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Question : If $\mathrm{K}+\frac{1}{\mathrm{~K}}+2=0$ and $\mathrm{K}<0$, then what is the value of $\mathrm{K}^{10}+\frac{1}{\mathrm{~K}^{11}}$?
Option 1: 1
Option 2: 0
Option 3: –1
Option 4: 2
Correct Answer: 0
Solution : Given, $\mathrm{K}+\frac{1}{\mathrm{~K}}+2=0$ ⇒ $\mathrm{K}^2+1+2\mathrm{K}=0$ ⇒ $(\mathrm{K}+1)^2=0$ $\therefore \mathrm{K}=-1$ So, $\mathrm{K}^{10}+\frac{1}{\mathrm{~K}^{11}}=\mathrm{(-1)}^{10}+\frac{1}{\mathrm{(-1)}^{11}}=1-1=0$ Hence, the correct answer is 0.
Question : In a triangle ABC, AD, BE, and CF are three medians. The perimeter of ABC is:
Option 1: equal to $(\overline {AD}+\overline{BE}+\overline{CF})$
Option 2: greater than $(\overline {AD}+\overline{BE}+\overline{CF})$
Option 3: less than $(\overline {AD}+\overline{BE}+\overline{CF})$
Option 4: none of these
Correct Answer: greater than $(\overline {AD}+\overline{BE}+\overline{CF})$
Solution : We know that the sum of any two sides of a triangle is greater than twice the median bisecting the third side. Here, D, E, and F are the midpoints of the sides BC, AC, and AB respectively. ∴ AB + AC
Question : Directions: In the following question, select the one which is different from the other three alternatives.
Option 1: 84, 67
Option 2: 112, 95
Option 3: 79, 63
Option 4: 167, 150
Correct Answer: 79, 63
Solution : Let's check the given options – First option: 84, 67; 84 – 67 = 17 Second option: 112, 95; 112 – 95 = 17 Third option: 79, 63; 79 – 63 = 16 ≠ 17 Fourth option: 167, 150; 167 – 150 = 17
Question : The base of a right prism is an equilateral triangle whose side is 10 cm. If the height of this prism is $10 \sqrt{3}$ cm, then what is the total surface area of the prism?
Option 1: $125 \sqrt{3}$ cm2
Option 2: $325 \sqrt{3}$ cm2
Option 3: $150 \sqrt{3}$ cm2
Option 4: $350 \sqrt{3}$ cm2
Correct Answer: $350 \sqrt{3}$ cm2
Solution :
Given: The base of a right prism is an equilateral triangle whose side is 10 cm. The height of this prism is $10 \sqrt{3}$ cm. The total surface area of the prism = [2(area of triangular base)] + [3(Area of rectangular sides)]
Question : Name the two research stations maintained by India in Antarctica.
Option 1: Gangotri and Himadri
Option 2: Sagar Nidhi and Yamunotri
Option 3: None of these
Option 4: Maitri and Bharati
Correct Answer: Maitri and Bharati
Solution : The correct answer is Maitri and Bharti.
India currently operates the Maitri and Bharati research stations in Antarctica. Bharati is a permanent research facility in the Antarctic built at India's request. Along with Maitri, it is one of two operational Indian research stations
Question : Select the most appropriate option to substitute the underlined segment in the given sentence. If no substitution is required, select 'No substitution required'. Any of the boy in my team are very intelligent.
Option 1: All the boy
Option 2: Some of boys
Option 3: No substitution required
Option 4: Some of the boys
Correct Answer: Some of the boys
Solution : The correct choice is the fourth option.
Explanation: The original sentence has a subject-verb agreement error. "Any" should be replaced with "some" to match the plural noun "boys". Additionally, "is" should be changed to "are" to agree with the plural subject
Question : If $a+\frac{1}{a}=P^2$, then find $a^2+\frac{1}{a^2}$.
Option 1: $p^2 - 2$
Option 2: $p^2 + 2$
Option 3: $p^4 - 2$
Option 4: $p^4 + 2$
Correct Answer: $p^4 - 2$
Solution : Given: $a+\frac{1}{a}=P^2$ Squaring both sides, we get: ⇒ $(a+\frac{1}{a})^2=(P^2)^2$ ⇒ $a^2+\frac{1}{a^2}+2\times a\times\frac{1}{a}=P^4$ $\therefore a^2+\frac{1}{a^2}=P^4-2$ Hence, the correct answer is $P^4-2$.
Question : Who among the following was a famous Indian choreographer?
Option 1: Kajol
Option 2: Saroj Khan
Option 3: Shreya Ghoshal
Option 4: Madhuri Dixit
Correct Answer: Saroj Khan
Solution : The correct answer is Saroj Khan.
Saroj Khan, born Nirmala Nagpal on November 22, 1948, in Bombay State (now Maharashtra), India, was a pioneering Indian dance choreographer in Hindi cinema. Renowned for her expertise in the dance form Mujra, she made history as
Question : If $27 x^3-64 y^3=(A x+B y)\left(C x^2-D y^2+12 x y\right)$, then the value of $4 A+B+3 C+2 D$ is:
Option 1: 5
Option 2: 3
Option 3: –3
Option 4: –4
Correct Answer: 3
Solution : Given: $27x^3 - 64y^3 = (Ax + By) (Cx^2 - Dy^2 + 12 xy)$ ⇒ $(3x)^3 - (4y)^3=(Ax + By) (Cx^2 - Dy^2 + 12 xy)$ ⇒ $(3x - 4y) (9x^2 + 16y^2 + 12 xy)=(Ax + By) (Cx^2 - Dy^2 + 12 xy)$ $\therefore$
Question : Select the correct indirect form of the given sentence.
The tailor said to him, “Your shirt will be ready by tomorrow.”
Option 1: The tailor told him that his shirt would be ready by the next day.
Option 2: The tailor told to him that your shirt will be ready by the next day.
Option 3: The tailor told him that your shirt would be ready by tomorrow.
Option 4: The tailor told him that his shirt will be ready by tomorrow.
Correct Answer: The tailor told him that his shirt would be ready by the next day.
Solution : The correct choice is the first option.
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