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Question : If $4\left(\operatorname{cosec}^2 57^{\circ}-\tan ^2 33^{\circ}\right)-\cos 90^{\circ}-y \tan ^2 66^{\circ} \tan ^2 24^{\circ}=\frac{y}{2}$, the value of $y$ is:
Option 1: $\frac{8}{3}$
Option 2: $\frac{3}{8}$
Option 3: $8$
Option 4: $\frac{1}{3}$
Correct Answer: $\frac{8}{3}$
Solution : $\operatorname{cosec}(90^{\circ} - \theta) = \sec \theta$ $\tan\theta = \frac{1}{\cot\theta}$ So, $4\left(\operatorname{cosec}^2 57^{\circ}-\tan ^2 33^{\circ}\right)-\cos 90^{\circ}-y \tan ^2 66^{\circ} \tan ^2 24^{\circ}=\frac{y}{2}$ ⇒ $(\operatorname{cosec}^{2}(90-33)^{\circ} - \tan^{2}33^{\circ}) - 0- y×\tan^{2}66^{\circ} × \tan^{2}(90-66)^{\circ}$ = $\frac{y}{2}$ ⇒ $4(\sec^{2}57^{\circ}- \tan^{2}33^{\circ}) - y × \tan^{2}66^{\circ} × \cot^{2}66^{\circ} = \frac{y}{2}$ ⇒ $4
Question : In the isosceles triangle ABC with BC is the unequal side of the triangle, and line AD is the median drawn from the vertex A to the side BC. If the length AC = 5 cm and the length of the median is 4 cm, then find the length of BC (in (cm).
Option 1: 5
Option 2: 3
Option 3: 4
Option 4: 6
Correct Answer: 6
Solution : Given: $\Delta ABC$ is an isosceles triangle Hence, AB = AC = 5cm From Apollonius's theory, we get, ⇒ $5^2+5^2=2(4^2+DC^2)$ ⇒ $25+25=16+DC^2$ ⇒ $DC^2=9$ ⇒ $DC = 3\ \text{cm} $ Since D is the median point on the side BC. $\therefore BD = DC =
Question : Constitutional Monarchy means
Option 1: The King writes the constitution
Option 2: The King interprets the constitution
Option 3: The King exercises power granted by constitution
Option 4: The King is elected by the people
Correct Answer: The King exercises power granted by constitution
Solution : Correct Answer is The King exercises power granted by constitution
Constitutional monarchies include the British Monarchy. This indicates that, even though The Sovereign is Head of State, it is up to an elected Parliament to draft and pass laws.
Question : A person has to travel a distance of 30 km. He finds that he has covered $\frac{5}{6}$th of the distance in 3 hours and 20 minutes. what is his speed in km/hr?
Option 1: 6
Option 2: 5.4
Option 3: 6.3
Option 4: 7.5
Correct Answer: 7.5
Solution : Given: Total distance = 30 km 3 hr 20 min $= 3 + \frac{20}{60} = 3 + \frac{1}{3} = \frac{10}{3}$ $\frac{5}{6}$th of the distance $= 30 × \frac{5}{6}= 25$ km Speed of the person = $\frac{25}{\frac{10}{3}}= 7.5$ km/hr Hence, the correct answer is 7.5 km/hr.
Question : Which of the following painters of Jahangir's reign was conferred the title of Nadir-Ul-Asra?
Option 1: Bishan Das
Option 2: Mansur
Option 3: Manohar
Option 4: Daulat
Correct Answer: Mansur
Solution : The correct option is Mansur
Mansur was in charge of recording plants and animals during Jahangir's reign. He adopted the name Ustad Mansur and the emperor gave him the honorific title Nadir-ul- 'Asr (meaning "Miracle of the Age"). Because of his skills and expertise, he
Question : A 6-digit number has digits as consecutive natural numbers. The number is always divisible by
Option 1: 4
Option 2: 5
Option 3: 2
Option 4: 3
Correct Answer: 3
Solution : A 6-digit number consisting of consecutive natural numbers is always divisible by 3. The sum of consecutive natural numbers is always divisible by 3. If the number is divisible by 3, then the sum of its digits will also be divisible by 3. An example
Question : Ramesh borrowed INR 15,000 at a certain rate of simple interest from a bank. He repaid (the principal but not interest) INR 6,000 after 5 years, and after 5 more years he paid INR 18,600 and settled his account. Find the rate of simple interest per annum.
Option 1: 12%
Option 2: 10%
Option 3: 8%
Option 4: 6%
Correct Answer: 8%
Solution : Total amount = 6000 + 18600 = 24600 Principal sum, $P = 15000$ Simple interest = Total amount - principal sum = 24600 - 15000 = 9600 $n_1 = 5$ years $n_2 = 5$ years $P_2$ = 15000 - 6000 = 9000 Total simple interest
Question : In $\triangle$PQR, a straight line parallel to the base, QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be:
Option 1: 5 : 11
Option 2: 6 : 5
Option 3: 11 : 6
Option 4: 11 : 5
Correct Answer: 5 : 11
Solution : Given: In $\triangle$PQR, QR || XY $\frac{PX}{XQ}=\frac{5}{6}$ Let PX = 5 units, XQ = 6 units So, PQ = 5 + 6 = 11 units In ∆ PXY and ∆ PQR, ∵ QR | | XY ∵ $\angle$X = $\angle$Q ; $\angle$Y =
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence. If there is no need to substitute it, select 'No substitution'. The Karaoke programme was planned by the club was a grand success.
Option 1: were planned by the club
Option 2: planned by the club
Option 3: has been planned by the club
Option 4: No substitution
Correct Answer: planned by the club
Solution : The correct answer is the second option.
The original sentence has a redundant or unnecessary use of the verb was. When constructing a sentence, it is generally more concise and grammatically correct to avoid unnecessary repetition of verbs.
In this case, the
Question : Select the option that corrects the misspelt words in the given sentence.
My freind is blessed with perfect gines.
Option 1: My friend is blessed with perfct gines.
Option 2: My freind is bllessed with perfct gines.
Option 3: My freind is blesed with perfect genes.
Option 4: My friend is blessed with perfect genes.
Correct Answer: My friend is blessed with perfect genes.
Solution : The correct choice will be the fourth option.
In the first option: Incorrect - perfct, gines; Correct - perfect, genes
In the second option: Incorrect - freind, bllessed, perfct, gines; Correct - friend, blessed, perfect, genes
In the third
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