The question asks to identify the enzyme produced by gastric glands that digests proteins. We need to recall the primary enzymes involved in protein digestion and their sites of production.
A) Pepsin is the enzyme produced by gastric glands that initiates the digestion of proteins into smaller polypeptides in the acidic environment of the stomach.
The question asks for the launch date of the GOBAR-DHAN scheme. This requires factual knowledge about government schemes and their timelines.
Correct Option: D) 30 April 2018
The problem involves finding an unknown number given the HCF (Highest Common Factor), LCM (Least Common Multiple) of two numbers, and one of the numbers. The fundamental relationship between HCF, LCM, and two numbers is that the product of the two numbers is equal to the product of their HCF and LCM.
D) \( 10^{8}7^{3} \) is the other number, which matches our calculated value.
The question asks for the adoption date of the Universal Declaration of Human Rights (UDHR) by the United Nations. This is a factual question requiring knowledge of a specific historical date related to international human rights.
D) 10 December 1948 — The Universal Declaration of Human Rights (UDHR) was indeed adopted by the United Nations General Assembly on 10 December 1948 at the Palais de Chaillot in Paris, France. This date is globally recognized as Human Rights Day.
This is a blood relation problem. We need to establish the relationships between the individuals mentioned in the problem statement step-by-step to determine how F is related to A. We will build a family tree or list out the relationships as we go.
B) Mother. As derived in the step-by-step analysis, F is the mother of A.
The question asks to identify the condition where the eye's power of accommodation decreases with ageing. This is a direct recall question related to common eye defects.
D) presbyopia — This condition is precisely defined as the loss of the eye's power of accommodation due to the natural ageing process, leading to difficulty in focusing on near objects.
If tan θ = \( \frac{b}{a} \), then \(\frac{a\cos\theta+b\sin\theta}{a\cos\theta-b\sin\theta}\) = ______
\(\frac{a^2-b^2}{a^2+b^2}\)
\(\frac{a-b}{a+b}\)
\(\frac{a^2+b^2}{a^2-b^2}\)
\(\frac{a+b}{a-b}\)
The problem provides the value of \(\tan \theta\) and asks us to simplify an expression involving \(\sin \theta\) and \(\cos \theta\). The most straightforward approach is to convert the given expression into terms of \(\tan \theta\) by dividing the numerator and denominator by \(\cos \theta\).
We are given that \(\tan \theta = \frac{b}{a}\).
We need to simplify the expression \[\frac{a\cos\theta+b\sin\theta}{a\cos\theta-b\sin\theta}\].
To introduce \(\tan \theta\) into the expression, we divide every term in the numerator and the denominator by \(\cos \theta\) (assuming \(\cos \theta \neq 0\)).
\[ \frac{\frac{a\cos\theta}{\cos\theta} + \frac{b\sin\theta}{\cos\theta}}{\frac{a\cos\theta}{\cos\theta} - \frac{b\sin\theta}{\cos\theta}} \]Using the identity \(\tan \theta = \frac{\sin \theta}{\cos \theta}\), we get:
\[ \frac{a + b\left(\frac{\sin\theta}{\cos\theta}\right)}{a - b\left(\frac{\sin\theta}{\cos\theta}\right)} = \frac{a + b\tan\theta}{a - b\tan\theta} \]Now, substitute \(\tan \theta = \frac{b}{a}\) into the simplified expression:
\[ \frac{a + b\left(\frac{b}{a}\right)}{a - b\left(\frac{b}{a}\right)} \]Simplify the numerator and the denominator:
\[ \frac{a + \frac{b^2}{a}}{a - \frac{b^2}{a}} \]To combine the terms, find a common denominator for the numerator and the denominator:
\[ \frac{\frac{a^2 + b^2}{a}}{\frac{a^2 - b^2}{a}} \]Multiply the numerator by the reciprocal of the denominator:
\[ \frac{a^2 + b^2}{a} \times \frac{a}{a^2 - b^2} \]Cancel out the common term \(a\):
\[ \frac{a^2 + b^2}{a^2 - b^2} \]Correct Option: C) \(\frac{a^2+b^2}{a^2-b^2}\)
The given sequence is an arithmetic progression (AP) because the difference between consecutive terms is constant. We need to find the tenth term of this AP. We can use the formula for the \(n\)-th term of an AP.
Identify the sequence type: Observe the given sequence: 2, 5, 8, 11, ……
Since the common difference is constant (\(d = 3\)), this is an arithmetic progression.
Identify the first term and common difference:
Recall the formula for the \(n\)-th term of an AP:
The formula for the \(n\)-th term (\(a_n\)) of an arithmetic progression is given by:
Calculate the tenth term (\(a_{10}\)):
We need to find the 10th term, so \(n = 10\). Substitute the values of \(a\), \(d\), and \(n\) into the formula:
B) 29 is the correct answer. The tenth term of the sequence is 29.
The question asks about the primary site for the complete digestion of carbohydrates, proteins, and fats in the human digestive system. To answer this, we need to recall the functions of different organs involved in digestion.
Therefore, the small intestine is where the complete digestion of all three macronutrients occurs.
Correct Option: C) Small intestine is the site where the complete digestion of carbohydrates, proteins, and fats takes place, facilitated by enzymes from the pancreas and the intestinal wall, as well as bile from the liver.
To find the greatest number that divides given numbers and leaves specific remainders, we first subtract the respective remainders from each number. The problem then reduces to finding the HCF (Highest Common Factor) of these new numbers. This HCF will be the greatest number that divides the original numbers, leaving the specified remainders.
Correct Option: A) 6