The value of \(\frac{0.5\times10.6-0.2\times1.4}{0.4}\) is:
To solve this problem, we need to follow the order of operations (PEMDAS/BODMAS). First, perform the multiplications in the numerator, then the subtraction, and finally the division by the denominator.
Calculate the first product in the numerator: \(0.5 \times 10.6\).
\[ 0.5 \times 10.6 = 5.3 \]Calculate the second product in the numerator: \(0.2 \times 1.4\).
\[ 0.2 \times 1.4 = 0.28 \]Substitute these values back into the expression for the numerator:
\[ 5.3 - 0.28 \]Perform the subtraction in the numerator:
\[ 5.3 - 0.28 = 5.02 \]Now, substitute the result back into the original expression:
\[ \frac{5.02}{0.4} \]Perform the division. To make the division easier, we can multiply both the numerator and the denominator by 10 to remove the decimal from the denominator:
\[ \frac{5.02 \times 10}{0.4 \times 10} = \frac{50.2}{4} \]Divide \(50.2\) by \(4\):
\[ \frac{50.2}{4} = 12.55 \]B) 12.55 is the correct value obtained after performing the operations in the correct order.
The question asks about the field in which Sumit Antil received the Padma Shri award in 2022. To answer this, one needs to recall general knowledge about prominent Indian awardees and their respective fields of contribution, specifically focusing on the Padma Shri awards for the year 2022.
D) Sports — Sumit Antil is an Indian para-athlete specializing in javelin throw. He won a gold medal in the men's javelin throw F64 category at the 2020 Summer Paralympics in Tokyo. For his outstanding achievements in sports, he was honored with the Padma Shri, India's fourth-highest civilian award, in 2022.
This question tests the understanding of properties of angles formed when a transversal intersects a pair of parallel lines. Specifically, it focuses on alternate interior angles.
Correct Option: A) 35° — As per the property of alternate interior angles, when two parallel lines are intersected by a transversal, alternate interior angles are equal. Since \(m\angle 1 = 35°\), then \(m\angle 2\) must also be \(35°\).
The problem involves finding an unknown number given the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers, and one of the numbers. We will use the fundamental property that for any two positive integers, the product of the numbers is equal to the product of their LCM and HCF.
Identify the given values:
Let the two numbers be \( A \) and \( B \). We are given \( A = 60 \). We need to find \( B \).
Recall the fundamental property relating LCM, HCF, and the two numbers:
\[ A \times B = \text{LCM}(A, B) \times \text{HCF}(A, B) \]Substitute the given values into the formula:
\[ 60 \times B = 1920 \times 4 \]Calculate the product of LCM and HCF:
\[ 1920 \times 4 = 7680 \]Now the equation becomes:
\[ 60 \times B = 7680 \]Solve for \( B \) by dividing both sides by 60:
\[ B = \frac{7680}{60} \]Perform the division:
\[ B = 128 \]Thus, the other number is 128.
D) 128
When a transversal line intersects two parallel lines, the interior angles on the same side of the transversal are supplementary, meaning their sum is 180°. We are given the ratio of these two angles, which allows us to find their individual measures and then calculate their positive difference.
Let the two parallel lines be \(L_1\) and \(L_2\), and the transversal line be \(T\). The two interior angles on the same side of the transversal are supplementary.
Let the measures of the two interior angles be \(3x\) and \(7x\), based on the given ratio of 3:7.
Since these angles are supplementary, their sum is 180°:
\[ 3x + 7x = 180^\circ \]Combine the terms:
\[ 10x = 180^\circ \]Solve for \(x\):
\[ x = \frac{180^\circ}{10} \]\[ x = 18^\circ \]Now, calculate the measures of the two angles:
The question asks for the positive difference between the measures of these two angles:
\[ \text{Difference} = 126^\circ - 54^\circ \]\[ \text{Difference} = 72^\circ \]C) 72° is the positive difference between the measures of the two interior angles.
The question asks to identify the river from which the Dhuandhar Falls originate. This requires knowledge of Indian geography, specifically the location of major waterfalls and the rivers associated with them.
Therefore, the Dhuandhar Falls originate from the Narmada River.
Correct Option: D) Narmada
The question asks us to identify the correct statement(s) regarding magnetic field lines of a bar magnet. We need to recall the properties of magnetic field lines, particularly their direction both inside and outside the magnet, and their continuity.
A) Only (a) is correct because magnetic field lines form continuous closed loops. Outside the magnet, they go from North to South, and inside the magnet, they go from South to North to complete the loop.
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate each conclusion based on these diagrams. The key is to assume the statements are true, even if they contradict common knowledge.
A) Only conclusions I and II follow.
To find the approximate value, we will first round off the given numbers to make the calculation easier. Then, we will follow the order of operations (BODMAS/PEMDAS) to solve the equation: multiplication first, then subtraction and addition from left to right.
The given equation is: \(17.89 - 0.0123 + 2.21 \times 3.63 = ?\)
Round off each number to a convenient value for approximation:
So, the approximate equation becomes: \(18 - 0 + 2 \times 4 = ?\)
According to the order of operations, multiplication comes before addition and subtraction.
\[ 2 \times 4 = 8 \]Substitute the multiplication result back into the equation:
\[ 18 - 0 + 8 \]\[ 18 + 8 \]\[ 26 \]Thus, the approximate value is 26.
B) 26 — The calculation following approximation and order of operations leads to 26.
The given series is 7, 7, 10, 50, 57, ?. We need to identify the pattern in the series to find the missing number. Let's analyze the relationship between consecutive terms.
The first term is 7, and the second term is 7. The operation could be multiplication by 1 or addition of 0.
\[ 7 \times 1 = 7 \] or \[ 7 + 0 = 7 \]The second term is 7, and the third term is 10. The difference is 3.
\[ 7 + 3 = 10 \]The third term is 10, and the fourth term is 50. This looks like multiplication by 5.
\[ 10 \times 5 = 50 \]The fourth term is 50, and the fifth term is 57. The difference is 7.
\[ 50 + 7 = 57 \]Let's list the operations and the numbers involved:
The pattern involves alternating operations: multiplication and addition. The numbers used in these operations are consecutive odd numbers: 1, 3, 5, 7.
Following the pattern, the next operation should be multiplication, and the next odd number after 7 is 9.
So, the missing term will be:
\[ 57 \times 9 = 513 \]Correct Option: C) 513