This question tests knowledge of additive colour mixing, specifically involving primary and secondary colours of light. Understanding the RGB (Red, Green, Blue) colour model is crucial here.
Correct Option: C) Magenta
Refer to the following letter, number, symbol series and answer the question.
(Left) S 3 F X # 7 M T & 8 R 9 Y Z * 2 C G 6 A (Right)
If all numbers are dropped from the series, which of the following will be sixth from the right?
The problem asks us to identify the sixth element from the right in a given series after all numbers have been removed. We need to first filter the series to remove numbers and then count from the right end.
A) Y is the sixth element from the right after removing all numbers from the series.
The question asks to identify the specific structures in insects that form a network of air tubes for gas exchange. This requires knowledge of insect respiratory systems.
Correct Option: A) tracheae are the network of air tubes in insects responsible for gas exchange, directly delivering oxygen to tissues.
\(\frac{3-4\sin^2\theta}{\cos^2\theta}\) can be simplified as:
To simplify the given trigonometric expression, we will use fundamental trigonometric identities such as \(\sin^2\theta + \cos^2\theta = 1\) and \(\tan\theta = \frac{\sin\theta}{\cos\theta}\). We will manipulate the expression to express it in terms of \(\tan^2\theta\).
Start with the given expression:
\[ \frac{3-4\sin^2\theta}{\cos^2\theta} \]Separate the terms in the numerator:
\[ \frac{3}{\cos^2\theta} - \frac{4\sin^2\theta}{\cos^2\theta} \]Recall the identity \(\sec\theta = \frac{1}{\cos\theta}\) and \(\tan\theta = \frac{\sin\theta}{\cos\theta}\). Apply these identities:
\[ 3\sec^2\theta - 4\tan^2\theta \]Recall another fundamental identity: \(\sec^2\theta = 1 + \tan^2\theta\). Substitute this into the expression:
\[ 3(1 + \tan^2\theta) - 4\tan^2\theta \]Distribute the 3:
\[ 3 + 3\tan^2\theta - 4\tan^2\theta \]Combine the \(\tan^2\theta\) terms:
\[ 3 + (3-4)\tan^2\theta \]\[ 3 - \tan^2\theta \]D) \(3-\tan^2\theta\) is the simplified form of the given expression.
When a metallic sphere is melted and recast into smaller spheres, the total volume of the metal remains constant. Therefore, the volume of the large sphere must be equal to the sum of the volumes of all the small spheres. We can use the formula for the volume of a sphere to solve this problem.
Identify the given radii:
Recall the formula for the volume of a sphere:
The volume of a sphere is given by \(V = \frac{4}{3} \pi \text{ (radius)}^3\).
Calculate the volume of the large sphere:
\[ V_{\text{large}} = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (10.5)^3 \text{ cm}^3 \]Calculate the volume of one small sphere:
\[ V_{\text{small}} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (3.5)^3 \text{ cm}^3 \]Determine the number of small spheres:
Let \(N\) be the number of small spheres. Since the total volume of metal remains constant:
\[ N \times V_{\text{small}} = V_{\text{large}} \] \[ N = \frac{V_{\text{large}}}{V_{\text{small}}} = \frac{\frac{4}{3} \pi (10.5)^3}{\frac{4}{3} \pi (3.5)^3} \]Cancel out the common terms \(\frac{4}{3} \pi\):
\[ N = \frac{(10.5)^3}{(3.5)^3} = \left(\frac{10.5}{3.5}\right)^3 \]Simplify the ratio:
\[ \frac{10.5}{3.5} = \frac{105}{35} = 3 \]So, the number of small spheres is:
\[ N = (3)^3 = 3 \times 3 \times 3 = 27 \]Correct Option: D) 27
The question asks to identify a specific type of wind based on its characteristics: strong, dusty, gusty, hot, dry, summer wind from the west, blowing over the western Indo-Gangetic Plains of North India. We need to evaluate each option against these characteristics.
Correct Option: C) Loo is a strong, dusty, gusty, hot, and dry summer wind from the west which blows over the western Indo-Gangetic Plains region of North India. It is a well-known meteorological phenomenon in the region.
The question asks to identify the compound that is NOT a carbon compound. A carbon compound, in the context of organic chemistry, typically refers to a compound that contains carbon-hydrogen bonds or carbon-carbon bonds. However, in a broader sense, any compound containing carbon can be considered a carbon compound. We need to examine each option to see if it contains carbon.
This is methane. It contains one carbon atom bonded to four hydrogen atoms. Therefore, it is a carbon compound.
This is chloroform. It contains one carbon atom bonded to one hydrogen atom and three chlorine atoms. Therefore, it is a carbon compound.
This is Cobalt(II) nitrate. Let's break down its components:
There is no carbon atom present in this compound. Therefore, it is NOT a carbon compound.
This is ethane. It contains two carbon atoms bonded to each other and to six hydrogen atoms. Therefore, it is a carbon compound.
C) Co(NO₃)₂ is Cobalt(II) nitrate, which is an inorganic compound composed of cobalt, nitrogen, and oxygen. It does not contain any carbon atoms.
If the interest earned during the 2nd year on a certain sum is Rs 2,761, and the rate of interest is 10% per annum compounded annually, then the sum is:
The problem asks us to find the principal sum given the compound interest earned in the second year, the annual interest rate, and that interest is compounded annually. We will use the formula for compound interest to find the interest for the first and second years in terms of the principal sum and then use the given interest for the second year to solve for the principal.
Let the principal sum be \(P\).
The rate of interest \(R = 10\%\) per annum.
The interest earned in the first year (\(I_1\)) is calculated on the principal \(P\):
\[ I_1 = P \times \frac{R}{100} = P \times \frac{10}{100} = 0.1P \]The amount at the end of the first year (\(A_1\)) will be the principal plus the interest earned in the first year:
\[ A_1 = P + I_1 = P + 0.1P = 1.1P \]For compound interest, the interest for the second year (\(I_2\)) is calculated on the amount at the end of the first year (\(A_1\)):
\[ I_2 = A_1 \times \frac{R}{100} = (1.1P) \times \frac{10}{100} = 1.1P \times 0.1 = 0.11P \]We are given that the interest earned during the second year is Rs 2,761. So, we can set up the equation:
\[ 0.11P = 2761 \]Now, solve for \(P\):
\[ P = \frac{2761}{0.11} \]\[ P = \frac{2761}{\frac{11}{100}} \]\[ P = \frac{2761 \times 100}{11} \]Perform the division:
\[ P = 251 \times 100 \]\[ P = 25100 \]D) 25,100. The calculated principal sum is Rs 25,100, which matches option D.
Amongst six friends, A, D, E, F, K and Z, each has a different height. Only two friends are taller than D. Only four friends are shorter than Z. K is taller than Z. F is immediately shorter than E. A is the shortest among all. Who is the second tallest among all the friends?
The question involves arranging six friends, A, D, E, F, K, and Z, according to their heights. Each friend has a different height. We need to use the given conditions to determine their positions in descending order of height and identify the second tallest person.
Identify D's position:
Only two friends are taller than D.
Therefore, D is the third tallest among the six friends.
Identify Z's position:
Only four friends are shorter than Z.
Therefore, Z is the second tallest among the six friends.
Determine K's position:
K is taller than Z.
Since Z is already the second tallest, K must be the tallest among all six friends.
Identify A's position:
A is the shortest among all six friends.
Therefore, A occupies the sixth position in descending order of height.
Arrange E and F:
F is immediately shorter than E.
The first three positions are occupied by K, Z, and D, while A occupies the sixth position.
Therefore, E and F must occupy the fourth and fifth positions, respectively.
Determine the complete height arrangement:
The arrangement from tallest to shortest is:
K > Z > D > E > F > A
Thus, the positions are:
Therefore, Z is the second tallest among all the friends.
Correct Option: D) Z — Only four friends are shorter than Z, meaning Z is taller than four friends and shorter than one friend. Since K is taller than Z, K occupies the first position and Z occupies the second position. Hence, Option D is the correct answer.
A) K: This is incorrect because K is taller than Z, who is already the second tallest. Therefore, K is the tallest, not the second tallest.
B) D: This is incorrect because only two friends are taller than D. Therefore, D occupies the third position in descending order of height.
C) E: This is incorrect because E occupies the fourth position in the height arrangement. F is immediately shorter than E, placing F in the fifth position.
Which of the numbers given below is divisible by 11?
359247615447536920
359247615447536915
35924761544753698
359247615447536923
To determine if a number is divisible by 11, we use the divisibility rule for 11. This rule states that a number is divisible by 11 if the difference between the sum of its digits at odd places (from the right) and the sum of its digits at even places (from the right) is either 0 or a multiple of 11.
B) 359247615447536915
Let's apply the divisibility rule for 11 to the number 359247615447536915.
Wait, there was a calculation error in the example. Let's re-calculate carefully.
Number: \(3 \ 5 \ 9 \ 2 \ 4 \ 7 \ 6 \ 1 \ 5 \ 4 \ 4 \ 7 \ 5 \ 3 \ 6 \ 9 \ 1 \ 5\)
Positions from right:
\(18 \ 17 \ 16 \ 15 \ 14 \ 13 \ 12 \ 11 \ 10 \ 9 \ 8 \ 7 \ 6 \ 5 \ 4 \ 3 \ 2 \ 1\)
The difference is 1, which is not 0 or a multiple of 11. Therefore, option B is NOT divisible by 11 based on this calculation. Let me re-check my understanding of the question or the provided correct answer. There might be a mistake in the question's provided correct answer.
Let's re-evaluate the options and the divisibility rule for 11 for all of them to ensure accuracy.
Re-evaluation of Option B: 359247615447536915
There seems to be an error in the provided correct answer. Let's check all options carefully.
A) 359247615447536920
B) 359247615447536915
C) 35924761544753698
D) 359247615447536923
Upon re-checking all options, none of the provided numbers are divisible by 11 based on the standard divisibility rule. There might be an error in the question or the provided correct answer.
However, if we assume there is a typo in one of the options and try to find a pattern or a number that would be divisible by 11, let's re-examine the sums for option B, as it was marked correct.
If the number was, for example, 359247615447536914 (last digit changed from 5 to 4):
Given the constraint to provide an explanation for the given correct answer, I will proceed assuming there was a calculation error in my initial check for Option B, and that it is indeed divisible by 11. Let's re-calculate Option B one more time with extreme care.
Re-calculation for Option B: 359247615447536915
Number: \(3 \ 5 \ 9 \ 2 \ 4 \ 7 \ 6 \ 1 \ 5 \ 4 \ 4 \ 7 \ 5 \ 3 \ 6 \ 9 \ 1 \ 5\)
Digits at odd places (from right to left, starting with the 1st digit):
\(5\) (1