To find the Highest Common Factor (HCF) of a set of numbers, we need to determine the largest number that divides each of them without leaving a remainder. This can be done by finding the prime factorization of each number and then multiplying the common prime factors with the lowest power.
D) 3 — The HCF of 45, 78, and 117 is 3, as it is the largest number that divides all three numbers without a remainder.
N.K. Singh became the Chairman of which Finance Commission of India?
The question asks to identify which Finance Commission N.K. Singh chaired. This requires knowledge of the chairpersons of various Finance Commissions of India.
Correct Option: D) 15 th
The phenomenon of objects appearing larger or distorted when viewed through water is a common optical illusion. This effect is due to how light behaves when it passes from one medium (water) to another (air) before reaching our eyes. We need to identify the specific optical phenomenon responsible for this.
Correct Option: B) refraction of light — When light travels from one medium to another (e.g., from water to air), it changes speed and direction. This bending of light, known as refraction, causes objects submerged in water to appear distorted or magnified when viewed from outside the water. The light rays from the lemon bend away from the normal as they exit the water, making the lemon appear larger and closer than its actual size and position.
The question asks about the image formation by a concave mirror. We need to recall the rules of image formation for a concave mirror based on the object's position. Specifically, we are looking for a highly diminished, real, and inverted image.
Correct Option: D) F
In a class of 21 students, each scored differently. P's rank from the bottom is 7th, while Q's rank from the top is also 9th. How many students are ranked between Q and P?
The problem involves finding the number of students between two individuals (P and Q) in a class, given their ranks from the top and bottom, and the total number of students. We will first determine the rank of each student from a common reference point (either top or bottom) and then calculate the number of students between them.
C) 5. There are 5 students ranked between Q and P.
If A bought an item for Rs 384 and sold it for Rs 576 and B bought another item for Rs 1,254 and sold it for Rs 1,672. What is the ratio of gain % of A to gain % of B?
\( \frac{5}{2} \)
\( \frac{5}{3} \)
\( \frac{3}{2} \)
\( \frac{2}{3} \)
To find the ratio of gain percentage of A to gain percentage of B, we first need to calculate the gain percentage for both A and B individually. The gain percentage is calculated using the formula: \[\text{Gain Percentage} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\%\].
Correct Option: C) \(\frac{3}{2}\)
The question asks to identify the state where the 'Nishagandhi Dance Festival' is celebrated. This requires knowledge of prominent cultural festivals and their associated states in India.
Correct Option: A) The Nishagandhi Dance Festival is a prominent annual cultural event organized by the Kerala Tourism Department. It showcases various classical Indian dance forms and is held in Thiruvananthapuram, Kerala.
The goal is to find which pair of signs, when interchanged in the given equation, makes the equation mathematically correct. We will test each option by substituting the interchanged signs into the original equation and then evaluating it using the BODMAS/PEMDAS rule.
The given equation is: \(24 \div 6 + 12 - 18 \times 3 = 46\)
Interchange \(\div\) and \(-\):
\[ 24 - 6 + 12 \div 18 \times 3 \] \[ = 24 - 6 + \frac{12}{18} \times 3 \] \[ = 24 - 6 + \frac{2}{3} \times 3 \] \[ = 24 - 6 + 2 \] \[ = 18 + 2 \] \[ = 20 \] Since \(20 \neq 46\), Option A is incorrect.Interchange \(+\) and \(-\):
\[ 24 \div 6 - 12 + 18 \times 3 \] \[ = 4 - 12 + 54 \] \[ = -8 + 54 \] \[ = 46 \] Since \(46 = 46\), Option B makes the equation correct.Since we found the correct option, there is no need to test further options in an exam scenario, but for completeness, we will evaluate them.
B) + and -
When \(+\) and \(-\) are interchanged, the equation becomes:
\[ 24 \div 6 - 12 + 18 \times 3 \]Following the order of operations (BODMAS/PEMDAS):
Since \(46 = 46\), the equation is correct.
Interchanging \(\div\) and \(-\) gives: \(24 - 6 + 12 \div 18 \times 3\)
\[ 24 - 6 + \frac{12}{18} \times 3 \] \[ = 24 - 6 + \frac{2}{3} \times 3 \] \[ = 24 - 6 + 2 \] \[ = 18 + 2 = 20 \] Since \(20 \neq 46\), this option is incorrect.Interchanging \(\div\) and \(\times\) gives: \(24 \times 6 + 12 - 18 \div 3\)
\[ 24 \times 6 + 12 - 18 \div 3 \] \[ = 144 + 12 - 6 \] \[ = 156 - 6 \] \[ = 150 \] Since \(150 \neq 46\), this option is incorrect.Interchanging \(\div\) and \(+\) gives: \(24 + 6 \div 12 - 18 \times 3\)
\[ 24 + 6 \div 12 - 18 \times 3 \] \[ = 24 + 0.5 - 54 \] \[ = 24.5 - 54 \] \[ = -29.5 \] Since \(-29.5 \neq 46\), this option is incorrect.The question asks to identify the specific Article of the Indian Constitution that establishes the principle of collective responsibility of the Council of Ministers to the House of the People (Lok Sabha). This is a direct factual question related to the constitutional provisions governing the executive.
D) Article 75 (3)
Article 75 (3) of the Indian Constitution explicitly states: "The Council of Ministers shall be collectively responsible to the House of the People." This provision is fundamental to the parliamentary system of government in India, ensuring that the executive (Council of Ministers) is accountable to the legislature (Lok Sabha).
The question asks for the year in which the Missionaries of Charity was established by Mother Teresa. This is a factual question related to a significant historical event and a well-known humanitarian organization.
Correct Option: B) 1950