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Question : If $\sqrt {0.05\times 0.5 \times a } = 0.5 \times 0.05 \times \sqrt b$, then $\frac{a}{b}$ is equal to:
Option 1: 0.0025
Option 2: 0.025
Option 3: 0.25
Option 4: 0.00025
Correct Answer: 0.025
Solution : $\sqrt {0.05\times 0.5 \times a } = 0.5 \times 0.05 \times \sqrt b$ On squaring both sides, ⇒ $ 0.05\times 0.5 \times a = 0.5 \times 0.05 \times 0.5 \times 0.05 \times b$ ⇒ $a = 0.5 \times 0.05 \times b$ ⇒ $\frac{a}{b} = 0.5
Question : For what value of k will the expression x6 – 18x3 + k be a perfect square?
Option 1: –9
Option 2: –81
Option 3: 9
Option 4: 81
Correct Answer: 81
Solution : Given: x6 – 18x3 + k Let x3 = y The given expression becomes y2 – 18y + k. Now break the expression into the form of (a – b)2 = a2 – 2ab + b2 So, y
Question : Which of the following state governments announced a four-year mentorship programme called 'Project Arohan', to provide guidance to students and improve their skills, in February 2022?
Option 1: Assam
Option 2: Uttar Pradesh
Option 3: Karnataka
Option 4: Himachal Pradesh
Correct Answer: Assam
Solution : The correct answer is Assam
To help students develop their abilities and receive assistance, the Assam government has started a four-year mentorship initiative named Project Arohan. To do this, Assam Chief Minister Himanta Biswa Sarma met with Anita Rajan, CEO of Tata STRIVE, a Tata
Question : Directions: UOKG is related to VPLH in a certain way based on the English alphabetical order. In the same way, KQWY is related to LRXZ. To which of the following is AMSW related to following the same logic?
Option 1: BNTX
Option 2: WKTC
Option 3: BOTY
Option 4: ZMRW
Correct Answer: BNTX
Solution : Given: UOKG is related to VPLH and KQWY is related to LRXZ.
Add 1 to the place value of the letters of UOKG and KQWY, to obtain the required code – UOKG→U + 1 = V; O + 1 = P; K + 1 =
Question : Direction: A bar graph showing the heights of six mountain peaks is given below. Study the bar graph and answer the question.
When the heights of the given peaks are written in ascending order, what is the average of the middle two peaks?
Option 1: 7950 m
Option 2: 7560 m
Option 3: 7650 m
Option 4: 7850 m
Correct Answer: 7850 m
Solution : The heights of the given peaks are written in ascending order as follows: 6000 m, 6500 m, 7500 m, 8200 m, 8600 m, 8800 m The average of the middle two peaks is $\frac{7500+8200}{2}=7850$ m Hence, the correct answer is 7850 m.
Question : Directions: In a certain code language, A + B means A is the mother of B; A – B means A is the brother of B; A × B means A is the wife of B; A ÷ B means A is the father of B. Based on the above, how is D related to F if B + C × D – E ÷ F?
Option 1: Brother's brother
Option 2: Mother's husband
Option 3: Wife's father
Option 4: Father's brother
Correct Answer: Father's brother
Solution : Given: B + C means B is the mother of C. D – E means D is the brother of E. C × D means C is the wife of D. E ÷ F means E is the father of F.
According to the
Question : Select the option that will improve the underlined part of the given sentence. In case no improvement is needed, select 'No improvement required'.
A clinical thermometer consists of a long, narrow, uniform glass tube.
Option 1: consisting of a
Option 2: No improvement required
Option 3: consist of a
Option 4: consisted in a
Correct Answer: No improvement required
Solution : The correct choice will be the second option.
The original sentence effectively conveys information about a clinical thermometer, providing clear and concise details about its composition. There is no need for improvement, as the sentence is grammatically correct and appropriately describes the
Question : Select the correct direct form of the given sentence.
She asked her mother why she was so upset that day.
Option 1: She said to her mother, “Why you are so upset today?”
Option 2: She said to her mother, “Why were you so upset that day?”
Option 3: She said to her mother, “Why are you so upset today?”
Option 4: She said to her mother, “Are you upset today?”
Correct Answer: She said to her mother, “Why are you so upset today?”
Solution : The third option is the correct answer.
Narration Conversion:
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold parts at 1, 2, and 3, which may improve the sentence. Choose the correct alternative. If no improvement is needed, your answer is 4.
I have studied such characters at a close hand.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The correct choice is the first option.
It best captures the intended meaning of the sentence. At close hand is an idiomatic expression that means observing or studying something or someone from a close distance. It implies that the speaker has had the opportunity to
Question : $3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]+\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]^3=?$
Option 1: $a^2-\frac{1}{a^3}$
Option 2: $a^3-\frac{1}{a^3}$
Option 3: $a^3+\frac{1}{a^3}$
Option 4: $a^2-\frac{1}{a^2}$
Correct Answer: $a^3-\frac{1}{a^3}$
Solution : $3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]+\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]^3$ Using $(a-b)^3=a^3 - b^3 -3ab(a-b)$ $=3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right] + \left[\mathrm{a^3}-\frac{1}{\mathrm{a^3}}-3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]\right]$ $=3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right] + \left[\mathrm{a^3}-\frac{1}{\mathrm{a^3}}\right]-3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]$ $=\left[\mathrm{a^3}-\frac{1}{\mathrm{a^3}}\right]$ Hence, the correct answer is $\mathrm{a^3}-\frac{1}{\mathrm{a^3}}$.
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