The question asks about the method of dating fossils by detecting the ratio of different forms of the same element. This technique is known as radiometric dating, which relies on the predictable decay of unstable atomic nuclei.
Correct Option: B) isotopes — Isotopes are atoms of the same element (same number of protons) but with different numbers of neutrons, leading to different atomic masses. Radioactive isotopes decay at a predictable rate, making them suitable for radiometric dating.
To find the sample space for tossing multiple coins, we need to determine the number of possible outcomes for each coin and then multiply these possibilities together. Each coin has two possible outcomes: Heads (H) or Tails (T).
Correct Option: D) 16
This is a blood relation question. We need to trace the relationships step-by-step from Nandini to Vani's paternal grandfather based on the given information.
Therefore, Nandini's only sister's father's father is Vani's paternal grandfather.
Correct Option: D) Paternal grandfather
An object of mass 13 kg is moving with a uniform velocity of 5 ms-1. What is the kinetic energy possessed by the object?
To find the kinetic energy of an object, we use the standard formula for kinetic energy, which relates the object's mass and its velocity. We will substitute the given values into this formula and calculate the result, ensuring the correct units are used.
The kinetic energy (\(KE\)) of an object is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]Substitute \(m = 13 \text{ kg}\) and \(v = 5 \text{ m/s}\) into the formula:
\[ KE = \frac{1}{2} \times 13 \text{ kg} \times (5 \text{ m/s})^2 \]The kinetic energy possessed by the object is \(162.5 \text{ J}\).
Correct Option: C) 162.5 J
This is a statement and assumption question. We need to identify which of the given assumptions is implicitly contained within the statement. An implicit assumption is something that is not directly stated but must be true for the statement to make sense or be valid. We should look for assumptions that are directly related to the core claim of the statement.
Correct Option: D) Only assumption I is implicit. This assumption is implicit because a person's ability to explain complex mathematical problems easily often implies a deep understanding and interest in the subject itself. It's a reasonable underlying condition for such a skill.
The question asks to identify the law associated with the heating effect of electric current. We need to recall the fundamental laws of electricity and their respective phenomena.
Correct Option: A) Joule’s law is directly associated with the heating effect of electric current, quantifying the heat produced in a conductor due to current flow.
The question asks to identify the element whose position in the Modern Periodic Table is anomalous because it can be placed in either Group 1 or Group 17. This anomaly arises from its electronic configuration and chemical properties, which show similarities to both alkali metals (Group 1) and halogens (Group 17).
B) H (Hydrogen) is the element whose position is anomalous in the Modern Periodic Table because it exhibits properties similar to both Group 1 (alkali metals) and Group 17 (halogens). It can lose one electron to form \(\text{H}^+\) or gain one electron to form \(\text{H}^-\text{.}\)
The problem asks us to find the frequency of a wave given its time period. Frequency and time period are inversely related. We will use the formula that connects these two quantities.
The unit for frequency is Hertz (Hz).
Correct Option: A) 25 Hz is the calculated frequency of the wave.
To find the next number in the series, we need to identify the pattern or rule governing the sequence of numbers: 4, 9, 20, 43. We will examine the differences between consecutive terms and look for a multiplicative or additive pattern.
The first term is 4, and the second term is 9.
\[ 4 \times 2 + 1 = 8 + 1 = 9 \]The second term is 9, and the third term is 20.
\[ 9 \times 2 + 2 = 18 + 2 = 20 \]The third term is 20, and the fourth term is 43.
\[ 20 \times 2 + 3 = 40 + 3 = 43 \]From the above steps, we can observe a clear pattern:
So, the general rule for the \(n\)-th term \(T_n\) is \(T_n = T_{n-1} \times 2 + (n-1)\).
The fourth term is 43. Following the pattern, we need to multiply 43 by 2 and then add 4 (since we added 1, 2, and 3 in the previous steps).
\[ 43 \times 2 + 4 = 86 + 4 = 90 \]Correct Option: D) 90
This question tests basic knowledge about common acid-base indicators. Litmus is a well-known natural indicator, and its original color before being exposed to acids or bases is a fundamental property.
Correct Option: D) Purple is the natural color of litmus when it is in a neutral state.