The question asks to identify the part of the human body to which vertebrae belong. This requires basic knowledge of human anatomy, specifically the skeletal system.
Correct Option: C) Spinal cord. Vertebrae are the individual bones that make up the vertebral column (spine), which encloses and protects the spinal cord. Therefore, vertebrae are an integral part of the structure that houses the spinal cord.
The problem asks us to find the missing term in a series of letter pairs. We need to identify the pattern in how the letters in each pair are related and how the pairs themselves progress.
D) JN — The first letter follows a pattern of increasing differences in alphabetical position (2, 3, 4, ...), and the second letter follows a similar pattern (3, 4, 5, ...).
To identify twin prime numbers, we need to understand the definitions of prime numbers and twin prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Twin prime numbers are pairs of prime numbers that differ by 2.
D) (3, 5)
Since both 3 and 5 are prime numbers and their difference is 2, (3, 5) is a pair of twin prime numbers.
X does 25% of a work in 20 days. Y joins X and they together finish the remaining work in 15 days. Y alone can do the whole work in __ days.
30 days
25 \( \frac{1}{3} \) days
26 \( \frac{2}{3} \) days
26 \( \frac{1}{3} \) days
This problem involves work and time. We need to calculate the individual work rates of X and Y to find out how long Y would take to complete the entire work alone. We will first find X's total time to complete the work, then calculate the combined work rate of X and Y, and finally deduce Y's individual work rate.
Calculate the total time X takes to complete the work:
X does 25% (or \(\frac{1}{4}\)) of the work in 20 days.
If X does \(\frac{1}{4}\) of the work in 20 days, then X will do the whole work (100%) in:
\[ \text{Time for X to complete work} = 20 \text{ days} \times 4 = 80 \text{ days} \]So, X's one day's work is \(\frac{1}{80}\) of the total work.
Calculate the remaining work:
Work done by X = 25% = \(\frac{1}{4}\).
Remaining work = \[1 - \frac{1}{4} = \frac{3}{4}\].
Calculate the combined one day's work of X and Y:
X and Y together finish the remaining \(\frac{3}{4}\) of the work in 15 days.
So, their combined one day's work is:
\[ \text{Combined one day's work} = \frac{\frac{3}{4}}{15} = \frac{3}{4 \times 15} = \frac{3}{60} = \frac{1}{20} \]Calculate Y's one day's work:
We know X's one day's work is \(\frac{1}{80}\).
Combined one day's work (X + Y) = \(\frac{1}{20}\).
Y's one day's work = (Combined one day's work) - (X's one day's work)
\[ \text{Y's one day's work} = \frac{1}{20} - \frac{1}{80} \]To subtract these fractions, find a common denominator, which is 80:
\[ \text{Y's one day's work} = \frac{4}{80} - \frac{1}{80} = \frac{3}{80} \]Calculate the time Y alone takes to complete the whole work:
If Y does \(\frac{3}{80}\) of the work in one day, then Y will do the whole work in:
\[ \text{Time for Y to complete work} = \frac{1}{\text{Y's one day's work}} = \frac{1}{\frac{3}{80}} = \frac{80}{3} \text{ days} \]Convert the improper fraction to a mixed number:
\[ \frac{80}{3} = 26 \frac{2}{3} \text{ days} \]Correct Option: C) 26 \( \frac{2}{3} \) days
To solve this problem, we need to expand the given expression \( (4x - 7)^{2} \) using the algebraic identity for \( (a - b)^{2} \).
Correct Option: D) \( 16x^{2} - 56x + 49 \)
This is an analogy question where you need to identify the relationship between the first pair of words and then apply the same relationship to the second pair to find the missing word.
Correct Option: C) Flood
The question asks to identify the law that is NOT related to gases. We need to evaluate each option and determine its primary subject matter.
From the analysis, Boyle's Law, Avogadro's Law, and Charles's Law are fundamental gas laws describing the behavior of gases. Joule's Law, particularly Joule heating, is primarily concerned with electricity and heat generation in conductors, not directly with the pressure, volume, or temperature relationships of gases in the same context as the other options.
B) Joule's Law is not primarily related to the behavior of gases in the same way as the other options. While Joule did work on the internal energy of ideal gases, the term "Joule's Law" often refers to Joule heating, which is about electrical current and heat generation, or to the broader concept of the mechanical equivalent of heat, not directly to the pressure-volume-temperature relationships of gases.
To find the principal amount, we will use the formula for compound interest. We are given the maturity value (Amount), the time period, and the annual interest rate. We need to rearrange the compound interest formula to solve for the Principal.
Identify the given values:
Recall the compound interest formula:
The formula for the amount \(A\) after \(n\) years when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Where:
Substitute the given values into the formula:
\[ 14400 = P \left(1 + \frac{20}{100}\right)^2 \]Simplify the expression:
\[ 14400 = P \left(1 + \frac{1}{5}\right)^2 \] \[ 14400 = P \left(\frac{5+1}{5}\right)^2 \] \[ 14400 = P \left(\frac{6}{5}\right)^2 \] \[ 14400 = P \left(\frac{36}{25}\right) \]Solve for \(P\):
To find \(P\), rearrange the equation:
\[ P = 14400 \times \frac{25}{36} \]Divide 14400 by 36:
\[ \frac{14400}{36} = 400 \]Now, multiply by 25:
\[ P = 400 \times 25 \] \[ P = 10000 \]So, the principal amount is Rs. 10,000.
C) Rs. 10,000/- is the principal amount. This matches our calculated value.
The smallest of the fractions among \( \frac{5}{8} \), \( \frac{3}{4} \), \( \frac{13}{16} \), \( \frac{7}{12} \) is __________.
\( \frac{5}{8} \)
\( \frac{3}{4} \)
\( \frac{13}{16} \)
\( \frac{7}{12} \)
To find the smallest fraction among a given set, we can convert all fractions to a common denominator, convert them to decimal form, or compare them pairwise. The most systematic method for comparing multiple fractions is to find a common denominator (LCM of the denominators) and then compare their numerators.
We can also convert each fraction to its decimal equivalent:
Comparing the decimal values (0.625, 0.75, 0.8125, 0.5833), the smallest value is 0.5833, which corresponds to \( \frac{7}{12} \).
Correct Option: D) \( \frac{7}{12} \)
If angles M and N measure 60° and 30° respectively, sin M × cot N = ?
\( \frac{1}{2} \)
\(\frac{\sqrt{3}}{2}\)
\( \frac{3}{2} \)
0
To solve this problem, we need to recall the standard trigonometric values for common angles like 30° and 60°. We will then substitute these values into the given expression and simplify to find the final result.
Given angles are \(M = 60^\circ\) and \(N = 30^\circ\).
The expression to evaluate is \( \sin M \times \cot N \).
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]
\[ \cot 30^\circ = \sqrt{3} \]
Substitute the values of \( \sin 60^\circ \) and \( \cot 30^\circ \) into the expression \( \sin M \times \cot N \):
\[ \sin 60^\circ \times \cot 30^\circ = \frac{\sqrt{3}}{2} \times \sqrt{3} \]
\[ \frac{\sqrt{3}}{2} \times \sqrt{3} = \frac{\sqrt{3} \times \sqrt{3}}{2} = \frac{3}{2} \]
Thus, \( \sin M \times \cot N = \frac{3}{2} \).
C) \( \frac{3}{2} \) is the correct answer, as derived from the step-by-step calculation.