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Question : If $\sin \theta = \frac{3}{11}$, then what is the value of $\cot \theta$?
Option 1: $\frac{3 \sqrt{7}}{11}$
Option 2: $\frac{4 \sqrt{7}}{11}$
Option 3: $\frac{4 \sqrt{7}}{3}$
Option 4: $\frac{3 \sqrt{7}}{28}$
Correct Answer: $\frac{4 \sqrt{7}}{3}$
Solution : Given, $\sin \theta=\frac{3}{11}$ We know, $\sin\theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$ Using Pythagoras theorem, we get, $\small (\text{Hypotenuse})^2 = (\text{Base})^2 + (\text{Perpendicular})^2$ Let base = $b$ ⇒ $11^2 = b^2 + 3^2$ ⇒ $b^2 = 121 - 9$ ⇒ $b = \sqrt{112} = 4\sqrt7$ ⇒ $\cot\theta =
Question : According to Ministry of Petroleum and Natural Gas, Government of India (2021-2022), which state in India is the largest producer of natural gas?
Option 1: Andhra Pradesh
Option 2: Maharashtra
Option 3: Tamil Nadu
Option 4: Assam
Correct Answer: Assam
Solution : The correct option is Assam.
According to the Ministry of Petroleum and Natural Gas, Assam remains the largest producer of natural gas in India as of 2021–2022. Their official reports state Assam consistently leads with a production of approximately 8.3 million Metric Standard Cubic Metres
Question : The Madheshi tribe is related to India and its neighbouring country __________.
Option 1: Nepal
Option 2: Sri Lanka
Option 3: Bangladesh
Option 4: Pakistan
Correct Answer: Nepal
Solution : The correct option is Nepal.
People of Indian descent living in Nepal's Terai are referred to as Madheshi people. The Madheshi people include many different cultural groupings, including Terai natives and traders. Many of these communities have cultural ties to those in West Bengal,
Question : Directions: Select the set in which the numbers are related similarly to the numbers of the following sets. (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.) (17, 12, 612) (6, 14, 252)
Option 1: (3, 6, 108)
Option 2: (11, 4, 144)
Option 3: (13, 7, 273)
Option 4: (2, 3, 12)
Correct Answer: (13, 7, 273)
Solution : Given: (17, 12, 612); (6, 14, 252)
Multiply the product of the first and second numbers by 3, to get the third number – (17, 12, 612)→17 × 12 × 3 = 612 (6, 14, 252)→6 × 14 × 3 = 252
Let's
Question : The LCM of $x^2-8x + 15$ and $x^2-5x + 6$ is:
Option 1: $(x-2)(x-3)^2(x-5)$
Option 2: $(x + 5) (x + 2) (x + 3)$
Option 3: $(x + 5) (x - 2) (x - 3)$
Option 4: $(x - 5) (x - 2) (x - 3)$
Correct Answer: $(x - 5) (x - 2) (x - 3)$
Solution : Given: The equations are $x^2- 8x + 15$ and $x^2- 5x + 6$. LCM is the product of every prime factor that is present in the numbers to the greatest power. The factors of $x^2-8x+15$ is given
Question : In the Panchayat Raj System, "the Panchayat Samiti'' is constituted at the:
Option 1: Block level
Option 2: District level
Option 3: State level
Option 4: Village level
Correct Answer: Block level
Solution : The correct answer is block-level.
The Panchayat Samiti is constituted at the intermediate level under India's Panchayat Raj System. It controls a collection of Gram Panchayats within a block, or taluka and is also known as the Block Panchayat or Block Development Committee.
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 problems of traffic crowding will not disappear soon.
(1) congestion
(2) concentration
(3) intensification
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The sentence can be improved using the first option.
It is a suitable word to replace crowding in the context of traffic problems. It refers to the state of being overcrowded or blocked, which is often used in the context of traffic issues.
The
Question : The minimum number of forces to keep a particle in equilibrium is
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 2
Solution : The correct option is 2.
The minimum of forces needed to maintain a particle in equilibrium is two. This is because a particle in equilibrium is not accelerating. The net force acting on a particle must be zero for it not to accelerate. A single
Question : Two positive whole numbers are such that the sum of the first number and twice the second number is 8, and their difference is 2. The numbers are:
Option 1: 7 and 5
Option 2: 6 and 4
Option 3: 4 and 2
Option 4: 3 and 5
Correct Answer: 4 and 2
Solution : Given: The sum of the first number and twice the second number is 8, and their difference is 2 Let the two numbers be x and y. x + 2y = 8 ..............................(i) x – y = 2 ...............................(ii) Subtracting equation (ii) from
Question : Kye Gompa, the largest centre of Buddhist learning in the Western Himalayas, is situated in the state/union territory of ________.
Option 1: Uttarakhand
Option 2: Himachal Pradesh
Option 3: Punjab
Option 4: Jammu & Kashmir
Correct Answer: Himachal Pradesh
Solution : The correct option is Himachal Pradesh.
Key Gompa, one of the largest monasteries in the Spiti Valley, is situated in the state of Himachal Pradesh in the Western Himalayas of India. The monastery is an impressive structure with a distinctive blend of Tibetan and
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