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Question : If $\sin A=\frac{\sqrt{3}}{2}, 0<A<90^{\circ}$, then find the value of $2(\operatorname{cosec} A + \cot A)$.
Option 1: $2 \sqrt{3}$
Option 2: $\sqrt{3}$
Option 3: $\frac{2}{\sqrt{3}}$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $2 \sqrt{3}$
Solution : Given: $\sin A\ =\ \frac{\sqrt{3}}{2}=\sin 60^\circ$ $\Rightarrow A\ =\ 60^\circ$ Now, putting the value of A, we get, $2(\operatorname{cosec} A + \cot A)$ $=\ 2(\operatorname{cosec} 60^\circ + \cot 60^\circ)$ $=\ 2(\frac{2}{\sqrt{3}}\ +\ \frac{1}{\sqrt{3}})$ $=\ 2(\frac{3}{\sqrt{3}})$ $=\ 2\sqrt{3}$ Hence the value of expression is $2\sqrt{3}$.
Question : Simplify $\frac{1 + \sin t}{4 - 4 \sin t} - \frac{1 - \sin t}{4 + 4 \sin t}$.
Option 1: $4\tan t .\sin t$
Option 2: $\tan t . \sec t$
Option 3: $\tan t - \sin t$
Option 4: $\tan t + \sin t$
Correct Answer: $\tan t . \sec t$
Solution : Given: $\frac{1 + \sin t}{4 -4\sin t} - \frac{1 - \sin t}{4 + 4\sin t}$ $=\frac{1 + \sin t}{4(1 - \sin t)} - \frac{1 - \sin t}{4(1 + \sin t)}$ $=\frac{(1 + \sin t)^{2} - (1 - \sin t)^{2}}{4 × (1+
Question : Which of the following pair of "Name of Ruler – Empire" is correctly matched? I. Mahapadma Nanda – Magadha Empire II. Ajatashatru – Maurya Empire
Option 1: Only II
Option 2: Neither I nor II
Option 3: Both I and II
Option 4: Only I
Correct Answer: Only I
Solution : The correct answer is Only I.
From 345 to 321 BCE, the Nanda Dynasty governed the northern Indian state of Magadhas. Mahapadma Nanda, popularly known as Ugrasena—the owner of a sizable army—founded it after vanquishing numerous kingdoms, including Kurus, Kalingas and Kasis.
Question : Ustad Amjad Ali Khan is associated with which of the following musical instruments?
Option 1: Sarangi
Option 2: Sitar
Option 3: Sarod
Option 4: Veena
Correct Answer: Sarod
Solution : The correct answer is Sarod.
Ustad Amjad Ali Khan also referred to as the "Sarod Samrat," is a renowned master in the art of sarod playing. In 2001, he received the Padma Vibhushan, the second-highest civilian award in India. The word "sarod" is Persian in
Question : Directions: What was the day of the week on 14th March 2010?
Option 1: Sunday
Option 2: Tuesday
Option 3: Saturday
Option 4: Monday
Correct Answer: Sunday
Solution : Code for months –
Code for days –
Question : Directions: Select the option that represents the letters that, when sequentially placed from left to right in the blanks below will complete the letter series. _utt_tt_ttu_
Option 1: uutt
Option 2: tutu
Option 3: ttuu
Option 4: tuut
Correct Answer: tuut
Solution : Given: _utt_tt_ttu_
To fill the series we have to divide the series→_ut / t_t / t_t / tu_ Let's check each option – First option: uutt; uut / tut / ttt / tut (No repeated pattern has been found.)
Question : Directions: The following equations have been solved based on a certain pattern. Find the correct answer for the unsolved equation on that basis. If 7 * 4 * 3 = 437, 8 * 6 * 4 = 648, then 4 * 3 * 6 = ?
Option 1: 346
Option 2: 364
Option 3: 643
Option 4: 463
Correct Answer: 364
Solution : Given: 7 * 4 * 3 = 437 8 * 6 * 4 = 648
Here, the numbers given in the equation are shuffled in a particular order, i.e., the second number replaces the first number, the third number replaces the second number, and the
Question : A thief stole jewelry from a shop at 8:15 p.m. and left on a bike at a speed of 60 km/hr. The police were informed at 8:30 p.m. If the police want to arrest the thief at 9:00 p.m., what should be the minimum speed of the police jeep?
Option 1: 60 km/hr
Option 2: 75 km/hr
Option 3: 80 km/hr
Option 4: 90 km/hr
Correct Answer: 90 km/hr
Solution : Total time travelled by the thief = 9:00 - 8:15 = 45 min = $\frac{3}{4}$ hour Speed of thief = 60 km/hr Distance travelled = 60 × $\frac{3}{4}$ = 45 km Total time travelled by the thief = 9:00 - 8:30 = 30 min
Question : Directions: A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. M can be represented by 01, 10, etc., and A can be represented by 56, 65, etc. Similarly, you have to identify the set for the word ROD.
Option 1: 58, 66, 78
Option 2: 67, 96, 57
Option 3: 56, 66, 86
Option 4: 58, 69, 65
Correct Answer: 67, 96, 57
Solution : Given: ROW
Number representations of each letter – R→58, 67, 76, 85, 99 O→55, 69, 78, 87, 96 D→57, 66, 75, 89, 98
Let's check the options – First option: 58, 66, 78; O and W cannot be represented by 66 and 78
Question : In which town The Supreme Court was established for the First time under the Regulating Act of 1773?
Option 1: Madras
Option 2: Assam
Option 3: Calcutta
Option 4: New Delhi
Correct Answer: Calcutta
Solution : The correct answer is Calcutta.
The Supreme Court was established for the first time under the Regulating Act of 1773 in Calcutta at Fort William, which was then the capital of British India. This marked a significant step in the British administration's effort to
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