The economic reforms were initiated by Narasimha Rao government in:
the 8th five-year plan
the 9th five-year plan
the 7th five-year plan
the 5th five-year plan
The question asks to identify the Five-Year Plan during which the economic reforms were initiated by the Narasimha Rao government. This requires knowledge of the timeline of India's Five-Year Plans and the period of the economic reforms.
Correct Option: A) the 8th five-year plan. The economic reforms were initiated in 1991 by the Narasimha Rao government. While 1991 was technically a period of Annual Plans, the 8th Five-Year Plan (1992-1997) is the plan period most closely associated with the implementation and continuation of these reforms under his tenure.
The question asks about the sources of H+ ions and OH- ions during a neutralisation reaction that form a water molecule. We need to recall the definitions of acids and bases in the context of their ion dissociation in aqueous solutions.
Thus, the H+ ion comes from the acid.
Thus, the OH- ion comes from the base.
Therefore, H+ comes from the acid and OH- comes from the base.
Correct Option: C) acid; base
This option correctly identifies that H+ ions come from the acid and OH- ions come from the base during a neutralisation reaction to form water.
The value of the product sin 90°. sin 89°. sin 88°. sin 87° ...... sin 0° is:
The problem asks for the value of a product of sine functions: \(\sin 90^\circ \cdot \sin 89^\circ \cdot \sin 88^\circ \cdot \sin 87^\circ \cdots \sin 0^\circ\). This is a product of sine values for angles decreasing from \(90^\circ\) down to \(0^\circ\) in steps of \(1^\circ\).
Identify the terms in the product:
The given product is \(P = \sin 90^\circ \cdot \sin 89^\circ \cdot \sin 88^\circ \cdot \sin 87^\circ \cdots \sin 1^\circ \cdot \sin 0^\circ\).
Recall the value of \(\sin 0^\circ\):
We know that the sine of \(0^\circ\) is \(0\).
\[ \sin 0^\circ = 0 \]Substitute the value into the product:
Since one of the terms in the product is \(\sin 0^\circ\), and its value is \(0\), the entire product will become \(0\) because any number multiplied by \(0\) results in \(0\).
\[ P = \sin 90^\circ \cdot \sin 89^\circ \cdot \sin 88^\circ \cdots \sin 1^\circ \cdot (0) \]\[ P = 0 \]Conclusion:
Therefore, the value of the product is \(0\).
A) 0 is the correct answer because the product includes \(\sin 0^\circ\), which is \(0\), making the entire product \(0\).
In this question, a group of numbers/symbols is coded using letters as per the table given below and the conditions which follow. The correct combination of codes following the conditions is your answer.
| Number/Symbol | = | 6 | 8 | < | ? | / | 2 | 5 | ! | @ | 7 | 3 | ^ |
| Code | G | L | F | M | E | N | D | P | C | R | T | B | V |
Conditions:
1. If the first element is a symbol and the last is a number, the first and last elements are coded as ¥ and ¥, respectively.
2. If the first element is an odd number and the last is an even number, the codes for these two are to be interchanged.
3. If both second and third elements are perfect squares, the third element is to be coded as the code for the second element.
How will '8 ? = 5 7 !' be coded?
The problem requires us to code a given sequence of numbers and symbols based on a provided coding table and a set of conditions. We need to first find the direct codes for each element in the sequence and then apply the conditions in the given order to modify the codes if necessary.
Find the length of the side of an equilateral triangle, if its area is 4\(\sqrt{3}\) sq. unit.
To find the length of the side of an equilateral triangle given its area, we use the formula for the area of an equilateral triangle. We will set the given area equal to the formula and solve for the side length.
Correct Option: D) 4 unit
If 16x² - 8x + 1 = 0, then what is the value of \(\left(16x^{2}+\frac{1}{4x^{2}}\right)\)?
The problem asks us to find the value of an expression involving \(x^2\) and \(\frac{1}{x^2}\) given a quadratic equation. We can manipulate the given quadratic equation to find a relationship between \(x\) and \(\frac{1}{x}\), and then use algebraic identities to solve for the required expression.
Start with the given equation:
\[ 16x^2 - 8x + 1 = 0 \]Recognize the perfect square identity:
The given equation resembles the expansion of \((a-b)^2 = a^2 - 2ab + b^2\).
Here, \(a^2 = 16x^2 \implies a = 4x\)
And \(b^2 = 1 \implies b = 1\)
Check the middle term: \(2ab = 2(4x)(1) = 8x\).
So, the equation can be written as:
Solve for \(x\):
Taking the square root of both sides:
Substitute the value of \(x\) into the expression to be evaluated:
The expression is \(\left(16x^{2}+\frac{1}{4x^{2}}\right)\).
Substitute \(x = \frac{1}{4}\) into the expression:
Start with the given equation:
\[ 16x^2 - 8x + 1 = 0 \]Divide the entire equation by \(x\) (since \(x=0\) would make \(1=0\), so \(x \neq 0\)):
\[ \frac{16x^2}{x} - \frac{8x}{x} + \frac{1}{x} = \frac{0}{x} \]\[ 16x - 8 + \frac{1}{x} = 0 \]Rearrange to find a relationship between \(x\) and \(\frac{1}{x}\):
\[ 16x + \frac{1}{x} = 8 \]Consider the expression to be evaluated:
\[ 16x^2 + \frac{1}{4x^2} \]Manipulate the expression to use the identity \((a+b)^2 = a^2 + b^2 + 2ab\):
We have \(16x + \frac{1}{x} = 8\). This doesn't directly give us \(16x^2 + \frac{1}{4x^2}\).
Let's try a different approach from step 2.
Start with the given equation:
\[ 16x^2 - 8x + 1 = 0 \]Divide the entire equation by \(4x\). We know \(x \neq 0\).
\[ \frac{16x^2}{4x} - \frac{8x}{4x} + \frac{1}{4x} = \frac{0}{4x} \]\[ 4x - 2 + \frac{1}{4x} = 0 \]Rearrange the terms:
\[ 4x + \frac{1}{4x} = 2 \]Square both sides of the equation:
\[ \left(4x + \frac{1}{4x}\right)^2 = 2^2 \]Expand the left side using the identity \((a+b)^2 = a^2 + b^2 + 2ab\):
Here \(a = 4x\) and \(b = \frac{1}{4x}\).
Isolate the required expression:
\[ 16x^2 + \frac{1}{16x^2} = 4 - 2 \]\[ 16x^2 + \frac{1}{16x^2} = 2 \]Notice the required expression is \(\left(16x^{2}+\frac{1}{4x^{2}}\right)\), not \(\left(16x^{2}+\frac{1}{16x^{2}}\right)\). This means the previous manipulation was slightly off for the target expression. Let's re-evaluate the target expression.
Start with the given equation:
\[ 16x^2 - 8x + 1 = 0 \]Recognize it as a perfect square:
\[ (4x - 1)^2 = 0 \]From this, we get:
\[ 4x - 1 = 0 \]\[ 4x = 1 \]Now, let's look at the expression we need to evaluate:
\[ 16x^2 + \frac{1}{4x^2} \]We know that \(4x = 1\). Let's use this to simplify the expression.
The first term is \(16x^2\). We can write this as \((4x)^2\).
Since \(4x = 1\), then \((4x)^2 = 1^2 = 1\).
So, \(16x^2 = 1\).
Now consider the second term: \(\frac{1}{4x^2}\).
We can rewrite the denominator as \(4x \cdot x\).
Since \(4x = 1\), the denominator becomes \(1 \cdot x = x\).
So, the second term is \(\frac{1}{x}\).
We need to find the value of \(\frac{1}{x}\).
From \(4x = 1\), we have \(x = \frac{1}{4}\).
Therefore, \[\frac{1}{x} = \frac{1}{\frac{1}{4}} = 4\].
Substitute these values back into the expression:
\[ 16x^2 + \frac{1}{4x^2} = 1 + 4 = 5 \]B) 5
The sign of magnification for mirrors is determined by the convention used for image height. Magnification (\(m\)) is defined as the ratio of the height of the image (\(h_i\)) to the height of the object (\(h_o\)). It is also related to the image distance (\(v\)) and object distance (\(u\)).
Definition of Magnification: The linear magnification (\(m\)) produced by a spherical mirror is given by:
\[ m = \frac{\text{Height of image} (h_i)}{\text{Height of object} (h_o)} = -\frac{\text{Image distance} (v)}{\text{Object distance} (u)} \]Sign Convention for Heights: According to the New Cartesian Sign Convention:
Real Image: A real image is always inverted. This means the image is formed below the principal axis, so its height (\(h_i\)) will be negative. Since \(h_o\) is always positive, the magnification \(m = h_i/h_o\) will be negative.
Virtual Image: A virtual image is always erect. This means the image is formed above the principal axis, so its height (\(h_i\)) will be positive. Since \(h_o\) is always positive, the magnification \(m = h_i/h_o\) will be positive.
Concave Mirror Behavior:
Therefore, for a concave mirror, the sign of magnification is positive when the image is virtual and negative when the image is real.
Correct Option: A) positive when the image is virtual and negative when the image is real
To identify the odd element, we need to determine the group and period of each element based on its atomic number. The periodic table arranges elements by increasing atomic number, and elements with similar chemical properties are placed in the same group. We will write the electronic configuration for each element to find its position.
Correct Option: B) A is the odd element because it is a halogen (Group 17), while elements B, C, and D are all alkali metals (Group 1).
The question asks to identify the region in India that receives the maximum rainfall from the Southwest Monsoon winds. This requires understanding the geography of India and the mechanism of the Southwest Monsoon.
Correct Option: A) The Western Ghats are a major mountain range located along the western coast of India. They are the first significant topographic barrier encountered by the moisture-laden Southwest Monsoon winds originating from the Arabian Sea. As these winds strike the Western Ghats, they are forced to ascend, leading to adiabatic cooling, condensation, and heavy orographic rainfall on their windward (western) slopes. This makes the Western Ghats region, particularly its western face, receive the maximum rainfall from the Southwest Monsoon.
The problem presents a proportion in the format \(a:b :: c:x\). This notation means that the ratio of the first two numbers is equal to the ratio of the next two numbers. We need to set up this equality as a fraction and then solve for the unknown variable \(x\).
Understand the Proportion: The given expression is \(18:30 :: 30:x\). In a proportion, the product of the means is equal to the product of the extremes. Alternatively, it can be written as an equality of two ratios:
\[ \frac{18}{30} = \frac{30}{x} \]Cross-Multiplication: To solve for \(x\), we cross-multiply the terms:
\[ 18 \times x = 30 \times 30 \]Simplify the Equation:
\[ 18x = 900 \]Isolate \(x\): Divide both sides by 18 to find the value of \(x\):
\[ x = \frac{900}{18} \]Calculate the Value of \(x\):
\[ x = 50 \]A) 50 is the correct answer. By setting up the proportion as an equality of ratios and solving for \(x\), we find that \(x = 50\).