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Question : Let C be a circle with centre O and radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).
Option 1: 2
Option 2: 13
Option 3: 6
Option 4: 8
Correct Answer: 8
Solution : Given: Radius = 5 cm OA = 12 cm We know that the angle between a tangent to a circle and the radius through the point of contact is always a right angle. From figure, OA = OR = 5 cm (radius) By applying Pythagoras
Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then what is the value of $\tan \theta$?
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $\frac{1}{ \sqrt{3}}$
Option 4: $\sqrt{3}$
Correct Answer: $\frac{1}{ \sqrt{3}}$
Solution : $\sin 2\theta = \frac{\sqrt{3}}{2}$ ⇒ $\sin 2\theta = \sin 60° $ ⇒ $2\theta = 60° $ ⇒ $\theta = 30° $ So, $\tan \theta = \tan 30° = \frac{1}{\sqrt{3}}$ Hence, the correct answer is $\frac{1}{\sqrt{3}}$.
Question : Directions: In the given question, select the related letter from the given alternatives. JLNP : OMKI :: SUWY : ?
Option 1: MLKI
Option 2: PLHD
Option 3: XVTR
Option 4: PCVI
Correct Answer: XVTR
Solution : Given: JLNP : OMKI :: SUWY : ?
Add 5 and 1 to the place value of the first and the second letter and subtract 3 and 7 from the place value of the third and the fourth letter
JLNP; J + 5 = O;
Question : Directions: Arrange the given words in the sequence in which they occur in the dictionary. 1. Range 2. Radar 3. Race 4. Rack 5. Rant
Option 1: 3, 4, 2, 1, 5
Option 2: 3, 4, 2, 5, 1
Option 3: 3, 2, 4, 1, 5
Option 4: 3, 2, 4, 5, 1
Correct Answer: 3, 4, 2, 1, 5
Solution : Given: 1. Range 2. Radar 3. Race 4. Rack 5. Rant
Step 1: Compare the first letter of each word. Since all the words start with the same letter R, move to the next letter. Step 2: Compare the second
Question : Which writ is issued when the court finds that there is unlawful arrest of a person?
Option 1: Prohibition
Option 2: Mandamus
Option 3: Quo warranto
Option 4: Habeas Corpus
Correct Answer: Habeas Corpus
Solution : The correct answer is Habeas Corpus.
Habeas corpus means to have the body of. Through this writ, the court examines the reason for his detention, and if there is no legal justification for his detention, he can be set free. Thus, a Habeas
If your age is between 18 to 27 years then you can definitely give this exam.
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed.) (56, 22, 26) (34, 20, 18)
Option 1: (78, 54, 44)
Option 2: (23, 8, 10)
Option 3: (58, 16, 21)
Option 4: (45, 12, 33)
Correct Answer: (78, 54, 44)
Solution : Given: (56, 22, 26); (34, 20, 18)
Here, (56, 22, 26)→(56 + 22) ÷ 3 = 78 ÷ 3 = 26 (34, 20, 18)→(34 + 20) ÷ 3 = 54 ÷ 3 = 18
Let's check the options – First option: (78, 54,
Question : What is the present worth of INR 1,100 due in 2 years at 5% simple interest per annum?
Option 1: INR 3,000
Option 2: INR 2,000
Option 3: INR 1,000
Option 4: INR 1,500
Correct Answer: INR 1,000
Solution : Let the present worth be INR $x$. We know that simple interest = Amount - Principal So, $1100−x=x\times(\frac{5}{100})\times2$ ⇒ $x+10x=11000$ ⇒ $x=\frac{11000}{11}$ ⇒ $x=1000$ Hence, the correct answer is INR 1,000.
Question : Directions: A tourist drives 10 km towards the West turns to the left and takes a drive of another 4 km. He then drives towards the East another 4 km and then turns to his right and drives 5 km. Afterwards, he turns to his left and travels 6 km. In which direction is he from the starting point?
Option 1: North
Option 2: East
Option 3: West
Option 4: South
Correct Answer: South
Solution : Firstly, we will draw the diagram as per the given instructions –
The direction from the starting position (A) to the final position (F) is south.
So, the tourist is in the south direction. Hence, the fourth option is correct.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
As he tried harder, his steps showed, his senses (was activated).
(1) is activated
(2) were activated
(3) were activate
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 2
Solution : The correct answer is the second option because 'was activated' should be replaced with 'were activated' as the helping verb 'was' doesn't agree with the plural subject violating the subject-verb agreement.
In the first option, 'is activated' is incorrect as per the subject-verb agreement and
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