To find out how many square beds can be accommodated in a rectangle, we need to calculate the number of beds that can fit along the length and the number of beds that can fit along the width. Then, multiply these two numbers to get the total number of beds.
Length of the rectangle \(L = 49 \text{ m}\)
Width of the rectangle \(W = 35 \text{ m}\)
Side of the square bed \(s = 7 \text{ m}\)
Number of beds along the length \[N_L = \frac{\text{Length of rectangle}}{\text{Side of bed}}\]
\[ N_L = \frac{49 \text{ m}}{7 \text{ m}} = 7 \]Number of beds along the width \[N_W = \frac{\text{Width of rectangle}}{\text{Side of bed}}\]
\[ N_W = \frac{35 \text{ m}}{7 \text{ m}} = 5 \]Total number of beds \(N_{\text{total}} = N_L \times N_W\)
\[ N_{\text{total}} = 7 \times 5 = 35 \]Therefore, 35 square beds can be accommodated in the rectangle.
Correct Option: D) 35
The question asks about India's next interplanetary mission after the Mars Orbiter Mission (MOM), specifically mentioning the context of 2021. This requires knowledge of ISRO's planned future missions around that period.
B) Venus — ISRO has been actively planning and working towards a Venus mission (Shukrayaan-1) as its next major interplanetary venture after the Mars Orbiter Mission. This was a well-known plan by 2021.
The problem asks us to identify the option that shares the same relationship as the given pair: Paisa : Rupee. We need to determine the relationship between 'Paisa' and 'Rupee' and then find an option where the first term is a smaller unit of the second term, specifically with a factor of 100.
A) Kilogram : Quintal
Just as 100 Paisa make 1 Rupee, 100 Kilograms make 1 Quintal. Both pairs exhibit a relationship where the first term is a smaller unit, and 100 units of the first term constitute one unit of the second term.
To find the maximum value of 'a', we need to minimize the values of 'b' and 'c'. The problem states that 'b' and 'c' are positive integers greater than zero. The smallest positive integer is 1.
Therefore, the maximum value 'a' can take is 6.
Correct Option: A) 6
If cos 2θ = \( \frac{1}{2} \), then the value of sin(75° − θ) will be:
\(\sqrt{2}\) + 1
\(\sqrt{2}\) - 1
\( \frac{1}{2} \)
\(\frac{1}{\sqrt{2}}\)
The problem requires us to find the value of \(\sin(75^\circ - \theta)\) given \(\cos(2\theta) = \frac{1}{2}\). We will first determine the value of \(\theta\) from the given cosine equation and then substitute it into the sine expression.
Given the equation:
\[ \cos(2\theta) = \frac{1}{2} \]We know that \(\cos(60^\circ) = \frac{1}{2}\). Therefore, we can equate the angles:
\[ 2\theta = 60^\circ \]Solving for \(\theta\):
\[ \theta = \frac{60^\circ}{2} = 30^\circ \]Now, substitute the value of \(\theta = 30^\circ\) into the expression \(\sin(75^\circ - \theta)\):
\[ \sin(75^\circ - 30^\circ) \]Simplify the expression:
\[ \sin(45^\circ) \]We know that the value of \(\sin(45^\circ)\) is \(\frac{1}{\sqrt{2}}\).
\[ \sin(45^\circ) = \frac{1}{\sqrt{2}} \]Correct Option: D) \(\frac{1}{\sqrt{2}}\) is the correct value for \(\sin(75^\circ - \theta)\).
If '÷' stands for addition, '×' stands for subtraction, '+' stands for division, and '−' stands for multiplication, then which of the following equations is correct?
20 ÷ 12 + 6 × 5 − 2 = 12
18 × 12 + 6 ÷ 3 − 2 = 12
20 × 12 + 4 ÷ 3 − 2 = 12
20 × 12 + 6 ÷ 5 − 2 = 12
This problem involves symbol substitution and then evaluating mathematical expressions. We need to replace the given symbols with their new meanings and then apply the order of operations (BODMAS/PEMDAS) to check which equation holds true.
Given symbol transformations:
We will evaluate each option by substituting the symbols and then performing the calculations.
Substitute the symbols:
\[ 20 + 12 \div 6 - 5 \times 2 \]Apply BODMAS/PEMDAS:
Since \(12 = 12\), Option A is correct.
Correct Option: A) \(20 \div 12 + 6 \times 5 \minus 2 = 12\)
The question asks to identify the conference where 'Agenda 21' was recommended. This requires knowledge of major international environmental summits and their outcomes.
A) Rio Summit, 1992
Agenda 21 was indeed a significant outcome of the United Nations Conference on Environment and Development (UNCED), popularly known as the Earth Summit or Rio Summit, held in Rio de Janeiro, Brazil, in June 1992. It is a non-binding, voluntarily implemented action plan of the United Nations with regard to sustainable development.
The given number series appears to be an alternating series, meaning there are two distinct patterns running concurrently. We need to identify these two patterns to find the missing number.
Let's write down the series:
\(40, 48, 41, 16, 42, 8, 43, ?\)
Identify the first alternating series (odd-positioned terms):
First term: \(40\)
Third term: \(41\)
Fifth term: \(42\)
Seventh term: \(43\)
This series is: \(40, 41, 42, 43, \dots\)
The pattern here is an increment of \(1\) for each subsequent term (\(40+1=41\), \(41+1=42\), \(42+1=43\)).
Identify the second alternating series (even-positioned terms):
Second term: \(48\)
Fourth term: \(16\)
Sixth term: \(8\)
Eighth term: \(?\)
This series is: \(48, 16, 8, ?\)
Determine the pattern for the second series:
The pattern seems to be division by a decreasing integer. The first division was by \(3\), the next by \(2\). Following this pattern, the next division should be by \(1\).
Apply the pattern to find the missing term:
The next term in the second series would be \(8 \div 1 = 8\).
A) The missing number is \(8\), derived from the second alternating series where each term is divided by a sequentially decreasing integer (\(3, 2, 1\)).
The question asks about the orbital period of GPS satellites. To answer this, one needs to recall the characteristics of the Global Positioning System (GPS) constellation, specifically the orbital period of its satellites.
Correct Option: D) Once every 12 hours. GPS satellites orbit the Earth approximately every 11 hours and 58 minutes, which is rounded to 12 hours for practical purposes. This means they complete two orbits per sidereal day.