This problem requires us to substitute the given symbols with their corresponding mathematical operators and then evaluate the expression following the order of operations (BODMAS/PEMDAS).
The given expression is: \(81 \text{ S } 28 \text{ R } 39 \text{ S } (98 \text{ Q } 7)\)
Substituting the operators, we get:
\[ 81 + 28 - 39 + (98 \div 7) \]BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, perform the addition:
\[ 81 + 28 = 109 \]Correct Option: C) 84
The question asks to identify the name of India's first and largest multinational air combat exercise hosted in 2024. This requires knowledge of recent defence exercises conducted by India.
Correct Option: C) Exercise Tarang Shakti
What is the mode of the data given below? [Give your answer correct to 2 decimal places.]
| Age in years | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | 75-85 |
| No. of patients | 31 | 34 | 13 | 19 | 30 | 28 | 29 |
To find the mode of grouped data, we first identify the modal class, which is the class interval with the highest frequency. Then, we use the formula for the mode of grouped data.
D) 26.25 — This is the correct mode calculated using the formula for grouped data.
Who were the defending champions at the 15th Hockey India Senior Women National Championship 2025?
Hockey Maharashtra
Hockey Punjab
Hockey Haryana
Hockey Jharkhand
The question asks about the defending champions of the 15th Hockey India Senior Women National Championship 2025. To answer this, one needs to know the winner of the previous edition, which was the 14th Hockey India Senior Women National Championship.
D) Hockey Jharkhand — Hockey Jharkhand won the 14th Hockey India Senior Women National Championship in 2024, making them the defending champions for the 15th edition in 2025.
The question asks to identify the classical Indian dance form that has Jagoi and Cholom as its two main divisions. This requires knowledge of the characteristics and sub-styles of various Indian classical dances.
Correct Option: B) Manipuri. Jagoi and Cholom are the two principal divisions of the Manipuri classical dance form. Jagoi represents the softer, feminine aspects, while Cholom represents the more vigorous, masculine aspects.
The question asks to identify which statement was NOT a provision of the Rowlatt Act. To answer this, we need to recall the key features and repressive measures introduced by the Rowlatt Act of 1919.
The Rowlatt Act's primary provisions focused on giving the government extraordinary powers of arrest and detention without trial. While it severely curtailed freedom of expression, it did not explicitly list "restrictions on freedom of expression" as a direct provision. Rather, its enforcement and the powers it granted led to such restrictions. The Act was more about procedural powers to deal with perceived sedition.
The question asks why the common cold, primarily caused by rhinoviruses, rarely affects the lower respiratory tract. This requires understanding the specific tropism (preference for certain tissues) of the virus and the physiological conditions it needs to thrive.
Correct Option: B) Rhinoviruses only infect the upper respiratory tract. This statement is the most accurate reason. Rhinoviruses have an optimal temperature for replication that is lower than core body temperature, making the cooler environment of the upper respiratory tract (nasal passages, throat) ideal for their growth and infection. While they can occasionally reach the lower tract, their ability to cause significant infection there is limited due to temperature constraints and other host defenses.
The problem asks for the sum of the products of the roots taken two at a time for a given cubic equation. This can be directly found using Vieta's formulas, which relate the coefficients of a polynomial equation to sums and products of its roots.
A general cubic equation is given by:
\[ ax^3 + bx^2 + cx + d = 0 \]The given equation is:
\[ x^3 - 3x^2 + 4x - 12 = 0 \]Comparing this with the general form, we can identify the coefficients:If \(\alpha\), \(\beta\), and \(\gamma\) are the roots of the cubic equation \( ax^3 + bx^2 + cx + d = 0 \), then Vieta's formulas state:
We need to find the sum of the products of the roots taken two at a time, which is \( \alpha\beta + \beta\gamma + \gamma\alpha \). Using the formula, we have:
\[ \alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a} \]Substitute the values of \( c \) and \( a \) from our equation:\[ \alpha\beta + \beta\gamma + \gamma\alpha = \frac{4}{1} \]\[ \alpha\beta + \beta\gamma + \gamma\alpha = 4 \]C) 4 is the correct answer, as calculated using Vieta's formulas.
This is a logical reasoning problem involving arrangement. We need to deduce the floor on which each person lives based on the given clues and then determine the number of people between G and K.
Since F lives on an odd-numbered floor (1, 3, or 5) and there are two people between F and L, let's consider the possibilities:
We have two blocks of people: (J, L) and (K, H).
Remaining floors are 2, 3, 6. The block (K, H) needs two consecutive floors. This can be (K on 6, H on 3) or (K on 3, H on 2). Let's try to fit it.
If K is on 6, H is on 3. The remaining person is G. G must be on floor 2.
Arrangement: F(1), G(2), H(3), L(4), J(5), K(6).
Let's check all conditions: J immediately above L (5 above 4 - Yes). Two people between F and L (G, H - Yes). F on odd (1 - Yes). H immediately below K (3 below 6 - No, K is on 6, H is on 3. This is incorrect. H is not immediately below K). So this case is invalid.
Let's re-evaluate the KH block. K must be immediately above H. The only consecutive floors available are 2 and 3. So K is on 3 and H is on 2.
Arrangement for Case 1 (revised):
Check conditions: J immediately above L (5 above 4 - Yes). Two people between F and L (H, K - Yes). F on odd (1 - Yes). H immediately below K (2 below 3 - Yes). All conditions met.
Remaining floors are 1, 4, 6. The block (K, H) needs two consecutive floors. No consecutive floors are available (1, 4, 6). So this case is invalid.
G is on floor 6 and K is on floor 3. The people living between them are J (floor 5) and L (floor 4). There are two people.
Correct Option: B) Two
The question asks about the primary physical factor influencing the compactness of rural settlements in dry regions like Rajasthan. In arid and semi-arid areas, the availability of essential resources dictates human settlement patterns. We need to identify which factor would most strongly lead to people congregating in close proximity.
Correct Option: C) Availability of water