his consumption?
Option 1: 7.2%
Option 2: 9.5%
Option 3: 8.7%
Option 4: 6.5%
Correct Answer: 8.7%
Solution : Let the initial price and initial consumption be 100. So, initial expenditure = 100 × 100 = 10,000 Price after increment of 26% = 126 Expenditure after increment of 15% = 11500 New Consumption = $\frac{11500}{126}$ = 91.27 Difference in consumption = 100 - 91.27
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