This problem can be solved using the concept of work and time. We need to calculate the individual work rates of a man and a woman, then combine them to find the total work rate of 2 men and 3 women, and finally determine the time taken to complete the work.
B) 6 days
The question asks about the purpose of the SHREYAS programme. To answer this, one needs to recall the objectives and focus areas of this specific government initiative.
A) providing industry-specific apprenticeship opportunities
The SHREYAS programme was launched by the Ministry of Human Resource Development (now Ministry of Education) in 2019. Its main objective is to provide industry apprenticeship opportunities to the general graduates undergoing higher education, thereby enhancing their employability. It aims to bridge the gap between education and industry requirements by offering credit-based apprenticeship courses.
The question asks for the location of the Kakrapar Atomic Power Station. This is a factual question related to general knowledge about India's nuclear power plants. To answer this, one needs to recall the geographical locations of major atomic power stations in India.
Correct Option: A) The Kakrapar Atomic Power Station (KAPS) is indeed located in Kakrapar, near Vyara in the Tapi district of Gujarat, India. It is operated by the Nuclear Power Corporation of India (NPCIL).
This is an analogy-based number series question. We need to find the relationship between the first pair of numbers (89 and 178) and then apply the same relationship to the third number (90) to find the missing fourth number.
Correct Option: B) 180
The problem is a coding-decoding type where each letter is assigned a specific numerical value. We need to identify the code for each letter given and then substitute these values into the target word 'PLDXMZ' to find its numerical representation.
The sequence of codes will be 9 (for P), 3 (for L), 2 (for D), 7 (for X), 5 (for M), 6 (for Z).
So, 'PLDXMZ' will be written as 932756.
C) 932756 is the correct representation of 'PLDXMZ' based on the given coding scheme.
The question asks us to identify which of the given assumptions are implicit in the statement: "The fundamental duties in Article 51A of the Indian Constitution obligates all citizens of the country." An implicit assumption is something taken for granted or presupposed by the statement, without being explicitly stated. We need to evaluate each assumption to see if the statement necessarily relies on it.
Correct Option: A) Neither assumption 1 nor 2 is implicit.
This problem can be solved using the Remainder Theorem. The Remainder Theorem states that if a polynomial \(P(x)\) is divided by a linear polynomial \((x-c)\), then the remainder is \(P(c)\). In this case, we are dividing by \((x+1)\), which means \(c = -1\). We will find the remainder for each polynomial by substituting \(x = -1\) and then equate the remainders to find the value of 'a'.
Let the first polynomial be \(P(x) = 4x^{3} + ax^{2} - 3x + 1\).
Let the second polynomial be \(Q(x) = x^{4} + x^{3} - x^{2} + 6\).
When \(P(x)\) is divided by \((x+1)\), the remainder is \(P(-1)\).
\[ P(-1) = 4(-1)^{3} + a(-1)^{2} - 3(-1) + 1 \]\[ P(-1) = 4(-1) + a(1) + 3 + 1 \]\[ P(-1) = -4 + a + 3 + 1 \]\[ P(-1) = a \]When \(Q(x)\) is divided by \((x+1)\), the remainder is \(Q(-1)\).
\[ Q(-1) = (-1)^{4} + (-1)^{3} - (-1)^{2} + 6 \]\[ Q(-1) = 1 + (-1) - (1) + 6 \]\[ Q(-1) = 1 - 1 - 1 + 6 \]\[ Q(-1) = 5 \]The problem states that both polynomials leave the same remainder when divided by \((x+1)\). Therefore,
\[ P(-1) = Q(-1) \]\[ a = 5 \]The value of 'a' is 5.
D) 5 — As calculated, the value of 'a' that makes the remainders equal is 5.
To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. We will examine the differences between consecutive terms to see if there's an arithmetic progression, a geometric progression, or a more complex pattern involving squares, cubes, or combinations of operations.
B) 19 — The pattern of differences between consecutive terms is \(2^1, 2^2, 2^3, 2^4, 2^5\). The differences are 2, 4, 8, 16, 32. Adding 8 to 11 gives 19, and adding 16 to 19 gives 35, which fits the series.
To find the ratio of the first number to the second number, we first need to determine the values of both numbers based on the given percentages. Once we have the individual numbers, we can express their ratio in the simplest form.
Find the first number: Given that 40% of the first number is 12. Let the first number be \(N_1\).
\[ 40\% \times N_1 = 12 \] \[ \frac{40}{100} \times N_1 = 12 \] \[ N_1 = \frac{12 \times 100}{40} \] \[ N_1 = \frac{1200}{40} \] \[ N_1 = 30 \]Find the second number: Given that 50% of the second number is 24. Let the second number be \(N_2\).
\[ 50\% \times N_2 = 24 \] \[ \frac{50}{100} \times N_2 = 24 \] \[ N_2 = \frac{24 \times 100}{50} \] \[ N_2 = \frac{2400}{50} \] \[ N_2 = 48 \]Calculate the ratio of the first number to the second number: The ratio is \(N_1 : N_2\).
\[ N_1 : N_2 = 30 : 48 \]To simplify the ratio, divide both numbers by their greatest common divisor (GCD). The GCD of 30 and 48 is 6.
\[ \frac{30}{6} : \frac{48}{6} \] \[ 5 : 8 \]Correct Option: D) 5 : 8
The question asks to identify the Indian actress appointed as an advocate for the UN's Sustainable Development Goals (SDGs) in 2019. This requires knowledge of current affairs and appointments related to international organizations.
Correct Option: C) Dia Mirza was appointed by UN Secretary-General Antonio Guterres as an advocate for the Sustainable Development Goals (SDGs) in 2019. She has been a long-standing advocate for environmental protection and sustainable development, also serving as a UN Environment Goodwill Ambassador for India.