The question asks for the chemical formula of bleaching powder. We need to identify the correct chemical representation among the given options.
Correct Option: B) \( \text{CaOCl}_2 \)
This is the correct chemical formula for bleaching powder (Calcium Oxychloride).
This question tests the fundamental rules of ray tracing for a convex lens. Understanding how parallel rays behave after refraction through a convex lens is crucial for comprehending image formation.
Correct Option: D) Principal focus
To determine the molecular formula of the second member of the alkene series, we need to understand the general formula for alkenes and identify the first few members of the series.
Therefore, the second member of the alkene series is Propene, with the molecular formula \(C_3H_6\).
Correct Option: A) C₃H₆ is the molecular formula for propene, which is the second member of the alkene series.
To find the ratio of marks obtained by A and C, we need to combine the given ratios of A:B and B:C. We can do this by making the common term (B) equal in both ratios.
In the first ratio, B is 4. In the second ratio, B is 2. To make them equal, we find the Least Common Multiple (LCM) of 4 and 2, which is 4.
Now we have:
Since the value of B is the same in both (4), we can combine them to get the ratio \(A:B:C = 3:4:2\).
From the combined ratio \(A:B:C = 3:4:2\), the ratio of A and C is \(A:C = 3:2\).
Correct Option: C) 3 : 2
A light ray travels from air into an optical fibre with an index of refraction of 1.45. If the angle of incidence on the end of the fibre is 22°, the angle of refraction inside the fibre is:
This problem involves the refraction of light as it passes from one medium (air) to another (optical fibre). We can use Snell's Law to determine the angle of refraction. Snell's Law relates the refractive indices of the two media and the angles of incidence and refraction.
Snell's Law is given by the formula:
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]Using a calculator, \(\sin(22^\circ) \approx 0.3746\).
One-third of a certain journey is covered at a speed of 25 km/h, one-fourth of the journey is covered at a speed of 30 km/h and the rest of the journey is covered at 50 km/h. The average speed (in km/h) of the whole journey is:
To find the average speed for the entire journey, we need to calculate the total distance traveled and the total time taken. The average speed is then the total distance divided by the total time. Since the total distance is not given, we can assume a convenient total distance, or represent it with a variable, say \(D\).
Let the total distance of the journey be \(D\) km.
First part of the journey:
Second part of the journey:
Third part of the journey (the rest):
Total time taken for the journey:
\[ T = t_1 + t_2 + t_3 = \frac{D}{75} + \frac{D}{120} + \frac{D}{120} \]
Find the least common multiple (LCM) of 75 and 120. The LCM of 75 (\(3 \times 5^2\)) and 120 (\(2^3 \times 3 \times 5\)) is \(2^3 \times 3 \times 5^2 = 8 \times 3 \times 25 = 600\).
\[ T = \frac{8D}{600} + \frac{5D}{600} + \frac{5D}{600} = \frac{(8+5+5)D}{600} = \frac{18D}{600} = \frac{3D}{100} \] hours.
Average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{\frac{3D}{100}} \]
\[ \text{Average Speed} = D \times \frac{100}{3D} = \frac{100}{3} \] km/h.
Convert the improper fraction to a mixed number:
\[ \frac{100}{3} = 33 \frac{1}{3} \] km/h.
C) 33\( \frac{1}{3} \)
Study the given letter, number, symbol series and answer the question that follows.
(Left) T ? L % 4 M 2 # B N @ 8 K # B 6 L * 3 P (Right)
How many such numbers are there that are immediately preceded by a symbol and also immediately followed by a letter?
The problem asks us to identify numbers in a given series that are immediately preceded by a symbol and immediately followed by a letter. We need to scan the series and apply this condition to each number.
Correct Option: A) 3
The question asks to identify the festival that is NOT celebrated in January every year. This requires knowledge of the approximate celebration dates of the listed Indian festivals.
B) Onam is the festival that is NOT celebrated in January every year. It is typically celebrated in August or September.
Amongst six people, D, E, F, G, H, and I, each has a different age. They are standing in a line according to their age in an increasing order. F is older than E but younger than D. D is younger than I. E is older than G. G is older than H. Who comes in the 4th position in increasing order of age?
We need to determine the relative ages of six people (D, E, F, G, H, I) and arrange them in increasing order of age. We will use the given clues to establish inequalities and then combine them to form a complete sequence.
This can be written as: \(E < F < D\)
Combining with the previous clue: \(E < F < D < I\)
This means \(G < E\). Combining with the sequence: \(G < E < F < D < I\)
This means \(H < G\). Combining with the sequence: \(H < G < E < F < D < I\)
The complete order of age in increasing order is: \(H < G < E < F < D < I\)
In this sequence:
Therefore, F comes in the 4th position.
Correct Option: A) F
Simplify:
\(\left(\frac{1}{512}\right)^{-\frac{2}{3}}\div\left(\frac{1}{64}\right)^{-\frac{4}{3}}\)
\(\frac{2}{3}\)
\(\frac{3}{4}\)
\(\frac{1}{4}\)
\(\frac{1}{6}\)
To simplify the given expression, we will use the properties of exponents, specifically the rules for negative exponents and fractional exponents. We will express the bases as powers of 2, then apply the exponent rules \((a^m)^n = a^{mn}\) and \(a^{-n} = \frac{1}{a^n}\) or \(\left(\frac{1}{a}\right)^{-n} = a^n\).
C) \(\frac{1}{4}\) is the simplified value of the given expression.