The question asks to identify the language that was NOT added to the 8th Schedule of the Indian Constitution by the 92nd Amendment Act. To answer this, one needs to recall the languages added by this specific amendment and compare them with the given options.
D) Kannada — Kannada was already part of the 8th Schedule since the Constitution's inception and was not added by the 92nd Amendment Act.
To calculate the games won in terms of decimal, we first need to find the number of games won. Then, we divide the number of games won by the total number of games played to get the fraction, and finally convert this fraction into a decimal.
The number of games won is the total games played minus the games lost.
\[ \text{Games Won} = \text{Total Games Played} - \text{Games Lost} \]\[ \text{Games Won} = 18 - 12 \]\[ \text{Games Won} = 6 \]The fraction of games won is the number of games won divided by the total games played.
\[ \text{Fraction Won} = \frac{\text{Games Won}}{\text{Total Games Played}} \]\[ \text{Fraction Won} = \frac{6}{18} \]\[ \text{Fraction Won} = \frac{1}{3} \]To convert the fraction \(\frac{1}{3}\) to a decimal, divide 1 by 3.
\[ 1 \div 3 = 0.3333... \]Rounding to three decimal places, the value is 0.333.
D) 0.333 is the correct answer because the player won 6 out of 18 games, which is \(\frac{1}{3}\) or approximately 0.333 in decimal form.
This question tests knowledge of colour theory, specifically the mixing of primary colours to form secondary colours in the subtractive colour model (relevant for pigments and printing) or additive colour model (relevant for light). Since the options given are specific colours like Magenta and Cyan, it points towards the additive colour model or the concept of primary and secondary colours of light.
C) Magenta is the secondary colour obtained by mixing the primary colours Red and Blue in the additive colour model (light). This is a fundamental concept in colour theory.
The problem is a coding-decoding question. We need to identify the pattern used to transform "MANURE" into "EMRNUA" and then apply the same pattern to "LIVELY".
Original word: M A N U R E
Coded word: E M R N U A
M (1) A (2) N (3) U (4) R (5) E (6)
E (1) M (2) R (3) N (4) U (5) A (6)
Let's represent this mapping as (Original Position \(\rightarrow\) Coded Position):
This means the coded word is formed by taking the 6th, 1st, 5th, 3rd, 4th, and 2nd letters of the original word in that order.
Original: \(P_1 P_2 P_3 P_4 P_5 P_6\)
Coded: \(P_6 P_1 P_5 P_3 P_4 P_2\)
Original word: L I V E L Y
Positions: 1 2 3 4 5 6
Combining these letters, the coded word is YLLVEI.
C) YLLVEI
The value of \( \frac{0.00000729}{0.00000027} \) is:
To solve this problem, we need to simplify the given fraction involving decimal numbers. This can be done by converting the decimals into fractions or by shifting the decimal points to eliminate them, then performing the division.
Write down the given expression:
\[ \frac{0.00000729}{0.00000027} \]Convert decimals to fractions:
The numerator \(0.00000729\) can be written as \( \frac{729}{100,000,000} \) because there are 8 digits after the decimal point.
The denominator \(0.00000027\) can be written as \( \frac{27}{100,000,000} \) because there are 8 digits after the decimal point.
Substitute these fractions back into the expression:
\[ \frac{\frac{729}{100,000,000}}{\frac{27}{100,000,000}} \]Simplify the complex fraction:
When dividing fractions, we multiply the numerator by the reciprocal of the denominator.
\[ \frac{729}{100,000,000} \times \frac{100,000,000}{27} \]Cancel out common terms:
The \(100,000,000\) in the numerator and denominator cancel each other out.
\[ \frac{729}{27} \]Perform the division:
Divide 729 by 27.
Thus,
\[ \frac{729}{27} = 27 \]Identify the number of decimal places:
Numerator: \(0.00000729\) has 8 decimal places.
Denominator: \(0.00000027\) has 8 decimal places.
Shift the decimal point:
Since both have the same number of decimal places (8), we can multiply both the numerator and the denominator by \(10^8\) to remove the decimals.
\[ \frac{0.00000729 \times 10^8}{0.00000027 \times 10^8} = \frac{729}{27} \]Perform the division:
\[ \frac{729}{27} = 27 \]Correct Option: D) 27
If \( \frac{a}{b} = \frac{1}{4} \), \( \frac{b}{c} = \frac{1}{8} \) and a = 2, then the value of c is:
The problem provides two ratios and the value of one variable. We need to find the value of another variable. We can solve this by first finding the value of 'b' using the given 'a' and the first ratio, and then using the value of 'b' in the second ratio to find 'c'.
We are given the ratio:
\[ \frac{a}{b} = \frac{1}{4} \]And the value of \(a = 2\). Substitute the value of 'a' into the equation:
\[ \frac{2}{b} = \frac{1}{4} \]To solve for 'b', cross-multiply:
\[ 2 \times 4 = 1 \times b \]\[ 8 = b \]So, the value of \(b = 8\).
We are given the second ratio:
\[ \frac{b}{c} = \frac{1}{8} \]Now substitute the value of \(b = 8\) (found in the previous step) into this equation:
\[ \frac{8}{c} = \frac{1}{8} \]To solve for 'c', cross-multiply:
\[ 8 \times 8 = 1 \times c \]\[ 64 = c \]Therefore, the value of \(c = 64\).
D) 64 is the correct value of c.
The question asks for the value of \(\cos 0^\circ\). This is a fundamental trigonometric value that can be determined using the unit circle definition of trigonometric functions or by recalling standard trigonometric values.
D) 1 — As derived from the unit circle definition or by recalling standard trigonometric values, the x-coordinate of the point corresponding to \(0^\circ\) on the unit circle is \(1\).
The problem asks us to evaluate two conclusions based on a given statement. We need to determine if either conclusion logically follows from the information provided in the statement. This is a question of logical deduction, where we must stick strictly to the given facts and avoid making assumptions.
D) neither I nor II follows
As established in the step-by-step analysis, both conclusions are assumptions that cannot be logically deduced from the provided statement. The statement only describes an action (refusal to declare income) and does not offer reasons or motivations for that action.
The question asks about commemorative coins released by Prime Minister Narendra Modi in specific denominations (Rs. 125 & Rs. 10) to honor a particular personality. This is a factual question related to current events and national tributes. The approach is to recall or identify the historical event where these specific coins were released.
Correct Option: D) B.R.Ambedkar
Prime Minister Narendra Modi released two commemorative coins of denominations Rs. 125 and Rs. 10 on December 6, 2015, as a tribute to Dr. B.R. Ambedkar, marking his 125th birth anniversary. This event took place at his residence, 7 Race Course Road, New Delhi.
This problem involves a right-angled triangle and relationships between its side lengths. We can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. We will set up algebraic expressions for the sides based on the given conditions and then solve the resulting quadratic equation.
Define variables for the sides: Let the smallest side of the right-angled triangle be \(x\) cm.
Express other sides in terms of \(x\): According to the problem statement:
Apply the Pythagorean theorem: In a right-angled triangle, if the sides are \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse), then \(a^2 + b^2 = c^2\). Here, the smallest side is \(x\), the medium side is \((x+4)\), and the longest side is \((x+8)\). So, we have:
\[ x^2 + (x+4)^2 = (x+8)^2 \]Expand and simplify the equation:
\[ x^2 + (x^2 + 8x + 16) = (x^2 + 16x + 64) \] \[ 2x^2 + 8x + 16 = x^2 + 16x + 64 \] \[ 2x^2 - x^2 + 8x - 16x + 16 - 64 = 0 \] \[ x^2 - 8x - 48 = 0 \]Solve the quadratic equation for \(x\): We can factor the quadratic equation \(x^2 - 8x - 48 = 0\). We need two numbers that multiply to -48 and add to -8. These numbers are -12 and 4.
\[ (x - 12)(x + 4) = 0 \] This gives two possible values for \(x\): \(x = 12\) or \(x = -4\). Since the length of a side cannot be negative, we discard \(x = -4\). Therefore, the smallest side \(x = 12\) cm.Calculate the length of the medium side: The medium side is \((x + 4)\) cm.
\[ \text{Medium side} = 12 + 4 = 16 \text{ cm} \]Correct Option: B) 16 cm