The question asks to identify the type of pathogen that causes Kala-azar. This requires knowledge of common diseases and their causative agents.
A) Protozoa
Kala-azar is caused by the protozoan parasite Leishmania donovani (or other Leishmania species), which is transmitted by the bite of infected sandflies. Therefore, protozoa are the correct causative agents.
The problem asks us to identify the odd one out from four given letter-clusters. We need to find a common pattern or rule that applies to three of the clusters and identify the cluster that does not follow this rule.
Options A, B, and C follow a consistent pattern where each subsequent letter is obtained by adding 2 to the alphabetical position of the previous letter. Option D does not follow this pattern.
Correct Option: D) JLMP
This problem involves calculating the combined work rate of two individuals to determine the time taken to complete a task together. We will use the concept of work and time, where the amount of work done per day (rate) is the reciprocal of the total time taken to complete the work.
Correct Option: D) 12 days
To find the area of a triangle given its three side lengths, we can first check if it's a right-angled triangle. If it is, the area can be calculated using the formula \(\frac{1}{2} \times \text{base} \times \text{height}\). If not, Heron's formula can be used. In this case, the side lengths (3 cm, 4 cm, 5 cm) form a Pythagorean triplet, indicating it's a right-angled triangle.
B) The area of the triangle is 6 cm², as calculated using the formula for a right-angled triangle.
If \(\frac{\cos A}{1-\sin A}+\frac{\cos A}{1+\sin A}\) = 4, then what will be the value of A?
To find the value of A, we need to simplify the given trigonometric expression by combining the fractions and then solve the resulting equation for A. We will use algebraic manipulation and fundamental trigonometric identities.
The given equation is:
\[ \frac{\cos A}{1-\sin A} + \frac{\cos A}{1+\sin A} = 4 \]Combine the fractions on the left-hand side by finding a common denominator:
\[ \frac{\cos A (1+\sin A) + \cos A (1-\sin A)}{(1-\sin A)(1+\sin A)} = 4 \]Expand the numerator:
\[ \frac{\cos A + \cos A \sin A + \cos A - \cos A \sin A}{1-\sin^2 A} = 4 \]Simplify the numerator and use the identity \(1-\sin^2 A = \cos^2 A\) in the denominator:
\[ \frac{2\cos A}{\cos^2 A} = 4 \]Cancel out one \(\cos A\) term (assuming \(\cos A \neq 0\)):
\[ \frac{2}{\cos A} = 4 \]Solve for \(\cos A\):
\[ \cos A = \frac{2}{4} \] \[ \cos A = \frac{1}{2} \]Find the angle A for which \(\cos A = \frac{1}{2}\). We know that \(\cos 60^\circ = \frac{1}{2}\).
Therefore, \(A = 60^\circ\).
Correct Option: B) 60°
This question asks to identify the cell organelle that is exclusively found in plant cells. To answer this, we need to recall the distinguishing features between plant and animal cells.
Correct Option: C) Plastids are organelles found exclusively in plant cells and some protists (like algae). They are involved in various functions, including photosynthesis (chloroplasts), pigment storage (chromoplasts), and food storage (leucoplasts).
The value of (\(\frac{\sin29^\circ}{\cos61^\circ}\) - 4(cos²31° + cos²59°) + (\(\frac{1}{\sqrt{3}}\))tan27° sin60° tan63°) is:
The problem requires evaluating a trigonometric expression. We will use complementary angle identities, specifically \(\sin(90^\circ - \theta) = \cos\theta\), \(\cos(90^\circ - \theta) = \sin\theta\), and \(\tan(90^\circ - \theta) = \cot\theta\), along with the identity \(\cos^2\theta + \sin^2\theta = 1\) and \(\tan\theta \cdot \cot\theta = 1\). We will also use standard trigonometric values for specific angles like \(\sin60^\circ\).
Evaluate the first term:
The first term is \(\frac{\sin29^\circ}{\cos61^\circ}\).
Since \(29^\circ + 61^\circ = 90^\circ\), we can write \(\sin29^\circ = \sin(90^\circ - 61^\circ) = \cos61^\circ\).
So, \[\frac{\sin29^\circ}{\cos61^\circ} = \frac{\cos61^\circ}{\cos61^\circ} = 1\].
Evaluate the second term:
The second term is \(-4(\cos^231^\circ + \cos^259^\circ)\).
Since \(31^\circ + 59^\circ = 90^\circ\), we can write \(\cos59^\circ = \cos(90^\circ - 31^\circ) = \sin31^\circ\).
Therefore, \(\cos^259^\circ = \sin^231^\circ\).
Substituting this into the expression:
\[ -4(\cos^231^\circ + \sin^231^\circ) \]Using the identity \(\cos^2\theta + \sin^2\theta = 1\):
\[ -4(1) = -4 \]Evaluate the third term:
The third term is \[(\frac{1}{\sqrt{3}})\tan27^\circ \sin60^\circ \tan63^\circ\].
We know that \(\sin60^\circ = \frac{\sqrt{3}}{2}\).
Also, since \(27^\circ + 63^\circ = 90^\circ\), we can write \(\tan63^\circ = \tan(90^\circ - 27^\circ) = \cot27^\circ\).
Substituting these values into the expression:
\[ \left(\frac{1}{\sqrt{3}}\right) \tan27^\circ \left(\frac{\sqrt{3}}{2}\right) \cot27^\circ \]Rearranging the terms:
\[ \left(\frac{1}{\sqrt{3}}\right) \left(\frac{\sqrt{3}}{2}\right) (\tan27^\circ \cot27^\circ) \]Using the identity \(\tan\theta \cdot \cot\theta = 1\):
\[ \left(\frac{1}{2}\right) (1) = \frac{1}{2} \]Combine all terms:
Now, add the results from steps 1, 2, and 3:
\[ 1 - 4 + \frac{1}{2} \] \[ -3 + \frac{1}{2} \]To combine, find a common denominator:
\[ \frac{-3 \cdot 2}{2} + \frac{1}{2} = \frac{-6}{2} + \frac{1}{2} = \frac{-6 + 1}{2} = \frac{-5}{2} \]A) \(-\frac{5}{2}\) is the correct value obtained after evaluating the expression.
The question asks for the founding year of PETA India. This requires factual knowledge about the organization's history.
Correct Option: A) 2000
The question asks to identify an animal hormone from the given options. Hormones are chemical messengers that regulate various physiological processes in living organisms. It's important to distinguish between plant hormones (phytohormones) and animal hormones.
Correct Option: C) Insulin is a peptide hormone produced by the beta cells of the pancreatic islets. It plays a crucial role in regulating carbohydrate and fat metabolism in the body, primarily by facilitating the absorption of glucose from the blood into liver, fat, and skeletal muscle cells.
What will be 41 \( \frac{2}{3} \) % of ₹84?
To find a percentage of a given amount, first convert the mixed fraction percentage into an improper fraction, then convert it to a decimal or a simple fraction. Finally, multiply this fraction or decimal by the given amount.
Convert the mixed fraction percentage to an improper fraction:
The given percentage is \(41 \frac{2}{3} \%\). First, convert the mixed fraction to an improper fraction:
\[ 41 \frac{2}{3} = \frac{(41 \times 3) + 2}{3} = \frac{123 + 2}{3} = \frac{125}{3} \]Convert the percentage to a fraction:
To convert a percentage to a fraction, divide it by 100:
\[ \frac{125}{3} \% = \frac{125}{3 \times 100} = \frac{125}{300} \]Simplify the fraction:
Both the numerator and the denominator are divisible by 25:
\[ \frac{125 \div 25}{300 \div 25} = \frac{5}{12} \]Calculate the percentage of ₹84:
Now, multiply this fraction by ₹84:
\[ \text{Amount} = \frac{5}{12} \times 84 \]Perform the multiplication:
Divide 84 by 12, which is 7:
\[ \text{Amount} = 5 \times 7 = 35 \]So, \(41 \frac{2}{3} \%\) of ₹84 is ₹35.
Correct Option: D) ₹35