The question asks to identify the characteristics of the Reserve Bank of India (RBI) from the given statements. We need to evaluate each statement based on the functions and roles of a central bank, specifically the RBI.
B) A, B and C
Statements A, B, and C accurately describe the functions of the Reserve Bank of India. Statement D describes the function of commercial banks.
The question asks for the specific physico-chemical process by which plants convert light energy into chemical energy. This is a fundamental concept in biology, particularly plant physiology.
Correct Option: C) Photosynthesis — This is the correct term for the process where plants convert light energy into chemical energy (in the form of sugars).
The problem asks us to modify a given set of five four-digit numbers by subtracting 3 from the first digit of each number. Then, we need to count how many of the resulting numbers have a first digit that is exactly divisible by 3.
The question asks for the primary reason why paper cups should replace plastic cups for selling tea in public places. This is a common environmental concern, and the answer relates to the impact of these materials on the environment after disposal.
Correct Option: D) Paper cups are biodegradable
This is the most crucial environmental advantage of paper cups over plastic cups. Biodegradability means that paper cups can break down naturally into harmless substances, reducing waste and pollution in landfills and natural ecosystems. This aligns with sustainable practices and efforts to combat plastic pollution.
The problem asks us to find the sum of all odd numbers in the given number series. We need to identify each odd number in the series and then add them up.
Correct Option: B) 80
The question asks to identify the incorrect statement among the given options related to sex determination and chromosomes. We need to evaluate each statement based on biological facts.
Correct Option: D) All children will inherit a Y chromosome from their mother.
The question asks to identify the raw material used for making Plaster of Paris (PoP). This requires knowledge of the chemical composition and common names of various compounds, particularly those related to calcium sulfates.
Correct Option: B) \(\text{CaSO}_4 \cdot 2\text{H}_2\text{O}\) is the chemical formula for gypsum, which is the primary raw material used to produce Plaster of Paris.
To find the total number of students in the class, we need to sum Sakshi's rank from the top, Ravina's rank from the bottom, and the number of students between them. We must be careful not to double-count any student.
Total number of students = (Sakshi's rank from top) + (Number of students between them) + (Ravina's rank from bottom - 1, since Ravina is already counted in her rank from bottom).
Alternatively, a simpler way is to sum all distinct positions:
Total students = (Students above Sakshi) + (Sakshi) + (Students between them) + (Ravina) + (Students below Ravina)
Total students = \( (18 - 1) + 1 + 3 + 1 + (13 - 1) \)
Total students = \( 17 + 1 + 3 + 1 + 12 \)
Total students = \( 34 \)
Or, directly sum the given ranks and the students in between, then subtract 2 because both Sakshi and Ravina are counted in their respective ranks:
\[ \text{Total students} = \text{Sakshi's rank from top} + \text{Ravina's rank from bottom} + \text{Students between them} - 2 \]This formula applies when there is no overlap (i.e., Sakshi's rank from top + Ravina's rank from bottom is greater than the total number of students, which is true here because Sakshi has a higher rank than Ravina).
\[ \text{Total students} = 18 + 13 + 3 = 34 \]Correct Option: C) 34
This question tests the understanding of magnification produced by spherical lenses and mirrors. The sign and magnitude of magnification provide clues about the nature of the image (real/virtual, erect/inverted) and the type of lens/mirror.
Correct Option: D) the lens is convex but the mirror is concave
The equation
(x+1)3−(x−1)3=0 is:
a linear equation with real roots
a quadratic equation with real roots
a quadratic equation with non-real roots
a linear equation with non-real roots
To determine the nature of the given equation, we need to expand and simplify it. By doing so, we can identify its degree and then analyze the nature of its roots based on the discriminant if it's a quadratic equation.
The given equation is:
\[ (x+1)^3 - (x-1)^3 = 0 \]We use the algebraic identities for the cube of a binomial:
Applying these identities to the terms in the equation:
Substitute these expanded forms back into the original equation:
\[ (x^3 + 3x^2 + 3x + 1) - (x^3 - 3x^2 + 3x - 1) = 0 \]Simplify the equation by removing the parentheses and combining like terms:
\[ x^3 + 3x^2 + 3x + 1 - x^3 + 3x^2 - 3x + 1 = 0 \]\[ (x^3 - x^3) + (3x^2 + 3x^2) + (3x - 3x) + (1 + 1) = 0 \]\[ 0 + 6x^2 + 0 + 2 = 0 \]\[ 6x^2 + 2 = 0 \]This is a quadratic equation of the form \( ax^2 + bx + c = 0 \), where \( a=6 \), \( b=0 \), and \( c=2 \). To find the nature of its roots, we calculate the discriminant \( \Delta = b^2 - 4ac \).
\[ \Delta = (0)^2 - 4(6)(2) \]\[ \Delta = 0 - 48 \]\[ \Delta = -48 \]Since the discriminant \( \Delta = -48 \) is less than zero \( (\Delta < 0) \), the quadratic equation has non-real (complex) roots.
The simplified equation is \( 6x^2 + 2 = 0 \), which is a quadratic equation because the highest power of \( x \) is 2. The discriminant is \( -48 \), which is negative, indicating that the roots are non-real.