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Question : $\triangle A B C$ inscribe in a circle with centre O. If AB = 9 cm, BC = 40 cm, and AC = 41 cm, then what is the circum-radius of the triangle?
Option 1: $20 \frac{1}{2} \mathrm{~cm}$
Option 2: $12 \frac{1}{2} \mathrm{~cm}$
Option 3: $18 \frac{1}{2} \mathrm{~cm}$
Option 4: $16 \frac{1}{2} \mathrm{~cm}$
Correct Answer: $20 \frac{1}{2} \mathrm{~cm}$
Solution : Given: $\triangle A B C$ inscribe in a circle with centre O. AB = 9 cm, BC = 40 cm, and AC = 41 cm Also, we can see $9^2+40^2=1681=41^2$ So, it is a right triangle. Hypotenuse = AC = 41 cm For
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: 72
Option 2: 75
Option 3: 63
Option 4: 69
Correct Answer: 75
Solution : Given:
The pattern can be observed running vertically along the columns. Column 1: ((2)2 + (6)2) + 3 = 4 + 36 + 3 = 43 Column 2: ((5)2 + (7)2) + 2 = 25 + 49 + 2
Question : If $\frac{1}{x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}}}=\frac{29}{79}$, where x, y, and z are natural numbers, then the value of $(2 x+3 y-z)$ is:
Option 1: 0
Option 2: 4
Option 3: 1
Option 4: 2
Correct Answer: 2
Solution : According to the question, $\frac{1}{x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}}}=\frac{29}{79}$ ⇒ $x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}} = \frac{79}{29}$ ⇒ $x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}} = 2+\frac{21}{29}$ Comparing both sides, we get $x=2$, and $\frac{1}{y+\frac{2}{z+\frac{1}{4}}} =\frac{21}{29}$ ⇒ $\frac{1}{y+\frac{2}{z+\frac{1}{4}}}={\frac{1}{1+\frac{8}{21}}}$ ⇒ $\frac{1}{y+\frac{2}{z+\frac{1}{4}}}={\frac{1}{1+\frac{2}{5+\frac{1}{4}}}}$ Comparing both sides, we get, $y= 1$ and $z= 5$ $\therefore$ $(2 x+3 y-z)= 2 × 2 + 3
Question : The major constituent of air is
Option 1: Nitrogen
Option 2: Carbon dioxide
Option 3: Oxygen
Option 4: Hydrogen
Correct Answer: Nitrogen
Solution : The correct option is Nitrogen.
Nitrogen is the most abundant element in the atmosphere (78%). This is inert, essential for life, a component of the nitrogen cycle, a diatomic gas that maintains atmospheric pressure and is employed in agriculture and industry.
Question : In which of the following months did the Australian Open take place in 2022?
Option 1: February
Option 2: March
Option 3: January
Option 4: April
Correct Answer: January
Solution : The correct option is January.
The Australian Open is a major tennis tournament held annually in Melbourne, Australia. In 2022, the tournament dates were from January 17 to January 30. The Australian Open is one of the four Grand Slam tournaments in tennis, along
Question : Rearrange the parts of the sentence in the correct order. The Supreme Court P. must remind the state to act constitutionally, Q. lawfully and justly in every case across the R. country, especially in sensitive matters involving S. those who oppose the party in office with peaceful means
Option 1: PQRS
Option 2: PQSR
Option 3: QPSR
Option 4: QRSP
Correct Answer: PQRS
Solution : The correct choice is the first option: PQRS.
The logical flow of the order is as follows:
The sentence begins by introducing the subject, "The Supreme Court". It then establishes the directive or duty that the Supreme Court must fulfil, which is to "remind the
Question : The digit in the unit's place of the product 49237 × 3995 × 738 × 83 × 9 is:
Option 2: 7
Option 3: 5
Option 4: 6
Correct Answer: 0
Solution : The product of unit digits of the 2nd and 3rd numbers is (5 × 8) = 40. The unit digit of this product is 0. So, the digit in the unit's place of the product of 49237 × 3995 × 738 × 83 × 9
Question : Which of the following statements are correct regarding the Centre-State Relations about the three lists of the Indian Constitution?
A. The subjects which are not included in any of the three lists are called Residuary subjects. B. If there is any conflict between the Union List and the State List, then the former prevails. C. When the Parliament enacts a law on the request of two or more states, then that law made by the Parliament on the State List applies to all the states.
Option 1: A and C only
Option 2: B and C only
Option 3: A, B and C
Option 4: A and B only
Correct Answer: A and B only
Solution : The correct option is A and B only.
The subjects that are not included in any of the three lists (Union List, State List, and Concurrent List) are called residual subjects. These subjects fall under the residuary powers of the Union
Question : Directions: Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: No pin is a tin. Some pins are wins. Conclusions: I. All wins are tins. II. Some wins are pins.
Option 1: Only conclusion I follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion II follows
Option 4: Neither conclusion I nor II follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All wins are tins – From the Venn diagram, it is evident that there is no direct relation between wins and tins.
Question : Inert gases are
Option 1: miscible with water
Option 2: not stable
Option 3: chemically unreactive
Option 4: chemically very reactive
Correct Answer: chemically unreactive
Solution : The correct option is chemically unreactive.
Inert gases, known as noble gases, exhibit chemical inertness due to their stable electron configurations. Their electron shells are filled, making it highly improbable for these gases to engage in chemical reactions with other elements.
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