To find the smallest square number exactly divisible by 12, 15, and 18, we first need to find the Least Common Multiple (LCM) of these numbers. Then, we will make the LCM a perfect square by multiplying it by the smallest possible factors.
The LCM is found by taking the highest power of all prime factors present in the numbers.
\[ \text{LCM}(12, 15, 18) = 2^2 \times 3^2 \times 5^1 = 4 \times 9 \times 5 = 180 \]For a number to be a perfect square, all the exponents in its prime factorization must be even. The prime factorization of the LCM is \(2^2 \times 3^2 \times 5^1\). Here, the exponent of 5 is 1 (odd).
To make it a perfect square, we need to multiply it by \(5^1\) so that the exponent of 5 becomes 2 (even).
The smallest square number will be:
\[ 180 \times 5 = (2^2 \times 3^2 \times 5^1) \times 5^1 = 2^2 \times 3^2 \times 5^2 \]Correct Option: C) 900
On which date did Jallianwala Bagh massacre take place?
13th April, 1919
30th April, 1919
30th April, 1920
13th April, 1920
The question asks for the exact date of the Jallianwala Bagh massacre. This is a factual recall question from modern Indian history. Candidates need to know the specific date associated with this significant event.
A) 13th April, 1919 is the correct date for the Jallianwala Bagh massacre. This event is a pivotal moment in India's struggle for independence.
The question asks to identify which of the given hydroelectric projects is located in the Indian state of Uttarakhand. This requires knowledge of the geographical locations of major hydroelectric projects in India.
Correct Option: B) The Tehri Hydro Power Complex is a major hydroelectric project located in Uttarakhand, India. It is built on the Bhagirathi River.
The problem involves decoding a word based on a given code. We need to identify the pattern or rule used to transform "MAHARAJA" into "ZNUNENWN" and then apply the same rule to "RAINDROP".
Correct Option: A) ENVAQEBC
The question asks to identify the scientist associated with the Theory of Relativity. This requires knowledge of significant contributions by prominent physicists.
Correct Option: D) Albert Einstein is widely recognized as the physicist who developed the Theory of Relativity. His Special Theory of Relativity (1905) and General Theory of Relativity (1915) fundamentally changed our understanding of space, time, mass, energy, and gravity.
This question asks for the definition of Net National Product (NNP). To answer this, we need to understand the relationship between Gross National Product (GNP) and NNP, particularly the role of depreciation.
Correct Option: A) NNP = GNP - Depreciation
The revenue earned by Company A in 2001 is ₹6,300 crore, that earned in 2010 is ₹8,100 crore and that earned in 2015 is ₹10,800 crore. What is the ratio of the increase in revenue between 2001 to 2010 and between 2010 to 2015?
To find the ratio of the increase in revenue between two periods, we first calculate the increase in revenue for each period and then form a ratio.
The ratio of the increase in revenue between the two periods is 2:3.
Correct Option: A) 2 : 3
The question asks for the location of the Bhabha Atomic Research Centre (BARC). This is a factual question requiring knowledge of important scientific institutions in India.
The Bhabha Atomic Research Centre (BARC) is headquartered in Trombay, Mumbai, Maharashtra. It was established in 1954 as the Atomic Energy Establishment, Trombay (AEET), and was renamed in 1967 in honor of its founder, Homi J. Bhabha.
Correct Option: D) Mumbai
Of the 360 students who sat for Class X Board exams, 10% scored A grade, 20% students scored B grade, 30% students scored C grade and 40% scored D grade. From the given pie chart, find the total number of students who scored Grade A and Grade B.
To find the total number of students who scored Grade A and Grade B, we need to calculate the percentages of students who scored these grades and sum them up. The pie chart visually represents these percentages.
Correct Option: A) 108
Choose the mirror image of CHIVALRY
To find the mirror image of the word "CHIVALRY," we need to visualize how each letter would appear if reflected in a vertical mirror. This involves reversing the order of the letters and flipping each letter horizontally.
Upon examining the options:
Correct Option: B) The mirror image is accurately represented.
