This question tests general knowledge about significant environmental observances. Specifically, it asks for the theme of World Environment Day for a particular year (2019). To answer this, one needs to recall or know the themes designated by the United Nations Environment Programme (UNEP) for World Environment Day in that specific year.
Correct Option: B) Air pollution
The question asks to identify the classical dance form associated with the erstwhile state of Andhra Pradesh. This requires knowledge of the origins and geographical affiliations of various Indian classical dance forms.
Correct Option: D) Kuchipudi is a classical Indian dance form that originated in a village named Kuchipudi in the Krishna district of Andhra Pradesh, India. It is known for its graceful movements, dramatic expressions, and storytelling.
The problem presents a number series, and we need to find the missing term. We will analyze the differences between consecutive terms to identify a pattern.
C) 86 – This number fits the established pattern of alternating differences (\(+2, +6, +2, +6, \dots\)).
The problem asks us to find the letter-cluster that has the same relationship with "RUNA" as "HIOF" has with "MNTK". We need to identify the pattern or rule applied to transform "MNTK" into "HIOF" and then apply the same rule to "RUNA".
The pattern observed is that each letter in the first cluster is shifted backward by 5 positions in the English alphabet to get the corresponding letter in the second cluster.
A) MPIV is the correct option as it follows the established pattern of shifting each letter back by 5 positions.
We are given a relationship between the sum and difference of two numbers, and the value of the smaller number. We need to find the larger number. We can set up an algebraic equation based on the given information and solve for the unknown larger number.
Let the larger number be \(L\) and the smaller number be \(S\).
From the problem statement, we are given that the smaller number is 24. So, \(S = 24\).
The sum of the two numbers is \(L + S\).
The difference between the two numbers (larger minus smaller) is \(L - S\).
According to the problem, "The sum of two numbers is 5 times their difference". We can write this as an equation:
\[ L + S = 5 \times (L - S) \]Now, substitute the value of \(S = 24\) into the equation:
\[ L + 24 = 5 \times (L - 24) \]Distribute the 5 on the right side of the equation:
\[ L + 24 = 5L - 5 \times 24 \] \[ L + 24 = 5L - 120 \]Now, we need to solve for \(L\). Gather terms involving \(L\) on one side and constant terms on the other side. Subtract \(L\) from both sides:
\[ 24 = 5L - L - 120 \] \[ 24 = 4L - 120 \]Add 120 to both sides:
\[ 24 + 120 = 4L \] \[ 144 = 4L \]Divide by 4 to find \(L\):
\[ L = \frac{144}{4} \] \[ L = 36 \]So, the larger number is 36.
Correct Option: D) 36
The question asks for the date of the first session of the Indian National Congress (INC). This is a factual question related to modern Indian history. Recalling the foundational events of the INC is key to answering this.
Correct Option: C) December 1885
If \(\sqrt{1225\times\sqrt{\frac{32}{x}}}\) = 70, find the value of x.
The problem requires us to solve for the variable \(x\) in a given equation involving square roots. We will systematically eliminate the square roots by squaring both sides of the equation and then isolate \(x\).
The given equation is:
\[ \sqrt{1225 \times \sqrt{\frac{32}{x}}} = 70 \]To eliminate the outermost square root, square both sides of the equation:
\[ \left(\sqrt{1225 \times \sqrt{\frac{32}{x}}}\right)^2 = 70^2 \]\[ 1225 \times \sqrt{\frac{32}{x}} = 4900 \]Now, isolate the remaining square root term by dividing both sides by 1225:
\[ \sqrt{\frac{32}{x}} = \frac{4900}{1225} \]Simplify the fraction on the right side. We know that \(1225 = 35^2\) and \(4900 = 70^2\). Also, \(4900/1225 = (4 \times 1225)/1225 = 4\).
\[ \sqrt{\frac{32}{x}} = 4 \]To eliminate the remaining square root, square both sides of the equation again:
\[ \left(\sqrt{\frac{32}{x}}\right)^2 = 4^2 \]\[ \frac{32}{x} = 16 \]Now, solve for \(x\). Multiply both sides by \(x\) and then divide by 16:
\[ 32 = 16x \]\[ x = \frac{32}{16} \]\[ x = 2 \]B) The value of \(x\) is 2, as derived through the step-by-step algebraic manipulation.
Simplify:
\(\frac{12.25+\frac{7}{8}\text{ of }56-9}{\left(25\div5\times10.25\right)+\frac{10}{9}\text{ of }\left(\frac{7}{2}-\frac{4}{5}\right)-2}\)
To simplify the given expression, we will follow the BODMAS/PEMDAS rule (Brackets, Orders/Exponents, Division, Multiplication, Addition, Subtraction). We will simplify the numerator and the denominator separately and then divide the numerator by the denominator.
The numerator is \(12.25 + \frac{7}{8} \text{ of } 56 - 9\).
The denominator is \[\left(25 \div 5 \times 10.25\right) + \frac{10}{9} \text{ of } \left(\frac{7}{2} - \frac{4}{5}\right) - 2\].
Substitute the simplified parts back into the denominator expression:
\[ 51.25 + 3 - 2 \]The simplified expression is \[\frac{\text{Numerator}}{\text{Denominator}} = \frac{52.25}{52.25}\].
\[ \frac{52.25}{52.25} = 1 \]Correct Option: B) 1
This problem can be solved using the concept of weighted averages or by setting up equations based on the definition of average. We are given the average salary of the entire staff, officers, and non-officers, along with the number of officers. We need to find the number of non-officers.
Let \(N_O\) be the number of officers and \(N_{NO}\) be the number of non-officers.
Let \(A_O\) be the average salary of officers and \(A_{NO}\) be the average salary of non-officers.
Let \(A_T\) be the average salary of the entire staff and \(N_T\) be the total number of staff.
From the problem statement, we have:
The total number of staff is the sum of officers and non-officers:
\[ N_T = N_O + N_{NO} = 12 + N_{NO} \]The total salary of the entire staff can be expressed as:
\[ \text{Total Salary} = A_T \times N_T \]The total salary can also be expressed as the sum of the total salary of officers and the total salary of non-officers:
\[ \text{Total Salary} = (A_O \times N_O) + (A_{NO} \times N_{NO}) \]Equating the two expressions for total salary:
\[ A_T \times (N_O + N_{NO}) = (A_O \times N_O) + (A_{NO} \times N_{NO}) \]Substitute the given values into the equation:
\[ 3560 \times (12 + N_{NO}) = (5400 \times 12) + (2600 \times N_{NO}) \]Perform the multiplication:
\[ 42720 + 3560 N_{NO} = 64800 + 2600 N_{NO} \]Rearrange the equation to solve for \(N_{NO}\). Group terms with \(N_{NO}\) on one side and constant terms on the other side:
\[ 3560 N_{NO} - 2600 N_{NO} = 64800 - 42720 \]Simplify both sides:
\[ 960 N_{NO} = 22080 \]Solve for \(N_{NO}\):
\[ N_{NO} = \frac{22080}{960} \]\[ N_{NO} = 23 \]Thus, the number of non-officers in the office is 23.
D) 23 is the correct number of non-officers calculated from the given average salaries and number of officers.
The question asks to identify the Indian state that implemented 'Kudumbashree', a women-oriented community-based poverty reduction program. This requires knowledge of specific state-level welfare initiatives.
Correct Option: C) Kerala is the state that implemented 'Kudumbashree', a women-oriented community-based poverty reduction programme. It was launched in 1997 by the Government of Kerala with the support of the Government of India and NABARD. It is one of the largest women's empowerment programs in the world, aiming at eradicating poverty through community action.