The problem describes the relationship between the three angles of a triangle. We know that the sum of angles in any triangle is 180°. By setting up an equation based on the given relationships and this property, we can find the measure of each angle and then identify the greatest one.
Define the smallest angle: Let the smallest angle of the triangle be \(x\).
Define the other angles:
Apply the angle sum property: The sum of the angles in a triangle is \(180^\circ\).
So, we can write the equation:
\[ x + 2x + 3x = 180^\circ \]Solve for \(x\):
\[ 6x = 180^\circ \] \[ x = \frac{180^\circ}{6} \] \[ x = 30^\circ \]Calculate each angle:
Identify the greatest angle: Comparing the three angles (\(30^\circ\), \(60^\circ\), \(90^\circ\)), the greatest angle is \(90^\circ\).
A) 90° is the greatest angle, as calculated from the given conditions.
What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and also ‘×’ and ‘÷’ are interchanged?
12 × 6 ÷ 9 − 3 + 2 =?
The problem requires us to evaluate a given mathematical expression after interchanging certain operators. We need to replace '+' with '-' and '-' with '+'. Similarly, we need to replace '×' with '÷' and '÷' with '×'. After performing these interchanges, we will evaluate the new expression following the BODMAS/PEMDAS rule (Brackets, Orders/Exponents, Division, Multiplication, Addition, Subtraction).
D) 19 is the correct answer. After interchanging the operators and evaluating the expression according to the BODMAS rule, the result is 19.
The question asks for the founding year of The English and Foreign Languages University (EFLU) located in Hyderabad. This is a factual question requiring knowledge of the history of educational institutions in India.
Correct Option: C) 1958
The nature of an image (real/virtual, erect/inverted, enlarged/smaller) can be determined by analyzing the sign and magnitude of its magnification. Magnification is a dimensionless quantity that describes the extent to which an image is enlarged or reduced relative to the object.
Understand Magnification Formula: The linear magnification (\(m\)) is defined as the ratio of the height of the image (\(h_i\)) to the height of the object (\(h_o\)):
\[ m = \frac{h_i}{h_o} \]Interpret the Sign of Magnification:
Interpret the Magnitude of Magnification:
Apply to the Given Value: The given magnification is \(m = -0.65\).
Combine the Interpretations: Based on the analysis, the image is real, inverted, and smaller.
B) real, inverted and smaller. This matches our interpretation that a negative magnification implies a real and inverted image, and a magnitude less than 1 implies a smaller image.
The boiling point of a compound is determined by the strength of the intermolecular forces of attraction between its molecules. Stronger intermolecular forces require more energy to overcome, leading to a higher boiling point. We need to analyze the types of intermolecular forces present in each given compound.
Considering the types and strengths of intermolecular forces:
Therefore, CH₃COOH will have the highest boiling point.
Correct Option: A) CH₃COOH has the highest boiling point because carboxylic acids form strong hydrogen-bonded dimers, which requires a significant amount of energy to break during boiling.
This is a linear arrangement puzzle. We need to deduce the seating positions of seven people (P, Q, R, S, T, U, V) based on the given clues. We will build the arrangement step-by-step, starting with the most restrictive clues.
Clue 1: Exactly two people are sitting to the left of T.
Since there are 7 people, this means T is in the 3rd position from the left.
_ _ T _ _ _ _
Clue 2: Only three people are sitting between T and P.
If T is at position 3, then P must be at position 7 (3 + 3 + 1 = 7) to have three people between them.
_ _ T _ _ _ P
Clue 3: Q is sitting second to the right of R who is to the immediate right of someone at the end.
"R is to the immediate right of someone at the end" means R is at the second position from either end. Since P is at the right end, R cannot be at the second position from the right end (as that would be P's left, not right). So, R must be at the second position from the left end.
_ R T _ _ _ P
Now, "Q is sitting second to the right of R". R is at position 2, so Q must be at position 4.
_ R T Q _ _ P
Clue 4: Q is not an immediate neighbour of P.
Our current arrangement is _ R T Q _ _ P. Q is at position 4 and P is at position 7. They are not immediate neighbours, so this clue is consistent with our arrangement.
Clue 5: S is sitting to the immediate right of U.
The remaining empty spots are position 1, position 5, and position 6. The only way S can be immediately to the right of U is if U and S occupy positions 5 and 6 respectively.
_ R T Q U S P
Final Arrangement:
The only person left is V, and the only empty spot is position 1 (the extreme left end).
V R T Q U S P
Identify the person at the extreme left end:
From the final arrangement, V is sitting at the extreme left end.
C) V — As per the step-by-step deduction, V is at the extreme left end of the line.
The question asks about the quorum required for a sitting of the Lok Sabha. Quorum refers to the minimum number of members required to be present for a legislative body to conduct business legally. This is a fundamental concept in parliamentary procedure.
D) One-tenth of the total number of Members of the House. This is directly stated in Article 100(3) of the Indian Constitution.
Vardhamana Mahavira was the ______ Tirthankara of Jainism.
The question asks to identify the ordinal position of Vardhamana Mahavira among the Tirthankaras of Jainism. This requires knowledge of the fundamental tenets and historical figures of Jainism.
Correct Option: C) 24 th
Vardhamana Mahavira was indeed the 24th Tirthankara of Jainism. His teachings are central to contemporary Jain practices and beliefs.
This problem involves analyzing inequalities to determine which conclusions logically follow from a given statement. We need to evaluate each conclusion based on the relationships established in the main statement.
D) Only conclusion II follows
The value of \(\sqrt{0.04}\) + \(\sqrt{6.25}\) + \(\sqrt{12.25}\) – 8.2 is ______.
To solve this problem, we need to calculate the square root of each decimal number and then perform the addition and subtraction operations in the given expression. The key is to correctly find the square roots of the decimal numbers.
We know that \(4 = 2^2\). For decimals, \[\sqrt{0.04} = \sqrt{\frac{4}{100}} = \frac{\sqrt{4}}{\sqrt{100}} = \frac{2}{10} = 0.2\].
We know that \(625 = 25^2\). For decimals, \[\sqrt{6.25} = \sqrt{\frac{625}{100}} = \frac{\sqrt{625}}{\sqrt{100}} = \frac{25}{10} = 2.5\].
We know that \(1225 = 35^2\). For decimals, \[\sqrt{12.25} = \sqrt{\frac{1225}{100}} = \frac{\sqrt{1225}}{\sqrt{100}} = \frac{35}{10} = 3.5\].
The expression is \(\sqrt{0.04} + \sqrt{6.25} + \sqrt{12.25} - 8.2\).
Substituting the calculated square root values:
\[ 0.2 + 2.5 + 3.5 - 8.2 \]B) The final calculated value is \(-2.0\), which matches option B.