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Question : Directions: If A – B means that A is the brother of B, A + B means that A is the sister of B, and A ÷ B means that A is the father of B, then which of the following expressions shows that P is the paternal uncle of R?
Option 1: P + Q ÷ R
Option 2: P ÷ Q – R
Option 3: P – Q ÷ R
Option 4: P – Q + R
Correct Answer: P – Q ÷ R
Solution : Let's check the options – First option: P + Q ÷ R According to the given expression, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
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.
A young man walks toward me with a stick slung across his back and a (1)_______ of sheep at his feet, which carry him down the path (2)______ a crowd of rowdy children. An older man follows, weatherworn but still (3)______, a rifle over his left shoulder. He clicks his tongue to (4)______ the flock. Behind him are two women on horses; I guess (5)______ are his wife and daughter.
Question: Select the most appropriate option to fill in the blank number 3.
Option 1: strong
Option 2: stick
Option 3: thin
Option 4: slow
Correct Answer: strong
Solution : The correct choice is the first option.
Strong is the appropriate choice in this context. This helps convey the intended meaning that an older man followed the young man, who seemed aged but showed great physical power, as he was holding a rifle over
Question : Given here are four sentences. The first sentence is in the correct order, while the rest of the sentences are jumbled. Pick the option that gives their correct order.
A. Environmental engineers are always trying to find solutions to the problem of pollution. B. They also have to deal with medical waste and radioactive leakages. C. The pollution caused by chemicals, oil spills, hazardous and toxic waste is especially dangerous. D. We can help them by avoiding such pollutants and by segregating waste for easy processing.
Option 1: ABDC
Option 2: ACBD
Option 3: ADBC
Option 4: ABCD
Correct Answer: ABCD
Solution : The correct choice is the fourth option.
A. Environmental engineers are always trying to find solutions to the problem of pollution. B. They also have to deal with medical waste and radioactive leakages. C. The pollution caused by chemicals, oil spills, and hazardous and toxic
Question : Directions: Which two signs should be interchanged to make the given equation correct? 588 ÷ 28 × 32 + 72 – 160 = 760
Option 1: – and +
Option 2: ÷ and –
Option 3: + and ×
Option 4: ÷ and +
Correct Answer: – and +
Solution : Given: 588 ÷ 28 × 32 + 72 – 160 = 760
Interchange the mathematical signs given in the equation with the signs given in the options one by one – First option: – and + ⇒ 588 ÷ 28 × 32 –
Question : Select the correct active form of the given sentence. AIDS will have been cured by the year 2070 by scientists.
Option 1: Scientists will have cured AIDS by the year 2070.
Option 2: Scientists cured AIDS by the year 2070.
Option 3: Scientists will cure AIDS by the year 2070.
Option 4: Scientists must have cured AIDS by the year 2070.
Correct Answer: Scientists will have cured AIDS by the year 2070.
Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the
Question : A 1.6 m tall observer is 45 metres away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in metres is: (Take$\sqrt{3}=1.732$)
Option 1: 25.98
Option 2: 26.58
Option 3: 27.58
Option 4: 27.98
Correct Answer: 27.58
Solution : AB = Height of observer = 1.6 m. CD = Height of tower = $h$ m. ∴ DE = ($h$ – 1.6) m BC = AE = 45 metres $\angle$DAE = 30° From $\triangle$DAE, $\tan 30°=\frac{DE}{AE}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{h-1.6}{45}$ ⇒ $h-1.6=15\sqrt{3}$ ⇒ $h – 1.6 =
Question : $\cos ^2 35^{\circ}+\cos 55^{\circ} \cdot \sin 35^{\circ}+\frac{\tan 34^{\circ}}{\cot 56^{\circ}}=$________.
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 1
Correct Answer: 2
Solution : We know that $\sin \theta = \cos (90°-\theta)$ And, $\tan \theta = \cot (90°-\theta)$ So, $\cos ^2 35^{\circ}+\cos 55^{\circ} \cdot \sin 35^{\circ}+\frac{\tan 34^{\circ}}{\cot 56^{\circ}}$ = $\cos ^2 35^{\circ}+\cos (90^{\circ}-35^{\circ}) \cdot\sin 35^{\circ}+\frac{\tan(90^{\circ}- 56^{\circ})}{\cot 56^{\circ}}$ = $\cos ^2 35^{\circ}+\sin 35^{\circ} \cdot \sin 35^{\circ}+\frac{\cot 56^{\circ}}{\cot 56^{\circ}}$ = $\cos
Question : Which of the following is the lowest ratio?
Option 1: 8 : 19
Option 2: 15 : 38
Option 3: 17 : 38
Option 4: 13 : 19
Correct Answer: 15 : 38
Solution : Here, the LCM of the denominators of all the options is 38. So, $\frac{8}{19} = \frac{8×2}{19\times 2}=\frac{16}{38}$ $ \frac{15}{38} $, $ \frac{17}{38}$ $ \frac{13}{19}= \frac{13×2}{19\times 2}=\frac{26}{38}$ $\therefore$ 15 : 38 is the lowest ratio. Hence, the correct answer is 15 : 38.
Question : The difference between the compound interest (compounding half-yearly) for 1 year and the simple interest for 1 year on a certain sum lent out at the annual rate of 10% is Rs, 25. What is the sum?
Option 1: Rs. 12000
Option 2: Rs. 6000
Option 3: Rs. 8000
Option 4: Rs. 10000
Correct Answer: Rs. 10000
Solution : Given, Difference between compound interest and simple interest = Rs. 25, Annual interest rate = 10% We know, Compound Interest for 1 year = $P[(1 + \frac{r}{100})^n- 1]$, where $r$ is the annual interest rate and $n$ is the number of compounding periods. Simple
Question : Directions: In the following question, correct the equation by interchanging two signs. 6 + 8 ÷ 4 – 4 = 8
Option 1: ÷ and =
Option 2: ÷ and +
Option 3: ÷ and –
Option 4: + and –
Correct Answer: + and –
Solution : Given: 6 + 8 ÷ 4 – 4 = 8
Let's check the options – First option: ÷ and = 6 + 8 = 4 – 4 ÷ 8 LHS→6 + 8 = 14 RHS→4 – 4 ÷ 8 = 4 – 0.5
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