To find the square root of 12996, we can use the long division method or estimate the range of the square root and then check the options. The long division method is precise, while estimation helps narrow down choices quickly.
We know that \(100^2 = 10000\) and \(120^2 = 14400\). Since 12996 is between 10000 and 14400, its square root must be between 100 and 120.
The last digit of 12996 is 6. For a number to have 6 as its last digit when squared, its square root must end in either 4 or 6 (since \(4^2 = 16\) and \(6^2 = 36\)).
We are looking for a number between 100 and 120 that ends in 4 or 6. The options that fit this criteria are 114 and 106 (from the given choices).
Since \(114^2 = 12996\), the square root of 12996 is 114.
D) 114 is the correct answer because \(114 \times 114 = 12996\).
The problem asks for the work done against air resistance. This can be determined by calculating the change in kinetic energy of the bullet, as the work done by non-conservative forces (like air resistance) is equal to the change in mechanical energy. Since the bullet starts and ends at the same level, there is no change in potential energy. Therefore, the work done against air resistance is equal to the loss in kinetic energy.
Since the velocities are in m/s, we should convert the mass to kilograms for consistency with SI units (Joules).
\[ m = 10 \text{ g} = 10 \times 10^{-3} \text{ kg} = 0.01 \text{ kg} \]The formula for kinetic energy is \(KE = \frac{1}{2}mv^2\).
\[ KE_i = \frac{1}{2} m v_i^2 = \frac{1}{2} (0.01 \text{ kg}) (1000 \text{ m/s})^2 \]\[ KE_i = \frac{1}{2} (0.01) (1,000,000) = 0.005 \times 1,000,000 = 5000 \text{ J} \]The work done against air resistance (\(W_{\text{air}}\)) is equal to the loss in kinetic energy, as potential energy change is zero.
\[ W_{\text{air}} = KE_i - KE_f \]\[ W_{\text{air}} = 5000 \text{ J} - 1250 \text{ J} = 3750 \text{ J} \]D) 3750
What will come in the place of the question mark ‘?’ in the following question?
76 ÷ 19 × 2 - 6 = _____?
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This rule dictates the sequence for performing mathematical operations: Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, and Subtraction. When division and multiplication (or addition and subtraction) appear together, they should be performed from left to right.
Correct Option: B) 2 is the correct answer.
This problem involves understanding cardinal directions and their opposites. When two people are running in exactly opposite directions, the direction of one person will be the exact opposite of the other person's direction.
Correct Option: C) South - East
This is a logical reasoning question where we need to determine which conclusions logically follow from the given statement. We must only use the information provided in the statement and avoid making assumptions or bringing in outside knowledge.
Correct Option: B) Neither (I) nor (II) follows.
Which of the following is not a homologous series?
To identify which option is not part of a homologous series, we need to understand the definition of a homologous series. A homologous series is a series of organic compounds with the same functional group but with each successive member differing by a \(\text{CH}_2\) group. This means they share a general formula.
Correct Option: C) \(\text{C}_4\text{H}_9\) is not a complete, stable organic compound that fits into the alkane homologous series. It represents an alkyl radical.
This problem involves substituting given symbol meanings into a mathematical expression and then evaluating it using the correct order of operations (BODMAS/PEMDAS).
The value of the expression is 155.
Correct Option: A) 155
The question asks for the Chairman of the State Bank of India (SBI) as of 2021. This is a factual question requiring knowledge of current affairs and important appointments in the banking sector.
Dinesh Kumar Khara was appointed as the Chairman of the State Bank of India on October 7, 2020, and continued in this role throughout 2021. Therefore, he was the Chairman of SBI as of 2021.
B) Dinesh Kumar Khara — Dinesh Kumar Khara assumed office as the Chairman of the State Bank of India on October 7, 2020, and was serving in this capacity throughout 2021.
The question asks to identify the tissue responsible for transporting food in plants. This is a fundamental concept in plant anatomy and physiology, specifically related to vascular tissues.
Correct Option: C) Phloem is the vascular tissue in plants responsible for transporting food, primarily sugars produced during photosynthesis, from the leaves to other parts of the plant where it is needed for energy or storage. This process is known as translocation.
This problem involves setting up a system of linear equations based on the given relationships between the ages of A, B, C, and D. We will define variables for each person's age and then solve for the age of A.
Define variables for the ages:
Formulate equations based on the given information:
Solve the system of equations:
Our goal is to find \(A\). We can express all variables in terms of \(A\).
Verify the ages (optional but good practice):
Correct Option: D) 26 years