To find the gain or loss percent, we need to determine the cost price (CP) for Himanshi and the selling price (SP) for Himanshi. The cost price will be the price at which she bought the t-shirt after the discount, and the selling price will be the marked price since she sold it at that price. We can assume a marked price to simplify calculations.
Correct Option: C) 25% gain
To determine the nature of the image formed by a concave mirror, we need to recall the rules of image formation for different object positions. Specifically, we will consider the case where the object is placed between the focus (\(F\)) and the centre of curvature (\(C\)) of a concave mirror.
A) real and inverted
As explained in the step-by-step analysis, when an object is placed between the focus and the centre of curvature of a concave mirror, the reflected rays converge to form a real image, which is also inverted and magnified, located beyond the centre of curvature.
To find the kinetic energy of an object, we use the standard formula for kinetic energy, which relates the object's mass and its speed. We will substitute the given values into this formula and calculate the result.
The kinetic energy (\(KE\)) of an object is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]Substitute \(m = 10 \text{ kg}\) and \(v = 5 \text{ m/s}\) into the kinetic energy formula:
\[ KE = \frac{1}{2} \times (10 \text{ kg}) \times (5 \text{ m/s})^2 \]The unit of kinetic energy is Joules (J).
Correct Option: D) 125 J
The question asks to identify which of the given options is NOT a simple permanent tissue. To answer this, we need to understand the classification of plant tissues, specifically distinguishing between simple permanent tissues and complex permanent tissues.
D) Xylem is a complex permanent tissue because it is composed of more than one type of cell (tracheids, vessels, xylem parenchyma, and xylem fibres) that work together to transport water and minerals. Therefore, it is NOT a simple permanent tissue.
This question tests general knowledge about the launch dates of popular media channels. To answer correctly, one needs to recall the specific launch date of Viacom18's Hindi movie channel, Rishtey Cineplex.
Correct Option: B) May 2016
If α and β are the roots of the quadratic equation
(5+\(\sqrt{2}\))x2−(4+\(\sqrt{5}\))x+(8+2\(\sqrt{5}\))=0
then the value of \(\frac{2\alpha\beta}{\alpha+\beta}\) is:
The problem asks us to find the value of an expression involving the roots of a given quadratic equation. We will use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. For a quadratic equation \(ax^2 + bx + c = 0\), the sum of the roots is \(\alpha + \beta = -b/a\) and the product of the roots is \(\alpha\beta = c/a\). We will calculate these values and then substitute them into the given expression.
Identify the coefficients of the quadratic equation.
The given quadratic equation is \((5+\sqrt{2})x^2 - (4+\sqrt{5})x + (8+2\sqrt{5}) = 0\).
Comparing this with the standard form \(ax^2 + bx + c = 0\), we have:
Calculate the sum of the roots, \(\alpha + \beta\).
Using Vieta's formulas, the sum of the roots is \(\alpha + \beta = -b/a\).
\[ \alpha + \beta = -\frac{-(4+\sqrt{5})}{5+\sqrt{2}} = \frac{4+\sqrt{5}}{5+\sqrt{2}} \]Calculate the product of the roots, \(\alpha\beta\).
Using Vieta's formulas, the product of the roots is \(\alpha\beta = c/a\).
\[ \alpha\beta = \frac{8+2\sqrt{5}}{5+\sqrt{2}} \]Substitute the values of \(\alpha + \beta\) and \(\alpha\beta\) into the expression \(\frac{2\alpha\beta}{\alpha+\beta}\).
\[ \frac{2\alpha\beta}{\alpha+\beta} = \frac{2 \left( \frac{8+2\sqrt{5}}{5+\sqrt{2}} \right)}{\frac{4+\sqrt{5}}{5+\sqrt{2}}} \]Simplify the expression.
Notice that the denominator \((5+\sqrt{2})\) cancels out:
\[ \frac{2\alpha\beta}{\alpha+\beta} = \frac{2(8+2\sqrt{5})}{4+\sqrt{5}} \]Factor out 2 from the numerator:
\[ \frac{2(8+2\sqrt{5})}{4+\sqrt{5}} = \frac{2 \cdot 2(4+\sqrt{5})}{4+\sqrt{5}} \] \[ = \frac{4(4+\sqrt{5})}{4+\sqrt{5}} \]Since \((4+\sqrt{5})\) is a common factor in the numerator and denominator, we can cancel it out:
\[ = 4 \]B) The value of the expression is 4.
The question asks for the real name of the renowned Indian film director 'Guru Dutt'. This is a factual recall question about a prominent personality in Indian cinema. To answer correctly, one needs to know the birth name of Guru Dutt.
Correct Option: B) Vasant Kumar Shivashankar Padukone is the full birth name of the legendary Indian filmmaker Guru Dutt. He was born on July 9, 1925, in Padukone, a village in the present-day Karnataka state. He is widely regarded as one of the greatest auteurs of Indian cinema.
The problem asks us to evaluate two conclusions based on a given statement. We need to determine which conclusion(s) logically follow from the statement. This is a question of logical deduction, where we must only infer what is directly supported by the statement, without introducing outside information or assumptions.
D) Conclusion I alone follows.
As established in the step-by-step analysis, Conclusion I is a necessary prerequisite for the statement to be made, while Conclusion II makes an assumption about popularity that is not supported by the sales data alone.
The melting point of tungsten is ___.
The question asks for the melting point of tungsten. This is a factual recall question related to the properties of elements, specifically a high-temperature material. Tungsten is known for having the highest melting point of all metals.
Correct Option: D) The melting point of tungsten is approximately \(3,380 \, \text{°C}\). This value is widely recognized and is the highest among all metals, making tungsten suitable for high-temperature applications.
The question asks about the condition under which true free fall occurs. Free fall is defined as the motion of an object where the only force acting upon it is gravity. We need to identify the environment where this condition is met.
Correct Option: D) in vacuum