\( \sqrt{\frac{?}{3136}}=\frac{1}{2} \). Find the value of the question mark.
The problem requires us to find the value of the question mark in a given equation involving a square root. We will solve this by isolating the question mark using algebraic manipulation, specifically by squaring both sides of the equation.
Let the question mark be represented by the variable \(x\). The given equation is:
\[ \sqrt{\frac{x}{3136}} = \frac{1}{2} \]To eliminate the square root, square both sides of the equation:
\[ \left(\sqrt{\frac{x}{3136}}\right)^2 = \left(\frac{1}{2}\right)^2 \]Simplify both sides:
\[ \frac{x}{3136} = \frac{1^2}{2^2} \] \[ \frac{x}{3136} = \frac{1}{4} \]To find the value of \(x\), multiply both sides by 3136:
\[ x = \frac{1}{4} \times 3136 \]Perform the division:
\[ x = \frac{3136}{4} \] \[ x = 784 \]Thus, the value of the question mark is 784.
B) 784 is the correct value for the question mark, as derived from the algebraic solution.
The frequency distribution of diameter (D) of 101 steel balls is given in the following table. Find the mean of the diameter in mm.
| D(mm) | 43 | 44 | 45 | 46 | 47 | 48 |
| No. | 13 | 15 | 22 | 21 | 16 | 14 |
To find the mean of a frequency distribution, we use the formula for the weighted average. Each diameter value (D) is multiplied by its corresponding frequency (No.), these products are summed, and then divided by the total number of observations (total frequency).
Correct Option: B) 45.5
This problem involves Ohm's Law. For an electric heater, its resistance is generally considered constant. We can first calculate the resistance of the heater using the initial given potential difference and current. Then, using this constant resistance and the new potential difference, we can find the new current.
According to Ohm's Law, \(V = IR\), where \(V\) is the potential difference, \(I\) is the current, and \(R\) is the resistance. We can rearrange this to find resistance:
\[ R = \frac{V_1}{I_1} \]Substitute the given values:
\[ R = \frac{60 \text{ V}}{4 \text{ A}} = 15 \, \Omega \]The resistance of the electric heater is \(15 \, \Omega\).
Since the resistance of the heater remains constant, we can use Ohm's Law again with the new potential difference and the calculated resistance to find the new current, \(I_2\):
\[ I_2 = \frac{V_2}{R} \]Substitute the values:
\[ I_2 = \frac{150 \text{ V}}{15 \, \Omega} = 10 \text{ A} \]Correct Option: C) 10 A
Evaluate
36 ÷ \( \frac{1}{4} \)
To evaluate the given expression, we need to perform division involving a whole number and a fraction. The key rule for dividing by a fraction is to multiply by its reciprocal.
Correct Option: B) 144
Calculate the energy of an object of mass 10 kg placed at a height of 6 m above the ground. Given, g = 9.8 m s-2
The problem asks to calculate the energy of an object placed at a certain height. This energy is gravitational potential energy. We will use the formula for gravitational potential energy, which depends on the mass of the object, the acceleration due to gravity, and the height.
Gravitational Potential Energy (\(PE\)) is given by the formula:
\[ PE = mgh \]The standard unit for energy in the International System of Units (SI) is Joules (\(J\)).
The energy of the object is \(588 \text{ J}\).
B) 588 J is the correct answer. The calculation yields 588, and the unit for energy is Joules.
The problem asks us to decode a word based on a given coding pattern. We need to identify the rule used to transform "LIVE" into "OREV" and then apply the same rule to "DEAD".
It appears the pattern is not uniform for all letters. Let's re-examine L to O. If we consider opposite letters, L's opposite is O. So, it seems all letters are replaced by their alphabetical opposites.
Let's verify this:
This pattern holds true for all letters in LIVE.
So, DEAD is coded as WVZW.
Correct Option: D) WVZW
The question asks to identify the Union Minister of Environment and Climate Change as of July 2018. This requires knowledge of the cabinet portfolios during that specific period.
As of July 2018, Dr. Harsh Vardhan was indeed the Union Minister of Environment, Forest and Climate Change. He held this portfolio along with the Ministry of Science & Technology and Ministry of Earth Sciences.
B) Dr. Harsh Vardhan — As of July 2018, Dr. Harsh Vardhan was the Union Minister of Environment, Forest and Climate Change. He served in this capacity from September 2017 to May 2019.
The area of the circumscribed circle of a right-angled triangle with sides 8 cm, 4\( \sqrt{5} \) cm and 12 cm will be ________.
To find the area of the circumscribed circle of a right-angled triangle, we first need to determine the radius of this circle. For a right-angled triangle, the hypotenuse is the diameter of its circumscribed circle. We will use the given side lengths to identify the hypotenuse and then calculate the radius and finally the area of the circle.
B) 36π cm2 is the correct area of the circumscribed circle.
The question asks to identify examples of potential energy. Potential energy is stored energy an object possesses due to its position, condition, or state. We will analyze each given scenario to determine if it represents potential energy.
D) A, B, C, D — All the given scenarios describe situations where potential energy is stored. A brick on a roof and water in a high reservoir have gravitational potential energy due to their height. A rotating clock spring and a compressed spring have elastic potential energy due to their deformation.
This question asks us to identify which assumptions are implicit in the given statement. An implicit assumption is something that is taken for granted or presupposed by the statement, even if not explicitly stated. We need to analyze if the statement logically requires the assumptions to be true.
Correct Option: B) Neither I nor II is implicit