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Question : Directions: Which answer figure will complete the pattern in the question figure?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : On comparing the question figure and all the option figures, the following figure will combine and make the complete pattern –
Hence, the second option is correct.
Question : In places, the groundwater is stored between layers of hard rock below the water table. This is known as a/an ______.
Option 1: pond
Option 2: lake
Option 3: well
Option 4: aquifer
Correct Answer: aquifer
Solution : The correct answer is an aquifer.
In some places, the groundwater is stored between layers of hard rock below the water table. This geological formation is known as an "aquifer." Aquifers act as natural reservoirs, holding and supplying water to wells and springs. They
Question : Which of the following Fundamental Rights cannot be suspended even when an ‘Emergency’ is declared in the country?
Option 1: Articles 22 and 23
Option 2: Articles 20 and 21
Option 3: Articles 19 and 20
Option 4: Articles 21 and 22
Correct Answer: Articles 20 and 21
Solution : The correct answer is Articles 20 and 21.
During a national emergency in India, Article 20 and Article 21 maintain their inviolable status.
Question : If $\tan\alpha=2$, then the value of $\frac{\operatorname{cosec}^{2}\alpha-\sec^{2}\alpha}{\operatorname{cosec}^{2}\alpha+\sec^{2}\alpha}$ is:
Option 1: $-\frac{15}{9}$
Option 2: $-\frac{3}{5}$
Option 3: $\frac{3}{5}$
Option 4: $\frac{17}{5}$
Correct Answer: $-\frac{3}{5}$
Solution : Given: $\tan\alpha=2$ We know that $\sec^{2}\alpha = 1 + \tan^{2}\alpha$ and $\operatorname{cosec}^{2}\alpha = 1 + \cot^{2}\alpha$ Since $\tan\alpha = 2$, we have $\sec^{2}\alpha = 1 + (2)^{2} = 5$ Also, $\cot\alpha = \frac{1}{\tan\alpha} = \frac{1}{2}$ So $\operatorname{cosec}^{2}\alpha = 1 + (\frac{1}{2})^{2} = \frac{5}{4}$ Putting the
Question : What is the value of $\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \div \frac{6}{25}\right)–\left(\frac{2}{7} \times \frac{6}{5} \div \frac{18}{42}\right)\right\}+\frac{19}{30}\right]$?
Option 1: $\frac{17}{15}$
Option 2: $\frac{13}{15}$
Option 3: $\frac{14}{15}$
Option 4: $\frac{11}{15}$
Correct Answer: $\frac{13}{15}$
Solution : $\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \div \frac{6}{25}\right)–\left(\frac{2}{7} \times \frac{6}{5} \div \frac{18}{42}\right)\right\}+\frac{19}{30}\right]$ $=\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \times \frac{25}{6}\right)–\left(\frac{2}{7} \times \frac{6}{5} \times \frac{42}{18}\right)\right\}+\frac{19}{30}\right]$ $=[\frac{1}{5}+(\frac{1}{6}\times 5–\frac{4}{5})+\frac{19}{30}]$ $=[\frac{1}{5}+(\frac{5}{6}–\frac{4}{5})+\frac{19}{30}]$ $=[\frac{1}{5}+\frac{1}{30}+\frac{19}{30}]$ $=\frac{26}{30}$ $=\frac{13}{15}$ Hence, the correct answer is $\frac{13}{15}$.
Question : If the radius of a circle is increased by 16%, its area increases by
Option 1: 34.56%
Option 2: 32%
Option 3: 16%
Option 4: 17.28%
Correct Answer: 34.56%
Solution : Let the radius of the original circle = $r$ So, the Area of the original circle = $\pi r^2$ Radius of circle after 16% increase = $r+\frac{16r}{100} =1.16r$ Area of new circle = $\pi \times 1.16^2 = 1.3456r^2$ Percentage increase in area $\frac{1.3456\pi r^2- \pi
Question : The radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and the bigger circle at E. Point A is joined to D. The length of AD is:
Option 1: 20 cm
Option 2: 19 cm
Option 3: 18 cm
Option 4: 17 cm
Correct Answer: 19 cm
Solution : Let the line BD intersect the bigger circle at point C. Join AC. OD $\perp$ BD ⇒ OD $\perp$ BC So, BD = DC ⇒ D is the midpoint of BC. Also, O is the midpoint of AB. In $\triangle$BAC, O is the midpoint
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
The gold is a precious metal.
(1) Gold
(2) A gold
(3) An gold
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The correct answer is the first option.
"The gold" should be replaced with "Gold" as articles never come before a material noun so the article "the" should be removed. "Gold" is correctly used as a noun referring to the precious metal. Therefore, the correct statement
Question : Formalised system of trading agreements with groups of countries is known as
Option 1: Trading blocks
Option 2: Trade ventures
Option 3: Trade partners
Option 4: Trade organisations
Correct Answer: Trading blocks
Solution : The Correct Answer is Trading blocks
Trading blocs are merely associations of nations that set the rules for international commerce. An example of an intergovernmental agreement is a trade bloc, which is frequently a component of a regional intergovernmental organization. In a trade bloc,
Question : ABCD is a rhombus with $\angle$ABC = 52°. The measure of $\angle$ACD is:
Option 1: 54°
Option 2: 26°
Option 3: 48°
Option 4: 64°
Correct Answer: 64°
Solution : Since opposite angles of a rhombus are equal So, $\angle$ADC = $\angle$ABC = 52° Also, $\angle$DAC = $\angle$DCA = $x$ (say) [since AD = DC] In $\triangle$ ADC, $\angle$ADC + $\angle$DAC + $\angle$DCA = 180° ⇒ $x+x+52°$ = 180° ⇒ $x$ = 64° ⇒ $\angle$DCA
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