The problem presents a series of three-letter words, and we need to find the next word in the sequence. This type of problem usually involves identifying a pattern based on the alphabetical positions of the letters.
D) OLD — The first letters of the series are A, E, I. These are the first three vowels in alphabetical order. Following this pattern, the next vowel is O. Among the given options, only 'OLD' starts with 'O'.
Solve the following:
-\( \frac{1}{4} \){-45-(-96) ÷ (-32)} = ?
To solve this problem, we need to follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). We will simplify the expression inside the curly braces first, then perform the multiplication.
First, simplify the expression inside the curly braces: \({-45-(-96) \div (-32)}\).
Inside the curly braces, we have subtraction and division. According to the order of operations, division comes before subtraction. So, calculate \({(-96) \div (-32)}\).
When dividing two negative numbers, the result is positive.
\[ (-96) \div (-32) = 3 \]Now substitute this value back into the expression inside the curly braces:
\[ -45 - (3) = -45 - 3 = -48 \]Now, substitute this result back into the original equation:
\[ -\frac{1}{4} \times (-48) \]Multiply \({-\frac{1}{4}}\) by \({-48}\).
When multiplying two negative numbers, the result is positive.
\[ -\frac{1}{4} \times (-48) = \frac{48}{4} = 12 \]D) The final calculated value is 12.
This problem involves setting up a system of two linear equations based on the given age relationships and then solving for the unknown ages. We will use variables to represent the current ages and translate the word problem into algebraic expressions.
C) 50
This is an analogy-based question where we need to identify the relationship between the first pair of words and then apply the same relationship to the second pair to find the missing word.
Therefore, 'Closet' is the correct answer as it represents the storage place for clothes, just as a refrigerator is the storage place for food.
Correct Option: B) Closet — A refrigerator is used to store food. Similarly, a closet is used to store clothes.
To find the kinetic energy of the body after 2 seconds, we first need to determine its velocity at that time. We can use the equations of motion under constant acceleration (due to gravity) to find the final velocity. Once the velocity is known, the kinetic energy can be calculated using the formula \(KE = \frac{1}{2}mv^2\).
We use the first equation of motion:
\[ v = u + at \]\[ v = 20 \text{ m/s} + (-10 \text{ m/s}^2) \times (2 \text{ s}) \]\[ v = 20 \text{ m/s} - 20 \text{ m/s} \]\[ v = 0 \text{ m/s} \]The kinetic energy is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]\[ KE = \frac{1}{2} \times (2 \text{ kg}) \times (0 \text{ m/s})^2 \]\[ KE = 0 \text{ J} \]The velocity of the body becomes 0 m/s after 2 seconds, which means it momentarily stops at its highest point before falling back down. Therefore, its kinetic energy at this instant is 0 J.
Correct Option: C) 0 J
How many triangles are present in the following figure?
To determine the total number of triangles in the given figure, we need to systematically count all possible triangles formed by the intersecting lines and shapes.
Let's break down the figure:
Adding these, we have:
Correct Option: C) 14
To find the simple rate of interest per annum, we use the simple interest formula. We are given the principal amount, the interest earned, and the time period. The key is to ensure the time period is expressed in years when calculating the annual rate.
Since the interest rate is required per annum, the time must be in years. There are 12 months in a year.
\[ T = \frac{3 \text{ months}}{12 \text{ months/year}} = \frac{1}{4} \text{ year} \]Where \(R\) is the rate of interest per annum.
Correct Option: A) 9.6%
This question asks us to identify implicit assumptions behind the argument: "Public smoking is an offence under the law." An implicit assumption is something that must be true for the argument to hold, but is not explicitly stated. We need to evaluate each given assumption in this context.
Correct Option: C) Only assumption 2 is implicit
The given Venn diagram represents the students who can speak different languages. According to it, the total number of students who can speak exactly two languages is ______.
To determine the number of students who can speak exactly two languages, we need to analyze the regions of the Venn diagram that represent intersections between two circles only.
Correct Option: D) L + M + O
The question asks to identify the recipient of the Hridaynath Mangeshkar Award in 2017. This requires knowledge of specific awards and their recipients in a given year, which is a common type of general knowledge question in competitive exams.
Correct Option: D) Javed Akhtar was indeed the recipient of the Hridaynath Mangeshkar Award in 2017 for his significant contributions to Indian cinema as a lyricist, poet, and screenwriter.