If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, and ‘÷’ means ‘+’, what will come in place of the question mark (?) in the following equation?
30 − 2 ÷ 4 + 12 × 6 =?
This problem involves substituting given symbol meanings into a mathematical expression and then evaluating the expression using the order of operations (BODMAS/PEMDAS).
The original equation is: \(30 - 2 \div 4 + 12 \times 6 = ?\)
Applying the new meanings:
So, the new equation is: \(30 \times 2 + 4 - 12 \div 6 = ?\)
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Operations are performed from left to right for division/multiplication and addition/subtraction.
First, perform multiplication and division from left to right:
Substitute these values back into the equation:
\[ 60 + 4 - 2 = ? \]B) The final calculated value is \(62\).
According to the Indian Constitution, the number of members of the Council of Ministers cannot be increased beyond ___ percent of the total number of members of the Legislative Assembly.
The question asks about the constitutional limit on the size of the Council of Ministers in a state, specifically as a percentage of the total members of the Legislative Assembly. This is a direct factual question related to a specific amendment to the Indian Constitution.
Correct Option: C) 15
The problem involves finding a pattern in a series of alphanumeric codes. Each code consists of two letters followed by a number. We need to identify the relationship between the letters and the number within each pair, and also the relationship between the first code and the second code in the given examples. Once the logic is established, we apply it to the third code to find its related counterpart.
D) UP 40 is the correct option as it follows the established pattern of advancing each letter by 3 positions in the alphabet and increasing the number by 5.
To find the single equivalent discount for successive discounts, we can assume an initial price (e.g., Rs. 100) and apply each discount sequentially. Alternatively, we can use a direct formula for successive discounts.
Alternative Method (Formula):
If two successive discounts are \(D_1\%\) and \(D_2\%\), the single equivalent discount \(D\) is given by the formula:
\[ D = \left(D_1 + D_2 - \frac{D_1 \times D_2}{100}\right)\% \]In this case, \(D_1 = 10\%\) and \(D_2 = 20\%\).
\[ D = \left(10 + 20 - \frac{10 \times 20}{100}\right)\% \]\[ D = \left(30 - \frac{200}{100}\right)\% \]\[ D = (30 - 2)\% \]\[ D = 28\% \]
D) 28% is the single equivalent discount.
To find the image position, we will use the magnification formula for spherical mirrors, which relates magnification (\(m\)), image distance (\(v\)), and object distance (\(u\)). We are given the magnification and object distance, and we need to calculate the image distance.
Correct Option: C) 45 cm behind the mirror
This problem involves analyzing statements about the relative ages of several individuals and determining which conclusions logically follow. We will represent the age relationships using inequalities and then evaluate each conclusion based on these established relationships.
This can be written as: \(R > T\)
Since T and N are twins, they have the same age: \(T = N\).
N is older than P, so: \(N > P\).
Combining these, we get: \(T = N > P\).
"Y is not younger than R" means Y is either older than R or the same age as R: \(Y \ge R\).
"R is older than K" means: \(R > K\).
Combining these, we get: \(Y \ge R > K\).
From step 1: \(R > T\)
From step 2: \(T = N > P\)
From step 3: \(Y \ge R > K\)
Let's chain them together:
So, the overall relationship can be visualized as:
\(Y \ge R > T (= N) > P\)
Also, \(R > K\)
From our combined relationships, we know \(R > T\) and \(T > P\), which implies \(R > P\).
We also know \(R > K\).
However, there is no direct relationship or transitive property that connects K and P. We only know that both K and P are younger than R. For example, if R is 10, T is 8, N is 8, P is 6, and K could be 7 (making K older than P) or K could be 5 (making K younger than P). Since we cannot definitively say K is older than P, Conclusion I does not follow.
From our combined relationships, we know \(Y \ge R\) and \(R > T\).
Since Y is either older than or the same age as R, and R is strictly older than T, it logically follows that Y must be strictly older than T. If \(Y = R\) and \(R > T\), then \(Y > T\). If \(Y > R\) and \(R > T\), then \(Y > T\). In both cases, \(Y > T\), which means T is younger than Y. Therefore, Conclusion II follows.
A) Conclusion II follows
The question asks to identify the correct timeline for the Twelfth Five Year Plan in India. This requires knowledge of the historical periods covered by India's Five Year Plans.
Correct Option: C) 2012 to 2017
The question asks to identify the group of elements that had not been discovered when Mendeleev published his periodic table. This requires knowledge of the historical context of Mendeleev's work and the discovery timeline of different element groups.
Correct Option: B) Noble gases were not discovered at the time of Mendeleev's periodic table (1869). Their inert nature made them difficult to detect, and they were only discovered towards the end of the 19th century.
The product of two consecutive positive integers is 552. If the smaller of these two integers is represented by x, which of the options below will correspond to the equation for finding out the value of x?
x2 + x + 552 = 0
x2 - x + 552 = 0
x2 + x - 552 = 0
x2 - x - 552 = 0
The problem asks us to form a quadratic equation based on the given information: the product of two consecutive positive integers is 552, and the smaller integer is represented by \(x\).
Correct Option: C) The equation derived is \(x^2 + x - 552 = 0\), which perfectly matches option C.
To find the number of sides of a polygon given the sum of its interior angles, we use the formula for the sum of interior angles of a polygon, which is \((n-2) \times 180°\), where \(n\) is the number of sides. We will set this formula equal to the given sum (900°) and solve for \(n\).
Correct Option: A) 7