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Question : Directions: In the following question two statements are given followed by two conclusions, I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions can be drawn from the given statement. Indicate your answer. Statements: Some kings are queens. All queens are beautiful. Conclusions: I. All kings are beautiful. II. All queens are kings.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Either conclusion I or II follows
Option 4: Neither Conclusion I nor Conclusion II follows
Correct Answer: Neither Conclusion I nor Conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All kings are beautiful – From the Venn diagram, it is evident that the circles representing kings and beautiful
Question : Which of the following is a FALSE statement?
Option 1: $\tan ^2 \mathrm{~A}=1-\sec ^2 \mathrm{~A}$
Option 2: $\sin \mathrm{A}=\tan \mathrm{A} \times \cos \mathrm{A}$
Option 3: $\operatorname{cosec}^2 A-1=\cot ^2 A$
Option 4: $\cos A \times \sec A=1$
Correct Answer: $\tan ^2 \mathrm{~A}=1-\sec ^2 \mathrm{~A}$
Solution : We know, $\sec^2 A = 1+ \tan^2 A$ $⇒1-\sec^2 A = -\tan^2 A$ Hence, the correct answer is $1-\sec^2 A = \tan^2 A$.
Question : The price of rice increased by 10%. By how much should we reduce the consumption, so that the expenditure does not increase on rice?
Option 1: $\frac{100}{11}$%
Option 2: $\frac{300}{7}$%
Option 3: $\frac{50}{3}$%
Option 4: $\frac{51}{7}$%
Correct Answer: $\frac{100}{11}$%
Solution : Given: The price of rice increased by 10%. Let the original price of the rice be 100. After the increase, the new price = (100 + 10) = 110 To not increase the expenditure, the consumption needs to be decreased. So, the decrease percentage =
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error".
What man can die (1) / better than (2) / serving his country? (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The error lies in the first part of the sentence.
In the original sentence, the phrase "what man can die" is used to introduce a question. "How" is a better fit for inquiring about the manner or way in which something can
Question : Directions: Select the triad in which the numbers are related in the same way as the numbers of the following triads. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 4 – 200 – 5 6 – 420 – 7
Option 1: 3 – 660 – 9
Option 2: 7 – 780 – 8
Option 3: 8 – 720 – 9
Option 4: 4 – 400 – 7
Correct Answer: 8 – 720 – 9
Solution : Given: (4 – 200 – 5); (6 – 420 – 7)
In the given triads, multiply the first number, the third number, and 10 to get the second number. 4 – 200 – 5→4 × 5 × 10 = 200 6
Question :
If a man were to sell his handcart for Rs. 720, he would incur a loss of 25%. Determine the price at which he must sell it to gain 25%.
Option 1: Rs. 1200
Option 2: Rs. 960
Option 3: Rs. 1152
Option 4: Rs. 768
Correct Answer: Rs. 1200
Solution : The selling price (SP) = Rs. 720 Loss % = 25% The cost price (CP) = $\frac{100}{100–\text{loss%}}$ × SP = $\frac{100}{75}×720$ = Rs. 960 For 25% profit, SP = $\frac{100+\text{Profit%}}{100}$ × CP = $\frac{100+25}{100}×960$ = Rs. 1200 Hence, the correct answer is Rs. 1200.
Question : Direction: Correct the following equation by interchanging the two signs and two numbers.
7 × 6 + 5 – 4 = 33
Option 1: –, × and 4, 5
Option 2: ×, + and 4, 5
Option 3: +, – and 5, 6
Option 4: ×, – and 5, 6
Correct Answer: +, – and 5, 6
Solution : Given: 7 × 6 + 5 – 4 = 33
Let's check from the options –
First option: –, × and 4, 5 ⇒ 7 – 6 + 4 × 5 = 33 = 7 – 6 + 20 = 21
Question : Directions: Select the option figure in which the given figure is embedded as its part (rotation is NOT allowed).
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of the question figure with all the option figures, it is evident that the given question figure is embedded only in the fourth option figure.
Hence,
Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? – and +, 6 and 3
Option 1: 7 – 3 × 2 ÷ 6 + 4 = 17
Option 2: 8 × 3 – 6 + 4 ÷ 2 = 49
Option 3: 7 + 6 ÷ 3 × 8 – 5 = 35
Option 4: 9 – 6 ÷ 4 + 3 × 7 = 8
Correct Answer: 8 × 3 – 6 + 4 ÷ 2 = 49
Solution : Let's check the options – First option: 7 – 3 × 2 ÷ 6 + 4 = 17 On interchanging the mathematical signs and numbers, we get – ⇒ 7 + 6 × 2 ÷
Question : Directions: Study the given pattern carefully and select the number that can replace the question mark (?) in it.
Option 1: 106
Option 2: 132
Option 3: 146
Option 4: 136
Correct Answer: 146
Solution : Add the square of the first number to the second number to get the third number – Row I: 82 + 9 = 64 + 9 = 73 Row III: 72 + 14 = 49 + 14 = 63 Similarly, in Row II:
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