This question asks about the unit used to measure the energy obtained from food. We need to identify the standard unit for energy content in food items.
Correct Option: A) Calories
The question asks about the typical volume of blood in an adult human body. This is a factual recall question related to human physiology. We need to identify the standard range for blood volume in adults.
Correct Option: C) 5
An average adult human body contains approximately 5 litres of blood. This is a well-established physiological fact.
The question asks to identify the person known as the "Father of video games." This is a factual recall question related to the history of technology and invention. We need to identify the individual credited with pioneering the development of video games.
Correct Option: D) Ralph H. Baer is widely acknowledged as the "Father of video games" due to his invention of the first home video game console, the Magnavox Odyssey, and his foundational work in the field.
If Sunita earns \( \frac{75}{4} \)% more than her boyfriend, find the approximate % her boyfriend earns less than Sunita.
To solve this problem, we first need to understand the relationship between Sunita's earnings and her boyfriend's earnings. We are given that Sunita earns a certain percentage more than her boyfriend. We need to find the percentage her boyfriend earns less than Sunita. This is a common type of percentage problem where a change is expressed relative to one base, and we need to find the equivalent change relative to a different base.
Sunita earns \( \frac{75}{4} \)% more than her boyfriend. Let's convert this percentage to a fraction:
\[ \frac{75}{4} \% = \frac{75}{4 \times 100} = \frac{75}{400} = \frac{3 \times 25}{16 \times 25} = \frac{3}{16} \]Let the boyfriend's earnings be \(B\). Since Sunita earns \( \frac{3}{16} \) more than her boyfriend, Sunita's earnings (\(S\)) can be expressed as:
\[ S = B + \frac{3}{16} B = B \left(1 + \frac{3}{16}\right) = B \left(\frac{16+3}{16}\right) = \frac{19}{16} B \]This means if the boyfriend earns 16 units, Sunita earns 19 units.
The difference between Sunita's earnings and her boyfriend's earnings is:
\[ S - B = \frac{19}{16} B - B = \left(\frac{19}{16} - 1\right) B = \left(\frac{19-16}{16}\right) B = \frac{3}{16} B \]We need to find what percentage this difference (\(S-B\)) is of Sunita's earnings (\(S\)).
\[ \text{Percentage less} = \frac{S - B}{S} \times 100\% \]Substitute the values:
\[ \text{Percentage less} = \frac{\frac{3}{16} B}{\frac{19}{16} B} \times 100\% \]The \(B\) and \( \frac{1}{16} \) terms cancel out:
\[ \text{Percentage less} = \frac{3}{19} \times 100\% \] \[ \text{Percentage less} = \frac{300}{19}\% \] \[ \text{Percentage less} \approx 15.789\% \]Rounding \(15.789\%\) to the nearest whole number gives \(16\%\).
Correct Option: A) 16%
To solve this problem, we will use the property that the sum of angles in a triangle is 180 degrees. Given the ratio of the angles, we can represent them using a common multiplier. Then, we will find the actual values of the angles and subsequently determine the ratio of the greatest angle to the smallest angle.
Let the angles of the triangle be \(2x\), \(3x\), and \(7x\), since their ratio is given as 2:3:7.
The sum of the angles in any triangle is 180 degrees. So, we can write the equation:
\[ 2x + 3x + 7x = 180^\circ \]Combine the terms on the left side:
\[ (2 + 3 + 7)x = 180^\circ \]\[ 12x = 180^\circ \]Solve for \(x\):
\[ x = \frac{180^\circ}{12} \]\[ x = 15^\circ \]Now, calculate the measure of each angle:
The question asks for the ratio of the greatest angle to the smallest angle. Greatest angle is \(105^\circ\) and smallest angle is \(30^\circ\).
Form the ratio:
\[ \frac{\text{Greatest Angle}}{\text{Smallest Angle}} = \frac{105^\circ}{30^\circ} \]Simplify the ratio by dividing both numerator and denominator by their greatest common divisor, which is 15:
\[ \frac{105 \div 15}{30 \div 15} = \frac{7}{2} \]So, the ratio of the greatest angle to the smallest angle is 7:2.
Correct Option: A) 7:2
The question asks to identify the specific type of wood traditionally used for making cricket bats. This is a factual recall question related to sports equipment manufacturing.
Correct Option: B) Willow
Which of the devices given below converts chemical energy to electrical energy?
The question asks to identify the device that converts chemical energy into electrical energy. We need to analyze the function of each given option to determine which one performs this specific energy conversion.
Correct Option: B) A battery is an electrochemical device that stores chemical energy and converts it into electrical energy through chemical reactions when connected to an external circuit.
The problem involves finding an angle based on its relationship with its complement. We will set up an algebraic equation using the definition of complementary angles and then solve for the unknown angle. Finally, we will calculate the difference between the angle and its complement.
Let the angle be \(x\). The complement of an angle \(x\) is \(90^\circ - x\).
According to the problem statement, the angle \(x\) is \(30^\circ\) more than one half of its complement. We can write this as an equation:
\[ x = \frac{1}{2}(90^\circ - x) + 30^\circ \]Now, we solve this equation for \(x\):
\[ x = 45^\circ - \frac{x}{2} + 30^\circ \]\[ x = 75^\circ - \frac{x}{2} \]To eliminate the fraction, multiply the entire equation by 2:
\[ 2x = 150^\circ - x \]Add \(x\) to both sides:
\[ 2x + x = 150^\circ \]\[ 3x = 150^\circ \]Divide by 3 to find \(x\):
\[ x = \frac{150^\circ}{3} \]\[ x = 50^\circ \]So, the angle is \(50^\circ\). Its complement is \(90^\circ - 50^\circ = 40^\circ\).
The problem asks for the difference between the greater and the smaller angles. The greater angle is \(50^\circ\) and the smaller angle is \(40^\circ\).
\[ \text{Difference} = 50^\circ - 40^\circ = 10^\circ \]A) \(10^\circ\) is the difference between the greater angle (\(50^\circ\)) and the smaller angle (\(40^\circ\)).
What are the factors of \( (x^{6}-x^{4}-x^{5}-x^{4}+x^{2}-4) \)?
(x-1)
(x+1)
Both (x-1) & (x+1)
Neither (x-1) nor (x+1)
To determine if \((x-1)\) or \((x+1)\) are factors of a polynomial, we can use the Factor Theorem. The Factor Theorem states that if \((x-a)\) is a factor of a polynomial \(P(x)\), then \(P(a) = 0\). Similarly, if \((x+a)\) is a factor, then \(P(-a) = 0\).
The given polynomial is \( P(x) = x^{6}-x^{4}-x^{5}-x^{4}+x^{2}-4 \).
Combine like terms:
\[ P(x) = x^{6} - x^{5} - x^{4} - x^{4} + x^{2} - 4 \]\[ P(x) = x^{6} - x^{5} - 2x^{4} + x^{2} - 4 \]According to the Factor Theorem, if \((x-1)\) is a factor, then \(P(1)\) must be equal to 0.
Substitute \(x=1\) into the simplified polynomial:
\[ P(1) = (1)^{6} - (1)^{5} - 2(1)^{4} + (1)^{2} - 4 \]\[ P(1) = 1 - 1 - 2(1) + 1 - 4 \]\[ P(1) = 1 - 1 - 2 + 1 - 4 \]\[ P(1) = 0 - 2 + 1 - 4 \]\[ P(1) = -1 - 4 \]\[ P(1) = -5 \]Since \(P(1) = -5 \neq 0\), \((x-1)\) is not a factor of the polynomial.According to the Factor Theorem, if \((x+1)\) is a factor, then \(P(-1)\) must be equal to 0.
Substitute \(x=-1\) into the simplified polynomial:
\[ P(-1) = (-1)^{6} - (-1)^{5} - 2(-1)^{4} + (-1)^{2} - 4 \]\[ P(-1) = 1 - (-1) - 2(1) + 1 - 4 \]\[ P(-1) = 1 + 1 - 2 + 1 - 4 \]\[ P(-1) = 2 - 2 + 1 - 4 \]\[ P(-1) = 0 + 1 - 4 \]\[ P(-1) = -3 \]Since \(P(-1) = -3 \neq 0\), \((x+1)\) is not a factor of the polynomial.D) Neither (x-1) nor (x+1) is a factor, as both \(P(1)\) and \(P(-1)\) are not equal to zero.
The question asks to identify the Indian power that confronted Ahmad Shah Abdali in the Third Battle of Panipat. This requires knowledge of major historical battles and the key players involved.
The Third Battle of Panipat was fought on January 14, 1761, between the Maratha Empire and the invading Afghan army of Ahmad Shah Abdali, supported by several Indian Muslim allies. The Marathas suffered a devastating defeat, which significantly weakened their power and halted their expansion in northern India.
C) Marathas — The Maratha Confederacy, under the command of Sadashivrao Bhau, fought against Ahmad Shah Abdali in the Third Battle of Panipat in 1761.