To determine the direction of Yogesh's home from his sister's home, we need to trace his path and find the net displacement. We can represent his movements on a coordinate plane or by summing up the total distance traveled in each cardinal direction (North, South, East, West).
A) South-west. Based on the step-by-step analysis, Yogesh's home is located to the South-west of his sister's home.
The question asks about the primary purpose of establishing protected areas. We need to identify the most comprehensive and overarching goal among the given options.
Correct Option: D) Conserve the natural ecosystem
If the volume of a cube is 512 cm³, then the measure of the main diagonal of the cube will be:
7\(\sqrt{3}\) cm
14\(\sqrt{3}\) cm
17\(\sqrt{3}\) cm
8\(\sqrt{3}\) cm
To find the main diagonal of a cube, we first need to determine the side length of the cube. This can be found using the given volume of the cube. Once the side length is known, we can apply the formula for the main diagonal of a cube.
Find the side length of the cube:
The formula for the volume of a cube is \(V = a^3\), where \(a\) is the side length of the cube.
Given the volume \(V = 512 \text{ cm}^3\).
So, we have:
\[ a^3 = 512 \]To find \(a\), we take the cube root of 512:
\[ a = \sqrt[3]{512} \]We know that \(8 \times 8 \times 8 = 64 \times 8 = 512\).
Therefore, the side length \(a = 8 \text{ cm}\).
Find the measure of the main diagonal of the cube:
The formula for the main diagonal (space diagonal) of a cube with side length \(a\) is \(d = a\sqrt{3}\).
Substitute the value of \(a = 8 \text{ cm}\) into the formula:
\[ d = 8\sqrt{3} \text{ cm} \]Correct Option: D) \(8\sqrt{3}\) cm
This problem involves arranging six friends (A, B, C, D, E, F) based on their heights using the given comparative statements. We will build a height order step-by-step, from tallest to shortest, to identify the third tallest person.
Correct Option: D) E
The question asks to identify the FALSE statement regarding blood circulation in fishes. We need to analyze each option based on the known facts about the circulatory system of fish.
C) The two-chambered heart provides double circulation. — This statement is false. Fish have a single circulatory system where blood passes through the heart only once per circuit. Double circulation involves two separate circuits (pulmonary and systemic) and requires a more complex heart (typically three or four chambers).
To determine which number is divisible by 2, 3, and 5, we need to apply the divisibility rules for each of these numbers. A number is divisible by 2 if its last digit is even. A number is divisible by 5 if its last digit is 0 or 5. A number is divisible by 3 if the sum of its digits is divisible by 3. We will check each option against these rules.
Correct Option: A) 3150 is divisible by 2 (ends in 0), by 5 (ends in 0), and by 3 (sum of digits \(3+1+5+0=9\) is divisible by 3).
This question tests the fundamental definition and characteristics of a concave mirror. Understanding the shape of a concave mirror and its relationship to the center of curvature is key to answering this question.
Correct Option: D) depression, opposite to
If x − \( \frac{1}{x} \) = 6, then the value of x³ − \( \frac{1}{x^3} \) is:
The problem requires us to find the value of \(x^3 - \frac{1}{x^3}\) given \(x - \frac{1}{x} = 6\). We can use the algebraic identity for the difference of cubes, \((a-b)^3 = a^3 - b^3 - 3ab(a-b)\), or rearrange it to find \(a^3 - b^3\).
B) 234
Refer to the following letter and number series and answer the question.
(Left) G C T 7 D 4 6 K 2 R Y 3 5 E S A 4 T Y 7 8 G T (Right)
How many such letters are there in the series which are immediately preceded by a letter and also immediately followed by a number?
The problem asks us to identify letters in a given series that satisfy two conditions: they must be immediately preceded by a letter and immediately followed by a number. We will scan the series from left to right, looking for sequences that match the pattern "Letter - Letter - Number".
A) Four. There are four instances where a letter is immediately preceded by a letter and immediately followed by a number: C T 7, R Y 3, S A 4, and T Y 7.
Each of Prem, Amit, Ram, Sudheer, Tejas, Uma and Vivek has an exam on a different day of a week, starting from Monday and ending on Sunday of the same week. Prem has the exam on Thursday. Only one person has the exam between Prem and Uma. Ram has the exam on the day immediately before Uma but not on a Monday. Only two people have exams between Ram and Tejas. Vivek’s exam is on one of the days before Sudheer and on one of the days after Amit. Who among the following has the exam on Monday?