The question asks for the substance responsible for the green color of leaves. This is a fundamental concept in biology, specifically related to plant physiology and photosynthesis.
A) Chlorophyll is the primary pigment found in the chloroplasts of plant cells. It is essential for photosynthesis and is responsible for absorbing light energy, particularly in the red and blue parts of the spectrum, while reflecting green light, which gives leaves their characteristic green color.
The given series is an alternating series, meaning there are two interleaved patterns. We need to identify these two patterns to find the next number in the sequence.
Thus, the complete series is \(9, 12, 10, 13, 11, 14\).
D) 14 is the correct answer because it follows the established alternating pattern where numbers at even positions increase by 1.
The question asks to identify the successor of Dr. Rajendra Prasad as the President of India. This requires knowledge of the chronological order of Indian Presidents.
Correct Option: C) S. Radhakrishnan was the second President of India, succeeding Dr. Rajendra Prasad.
To determine the IUPAC name of an alkane, we need to identify the longest continuous carbon chain and count the number of carbon atoms in it. The prefix for the name is derived from this count, and the suffix for alkanes is "-ane".
D) Propane is the correct IUPAC name for \(\text{CH}_3 \text{CH}_2 \text{CH}_3\) because it has three carbon atoms and is an alkane.
If cos² x + sin x = \( \frac{5}{4} \), then find the value of 'sin x'.
\( \frac{3}{2} \)
\( \frac{-1}{2} \)
\( \frac{3}{4} \)
\( \frac{1}{2} \)
The problem requires finding the value of 'sin x' given a trigonometric equation involving both cos² x and sin x. The key is to use the fundamental trigonometric identity \(\cos^2 x + \sin^2 x = 1\) to express the entire equation in terms of 'sin x' only. This will result in a quadratic equation in 'sin x', which can then be solved for 'sin x'.
Rewrite the given equation:
We are given the equation:
\[ \cos^2 x + \sin x = \frac{5}{4} \]We know the fundamental trigonometric identity:
\[ \cos^2 x + \sin^2 x = 1 \]From this, we can express \(\cos^2 x\) in terms of \(\sin^2 x\):
\[ \cos^2 x = 1 - \sin^2 x \]Substitute into the original equation:
Substitute \(1 - \sin^2 x\) for \(\cos^2 x\) in the given equation:
\[ (1 - \sin^2 x) + \sin x = \frac{5}{4} \]Rearrange into a quadratic equation:
Move all terms to one side to form a standard quadratic equation. Let \(y = \sin x\) for simplicity:
\[ 1 - y^2 + y = \frac{5}{4} \]Multiply by 4 to clear the fraction:
\[ 4(1 - y^2 + y) = 5 \]\[ 4 - 4y^2 + 4y = 5 \]Rearrange the terms to the standard quadratic form \(ay^2 + by + c = 0\):
\[ 4y^2 - 4y + 5 - 4 = 0 \]\[ 4y^2 - 4y + 1 = 0 \]Solve the quadratic equation:
This is a perfect square trinomial:
\[ (2y - 1)^2 = 0 \]Take the square root of both sides:
\[ 2y - 1 = 0 \]\[ 2y = 1 \]\[ y = \frac{1}{2} \]Substitute back for 'sin x':
Since we let \(y = \sin x\), we have:
\[ \sin x = \frac{1}{2} \]D) \( \frac{1}{2} \)
The value of \(\sin x\) obtained from solving the quadratic equation is \(\frac{1}{2}\).
To compare the efficiencies of P, Q, and R, we need to understand that efficiency is inversely proportional to the time taken to complete a job. If someone takes less time, they are more efficient. We can find the work done per day for each person and then express these rates as a ratio.
If P takes 18 days to complete a job, P's work per day is \(\frac{1}{18}\) of the job.
If Q takes 15 days to complete a job, Q's work per day is \(\frac{1}{15}\) of the job.
If R takes 10 days to complete a job, R's work per day is \(\frac{1}{10}\) of the job.
The ratio of their efficiencies (work done per day) is:
\[ \text{Efficiency of P} : \text{Efficiency of Q} : \text{Efficiency of R} = \frac{1}{18} : \frac{1}{15} : \frac{1}{10} \]The least common multiple (LCM) of 18, 15, and 10 is 90.
Multiply each fraction by the LCM (90) to convert them into whole numbers:
\[ \frac{1}{18} \times 90 = 5 \] \[ \frac{1}{15} \times 90 = 6 \] \[ \frac{1}{10} \times 90 = 9 \]The ratio of their efficiencies is \(5 : 6 : 9\).
Correct Option: D) 5 : 6 : 9
The question asks to identify the color of white light that has the maximum wavelength. This relates to the dispersion of white light into its constituent colors, commonly remembered by the acronym VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
Correct Option: B) Red
Red light has the longest wavelength in the visible spectrum, typically ranging from approximately 620 nm to 750 nm.
The question asks to identify the type of naval vessel 'INS Vikramaditya'. This requires knowledge of prominent Indian naval assets.
A) Aircraft carrier - 'INS Vikramaditya' is indeed an aircraft carrier, serving as a flagship of the Indian Navy. It is a modified Kiev-class aircraft carrier, originally built for the Soviet Navy as 'Baku' and later serving the Russian Navy as 'Admiral Gorshkov' before being acquired and extensively refitted by India.
The problem involves properties of remainders in division. We are given the remainder when a natural number 'n' is divided by 4. We need to find the remainder of an expression involving 'n' when divided by the same number. We can use the definition of division with remainder or substitute a specific value for 'n' that satisfies the given condition.
Alternative Method (using a specific value for n):
A) 1 — As shown by both methods, the remainder when \((2n + 3)\) is divided by 4 is 1.
The question asks to identify which of the given options is NOT an infectious disease. An infectious disease is caused by pathogenic microorganisms, such as bacteria, viruses, fungi, or parasites, and can be spread, directly or indirectly, from one person to another. Non-infectious diseases, also known as non-communicable diseases (NCDs), are not caused by pathogens and cannot be spread from person to person. They are often chronic and result from a combination of genetic, physiological, environmental, and behavioral factors.
Correct Option: A) Diabetes is a non-infectious disease. It is a chronic metabolic disorder where the body either doesn't produce enough insulin or can't effectively use the insulin it produces, leading to high blood glucose levels. It is not caused by a pathogen and cannot be transmitted from person to person.