This question tests the understanding of the definitions and hierarchical relationships between different quadrilaterals: trapezium, parallelogram, rectangle, square, and rhombus. We need to evaluate each statement based on these definitions.
A trapezium only requires one pair of parallel sides. A parallelogram requires two pairs of parallel sides. Therefore, not every trapezium is a parallelogram. For example, an isosceles trapezium has only one pair of parallel sides and is not a parallelogram.
A parallelogram has two pairs of parallel sides. A square has two pairs of parallel sides, all sides equal, and all angles \(90^\circ\). Clearly, a general parallelogram (e.g., a non-square rectangle or a non-square rhombus) is not a square.
A rectangle has opposite sides parallel, all angles \(90^\circ\), and opposite sides equal. A square has all these properties PLUS all four sides equal. Therefore, a rectangle where adjacent sides are not equal (e.g., a rectangle with length \(5\) and width \(3\)) is not a square.
A square has all four sides equal and all four angles \(90^\circ\). A rhombus is defined as a parallelogram with all four sides equal. Since a square has all four sides equal, it satisfies the definition of a rhombus. The additional property of a square (all angles \(90^\circ\)) does not contradict the definition of a rhombus; rather, it makes a square a special type of rhombus.
C) Only d
Statement d) "Every square is a rhombus" is true because a square possesses all the properties of a rhombus (all four sides are equal).
The question asks to identify the local self-governing body responsible for areas that are in transition from rural to urban. This requires knowledge of the different tiers of local self-governance in India and their respective jurisdictions.
D) Nagar Panchayat is the correct answer. A Nagar Panchayat (or Town Panchayat) is constituted for areas that are in transition from a rural area to an urban area, as per the 74th Constitutional Amendment Act.
Raghu invests Rs 5,00,000 in the name of his daughter, who is 16 years old, in a scheme that pays 5% compound interest per annum, compounded annually. What will be the total amount due to the daughter when she turns 18 years old?
This problem involves calculating the future value of an investment under compound interest. We need to determine the principal amount, the interest rate, and the duration for which the interest will be compounded. The formula for compound interest will be applied to find the total amount.
The investment will accrue interest from when the daughter is 16 until she turns 18. So, the time period is \(18 - 16 = 2\) years.
The formula for the amount (\(A\)) with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Substituting the values:
\[ A = 5,00,000 \left(1 + \frac{5}{100}\right)^2 \] \[ A = 5,00,000 (1 + 0.05)^2 \] \[ A = 5,00,000 (1.05)^2 \]Correct Option: D) Rs 5,51,250
Express 0.13\(\overline{241}\) in the form \( \frac{p}{q} \), where p and q are integers, and q ≠ 0.
\(\frac{3807}{24975}\)
\(\frac{3287}{21780}\)
\(\frac{3337}{24160}\)
\(\frac{3307}{24975}\)
To express a non-terminating repeating decimal in the form \(\frac{p}{q}\), we use an algebraic method. We assign the decimal to a variable, multiply it by powers of 10 to align the repeating parts, and then subtract the equations to eliminate the repeating part.
Let the given number be \(x\):
\[ x = 0.13\overline{241} = 0.13241241241... \]Identify the non-repeating part and the repeating part. The non-repeating part is "13" (2 digits) and the repeating part is "241" (3 digits).
Multiply \(x\) by a power of 10 such that the non-repeating part is to the left of the decimal point. Since there are 2 non-repeating digits after the decimal, multiply by \(10^2 = 100\):
\[ 100x = 13.\overline{241} \quad \text{(Equation 1)} \]Multiply \(x\) by a power of 10 such that the non-repeating part and one block of the repeating part are to the left of the decimal point. Since there are 2 non-repeating digits and 3 repeating digits, multiply by \(10^{(2+3)} = 10^5 = 100000\):
\[ 100000x = 13241.\overline{241} \quad \text{(Equation 2)} \]Subtract Equation 1 from Equation 2 to eliminate the repeating part:
\[ 100000x - 100x = 13241.\overline{241} - 13.\overline{241} \]This simplifies to:
\[ 99900x = 13228 \]Solve for \(x\):
\[ x = \frac{13228}{99900} \]Simplify the fraction by finding the greatest common divisor (GCD). Both the numerator and the denominator are divisible by 4:
\[ \frac{13228 \div 4}{99900 \div 4} = \frac{3307}{24975} \]Check if further simplification is possible. The numerator 3307 is a prime number. Therefore, the fraction is in its simplest form.
Correct Option: D) \(\frac{3307}{24975}\)
The question asks us to evaluate two statements regarding the magnetic field produced by a current-carrying straight conductor. We need to recall the properties of magnetic fields and how they are detected and influenced by current direction.
A) Only b is correct, as statement (a) is incorrect and statement (b) is correct.
The question asks to identify the Union Minister who introduced The National Anti-Doping Bill, 2021, in the Parliament. This requires knowledge of recent legislative developments related to sports and the portfolios of Union Ministers.
C) Anurag Thakur — Anurag Thakur, as the then Union Minister of Youth Affairs and Sports, introduced The National Anti-Doping Bill, 2021, in the Lok Sabha on December 17, 2021. This bill aimed to provide a statutory framework for the National Anti-Doping Agency (NADA) and the National Dope Testing Laboratory (NDTL) and to strengthen anti-doping activities in sports.
Among six students, K, L, M, N, O, and P, each scores different marks in an examination. M scores more marks than only three other students. K scores more marks than N. P scores less marks than M. O scores more marks than L. P scores more marks than K. L scores more marks than M. Who scores the highest marks among all six students?
To determine the nature and focal length of a lens combination, we first calculate the equivalent power of the combination. Then, using the relationship between power and focal length, we find the focal length. The sign of the equivalent power or focal length will indicate whether the combination acts as a convex (converging) or concave (diverging) lens.
Therefore, the lens combination will act as a convex lens having a focal length of 25 cm.
Correct Option: C) Convex lens having focal length 25 cm
To solve this problem, we need to compare the position of digits in the original number with their positions after arranging the digits in ascending order. We will list the original number, then arrange its digits, and finally identify digits that maintain their original position.
D) Two — As identified in the step-by-step analysis, the digits '3' and '8' retained their original positions after the digits of the number were arranged in ascending order.