Pick the figure that will complete the given series.
Problem Figures:
Answer Figures:
The problem involves identifying a pattern in a series of figures and selecting the figure that logically completes the sequence.
The correct figure should have a square inside a circle, which matches option B.
Correct Option: B) A square inside a circle.
To solve this problem, we need to calculate the total marks Suvir obtained in all 15 tests. Then, we calculate the total marks Ruchira has obtained so far in 11 tests. To match Suvir's performance, Ruchira must achieve the same total marks over 15 tests. We can then find the remaining marks Ruchira needs and divide by the number of remaining tests to find the required average score.
C) 34.5
The question asks for the number of sons X has. We need to determine if the given statements, individually or together, provide enough information to answer this specific question. We will analyze each statement separately and then combine them.
B) Neither 1 nor 2 alone is sufficient
As established, neither statement individually nor both statements combined provide any information about X or the number of sons X has. The question cannot be answered from the given information.
Find the next figure for the given series:
Problem Figures:
Answer Figures:
The problem involves identifying the pattern in a series of figures and determining the next figure in the sequence. Each figure contains two letters separated by a horizontal line, and the letters seem to follow a specific pattern.
Correct Option: D) L over mirrored L
The above Venn diagram represents the students who play 3 sports M, N and L in a class. Total number of students who play game M is:
The Venn diagram represents students who play sports M, N, and L. To find the total number of students who play sport M, we need to sum all the numbers in the circle labeled M, including those who play multiple sports.
Correct Option: C) 32
Which of the following statements is/are true?
A. Solid CO2 is known as dry ice.
B. The particles of liquid absorb energy from the surrounding to regain the energy lost during evaporation.
C. Solid CO2 gets converted directly to the gaseous state.
All are false
A and C are false, B is true
A and C are true, B is false
All are true
The question asks to identify the true statements among the given options regarding states of matter and related phenomena. We will evaluate each statement individually based on fundamental scientific principles.
Solid carbon dioxide (\(\text{CO}_2\)) is indeed commonly known as dry ice. It is called "dry" ice because it does not melt into a liquid when heated; instead, it sublimes directly into a gas. This property makes it useful for refrigeration where liquid water would be undesirable.
Evaporation is a surface phenomenon where liquid particles with sufficient kinetic energy escape into the gaseous state. When these high-energy particles leave the liquid, the average kinetic energy of the remaining liquid particles decreases, leading to a drop in temperature. To maintain thermal equilibrium or continue evaporation, the remaining liquid particles absorb energy (heat) from the surroundings. This absorption of energy helps them regain the lost kinetic energy and allows more particles to evaporate, which is why evaporation causes cooling.
As mentioned in the evaluation of Statement A, solid carbon dioxide (dry ice) undergoes sublimation. Sublimation is the process where a substance changes directly from a solid to a gas without passing through the liquid phase. This occurs at atmospheric pressure for dry ice.
D) All are true
Based on the evaluation:
Since all three statements are correct, option D is the correct answer.
To find the Selling Price (SP) when the Marked Price (MP) and discount percentage are given, we first calculate the discount amount. The discount is always calculated on the Marked Price. Once the discount amount is found, we subtract it from the Marked Price to get the Selling Price.
The discount amount is 12% of the Marked Price.
\[ \text{Discount Amount} = \frac{\text{Discount Percentage}}{100} \times \text{MP} \]\[ \text{Discount Amount} = \frac{12}{100} \times 160 \]\[ \text{Discount Amount} = 0.12 \times 160 \]\[ \text{Discount Amount} = 19.2 \]The Selling Price is the Marked Price minus the Discount Amount.
\[ \text{SP} = \text{MP} - \text{Discount Amount} \]\[ \text{SP} = 160 - 19.2 \]\[ \text{SP} = 140.8 \]Correct Option: A) 140.8
What are the roots of the equation 2x2 + 4x = 30?
To find the roots of a quadratic equation, we first need to rearrange it into the standard form \(ax^2 + bx + c = 0\). Then, we can solve it using factorization, completing the square, or the quadratic formula. In this case, factorization will be a straightforward method after simplification.
Rearrange the equation into standard form:
The given equation is \(2x^2 + 4x = 30\).
Subtract 30 from both sides to get it into the standard form \(ax^2 + bx + c = 0\):
Simplify the equation:
Notice that all coefficients are divisible by 2. Divide the entire equation by 2 to simplify:
\[ \frac{2x^2}{2} + \frac{4x}{2} - \frac{30}{2} = \frac{0}{2} \]\[ x^2 + 2x - 15 = 0 \]Factorize the quadratic equation:
We need to find two numbers that multiply to \(-15\) and add up to \(2\). These numbers are \(5\) and \(-3\).
So, we can factor the quadratic equation as:
\[ (x + 5)(x - 3) = 0 \]Find the roots:
For the product of two factors to be zero, at least one of the factors must be zero.
Thus, the roots of the equation are \(-5\) and \(3\).
Correct Option: C) −5, 3
The problem presents a series of letter sets, and we need to find the next set by identifying the pattern. We will analyze the pattern for the first letter and the second letter in each set separately.
The pattern for the first letter is an incrementing addition: +2, then +3. Following this pattern, the next increment should be +4.
So, the first letter of the next set is L.
The pattern for the second letter is an incrementing subtraction: -2, then -3. Following this pattern, the next subtraction should be -4.
So, the second letter of the next set is M.
The next letter set is LM.
A) LM — This matches our derived pattern where the first letter follows a +2, +3, +4 sequence and the second letter follows a -2, -3, -4 sequence.
Find the odd figure out from among the given figures.
The task is to identify the figure that is different from the others based on a common characteristic shared by the majority.
Correct Option: D) The figure with a single dot inside a circle is the odd one out.