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Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: 1. Some vegetables are fruits. 2. Potato is a vegetable. Conclusions: I. Potato is a fruit. II. Potato is not a fruit. III. All vegetables are fruits. IV. Some vegetables are not fruits.
Option 1: None of the conclusions follow
Option 2: Only conclusion I follows
Option 3: Only conclusion IV follows
Option 4: Only conclusion III follows
Correct Answer: None of the conclusions follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyze the conclusions – Conclusion I: Potato is a fruit – From the Venn diagram, it is evident that there is no definite relation between potato and
Question : Directions: In the following question, select the number that can be placed at the sign of the question mark (?) from the given alternatives.
Option 1: 4
Option 2: 6
Option 3: 8
Option 4: 16
Correct Answer: 4
Solution : The sum of the numbers given in all four blocks except the centre block is equal to the multiplication of digits given in the centre block.
In the first figure – (5 + 6 + 7 + 9) = 27; 93→9 × 3 =
Question : Directions: After interchanging which two signs will the value of the given expression be 37? 27 + 3 ÷ 81 × 93 – 57
Option 1: + and ÷
Option 2: – and +
Option 3: × and +
Option 4: ÷ and –
Correct Answer: × and +
Solution : Given: 27 + 3 ÷ 81 × 93 – 57
Replace the given symbols in the options one by one with the original symbols in the given equation. First options: + and ÷ 27 + 3 ÷ 81 × 93 – 57 On
Question : Directions: In the following question, some parts of the sentence may have 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."
One (1) / may help (2) / oneself. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The correct option is the fourth option.
There is no error in the sentence, as when "one" is used as a subject, it should be followed by an object containing "one".
The correct sentence is: "One may help oneself."
Question : Select the most appropriate option to fill in the blank. She frankly confessed that she couldn’t __________ to purchase a car then.
Option 1: spend
Option 2: afford
Option 3: stand
Option 4: tolerate
Correct Answer: afford
Solution : The second option is the correct choice.
The sentence suggests that the person confessed she couldn't do something related to purchasing a car. The word that fits best in this context is afford, which means to have the financial means or resources to buy or
Question : Directions: In the following question, identify the correct response from the given premises stated according to the following symbols. In a certain code language, + represents ×, – represents +, × represents ÷ and ÷ represents –. What is the answer to the following equation? 80 × 16 ÷ 4 + 2 – 8 = ?
Option 1: 11
Option 2: 64
Option 3: 30
Option 4: 5
Correct Answer: 5
Solution : Given: 80 × 16 ÷ 4 + 2 – 8 = ?
On replacing the symbols as per the instruction, the equation becomes – = 80 ÷ 16 – 4 × 2 + 8 = 5 – 4 × 2 + 8 = 5 –
Question : A tradesman marks his goods 25% above the cost price and allows his customers a discount of 12% on their bill. How much % profit do tradesmen realize?
Option 1: 13%
Option 2: 11%
Option 3: 12%
Option 4: 10%
Correct Answer: 10%
Solution : Let the cost price be Rs.100. Marked price = 100 +2 5 = Rs. 125 Discount = 12% of marked price Selling price = 88% of marked price = 0.88 × 125 = Rs. 110 Profit = 110 – 100 = 10 Profit % =
Question : Which of the following are also called the amphibians of the plant kingdom?
Option 1: Pteridophytes
Option 2: Thallophytes
Option 3: Angiosperms
Option 4: Bryophytes
Correct Answer: Bryophytes
Solution : The correct option is Bryophytes.
The term "amphibians of the plant kingdom" is often used to refer to bryophytes. Bryophytes are a group of non-vascular plants that include mosses, liverworts and hornworts. They are called "amphibians" because they are typically found in moist environments
Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.
Option 1: $4 \sqrt{2} \mathrm{~cm}^2$
Option 2: $7 \sqrt{2} \mathrm{~cm}^2$
Option 3: $5 \sqrt{2} \mathrm{~cm}^2$
Option 4: $6 \sqrt{2} \mathrm{~cm}^2$
Correct Answer: $5 \sqrt{2} \mathrm{~cm}^2$
Solution : Given: 1st side = 4 cm 2nd side = 5 cm Angle between them = $45^\circ$ We know that, Area of triangle = $\frac{1}{2}\times\text{1st side × 2nd side}\times\sin\theta$ = $\frac{1}{2}\times4\times5\times\sin45^\circ$ = $10\times\frac{1}{\sqrt2}$ = $5\sqrt2$ Hence, the correct answer is $5\sqrt2\ cm^2$.
Question : If $x^2-\sqrt{7} x+1=0$, then what is the value of $x^5+\frac{1}{x^5} ?$
Option 1: $19 \sqrt{7}$
Option 2: $21 \sqrt{7}$
Option 3: $25 \sqrt{7}$
Option 4: $27 \sqrt{7}$
Correct Answer: $19 \sqrt{7}$
Solution : Given: $x^2-\sqrt{7} x+1=0$ Dividing by $x$, we get: ⇒ $x+\frac{1}{x}=\sqrt{7}$ Now, Squaring both sides, we get: ⇒ $(x+\frac{1}{x})^2=(\sqrt{7})^2$ ⇒ $x^2+\frac{1}{x^2}+2=7$ ⇒ $x^2+\frac{1}{x^2}=5$ Similarly, Cubing both sides, we get: ⇒ $(x+\frac{1}{x})^3=(\sqrt{7})^3$ ⇒ $x^3+\frac{1}{x^3}+3(x\times\frac{1}{x})(x+\frac{1}{x})=7\sqrt7$ ⇒ $x^3+\frac{1}{x^3}+3\sqrt 7=7\sqrt7$ ⇒ $x^3+\frac{1}{x^3}=4\sqrt7$ Now, $x^5+\frac{1}{x^5}=(x^3+\frac{1}{x^3})\times(x^2+\frac{1}{x^2})-(x+\frac{1}{x})$ = $4\sqrt7\times5-\sqrt7$ = $20\sqrt7-\sqrt7$ =
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