The question asks to identify the major bank that launched the 'Unnati Credit Card' in 2017 with the aim of increasing credit inclusion in India. This requires knowledge of specific product launches by Indian banks.
Correct Option: B) SBI
State Bank of India (SBI) launched the 'Unnati Credit Card' in 2017. This card was specifically designed to help individuals, particularly those in semi-urban and rural areas, build a credit history. It is offered against a Fixed Deposit (FD) of a minimum of ₹25,000, making it accessible to a broader segment of the population and promoting credit inclusion.
This question asks to identify the form of energy that is NOT an output during the act of riding a bicycle. We need to consider the energy transformations that occur when a person pedals a bicycle.
D) Chemical energy — Chemical energy is the stored energy in the rider's body (from food) that is converted into other forms of energy to power the bicycle. It is the input, not an output, of the riding process.
The pH of a solution is a measure of its hydrogen ion concentration. It is defined by the negative logarithm (base 10) of the hydrogen ion concentration. We will use this relationship to calculate the initial and final hydrogen ion concentrations and then determine the change.
The pH of a solution is given by the formula:
\[ \text{pH} = -\log_{10}[\text{H}^+] \]Given initial pH = 3.
\[ 3 = -\log_{10}[\text{H}^+] \]\[ \log_{10}[\text{H}^+] = -3 \]\[ [\text{H}^+]_{\text{initial}} = 10^{-3} \text{ M} \]Given final pH = 6.
\[ 6 = -\log_{10}[\text{H}^+] \]\[ \log_{10}[\text{H}^+] = -6 \]\[ [\text{H}^+]_{\text{final}} = 10^{-6} \text{ M} \]To find out how many times the concentration has decreased, we can take the ratio of the initial concentration to the final concentration:
\[ \text{Ratio} = \frac{[\text{H}^+]_{\text{initial}}}{[\text{H}^+]_{\text{final}}} \]\[ \text{Ratio} = \frac{10^{-3}}{10^{-6}} \]\[ \text{Ratio} = 10^{(-3 - (-6))} \]\[ \text{Ratio} = 10^{(-3 + 6)} \]\[ \text{Ratio} = 10^3 \]\[ \text{Ratio} = 1000 \]Therefore, the \(\text{H}^+\) ion concentration has decreased 1000 times.Correct Option: C) decreases 1000 times
Based on the given data, the percentage of literates in City C is ______ (round to one decimal).
| City | Population | Literate | Illiterate | % of literates |
| A | 200 | 150 | 50 | - |
| B | - | 200 | 100 | 66.6 |
| C | 150 | 50 | 100 | - |
| D | 120 | - | 90 | 25 |
To find the percentage of literates in City C, we need to use the given data for City C. The percentage of literates is calculated by dividing the number of literates by the total population and then multiplying by 100.
Correct Option: D) 33.3
The question asks to identify the Indian entrepreneur who was the co-founder and owner of SpiceJet as of 2018. This requires knowledge of prominent figures in the Indian aviation industry and their association with specific airlines.
Correct Option: A) Ajay Singh is the co-founder of SpiceJet and played a crucial role in its establishment in 2005. He later re-acquired the airline in 2015 when it was facing financial difficulties and has since been its Chairman and Managing Director, thus being its owner as of 2018.
To determine implicit assumptions, we need to identify what must be true for the argument to make sense and for the advice to be logically given and potentially acted upon. An assumption is something taken for granted or accepted as true without proof.
Correct Option: D) Both 1 and 2 are implicit.
This question tests the understanding of refraction, specifically how a ray of light behaves when it passes from a denser medium to a rarer medium. Key concepts involved are Snell's Law, the definition of denser and rarer media in terms of refractive index, and the relationship between refractive index and the speed of light.
Combining these two observations, the light ray bends away from the normal and speeds up.
A) away from the normal and speeds up - This option correctly describes both the bending direction and the change in speed when light travels from a denser to a rarer medium.
To find the mean of the first five triangular numbers, we first need to identify what triangular numbers are and then calculate the first five of them. After that, we will sum these numbers and divide by the count (which is five) to find their mean.
\[ \text{Sum} = 1 + 3 + 6 + 10 + 15 = 35 \]
\[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{35}{5} = 7 \]
Correct Option: A) 7 is the mean of the first five triangular numbers.
We are given an equation involving cosecant and cotangent. We can use the fundamental trigonometric identity relating cosecant and cotangent to form a system of equations, or directly manipulate the given equation to find the value of cot \(\theta\).
We are given the equation:
\[ \text{cosec } \theta + \text{cot } \theta = 2 \quad \ldots(1) \]We know the fundamental trigonometric identity:
\[ \text{cosec}^2 \theta - \text{cot}^2 \theta = 1 \]This identity can be factored as a difference of squares:
\[ (\text{cosec } \theta - \text{cot } \theta)(\text{cosec } \theta + \text{cot } \theta) = 1 \]Substitute the value from equation (1) into this factored identity:
\[ (\text{cosec } \theta - \text{cot } \theta)(2) = 1 \]Solve for \(\text{cosec } \theta - \text{cot } \theta\):
\[ \text{cosec } \theta - \text{cot } \theta = \frac{1}{2} \quad \ldots(2) \]Now we have a system of two linear equations with \(\text{cosec } \theta\) and \(\text{cot } \theta\):
\[ \begin{cases} \text{cosec } \theta + \text{cot } \theta = 2 \quad (1) \\ \text{cosec } \theta - \text{cot } \theta = \frac{1}{2} \quad (2) \end{cases} \]To find \(\text{cot } \theta\), subtract equation (2) from equation (1):
\[ (\text{cosec } \theta + \text{cot } \theta) - (\text{cosec } \theta - \text{cot } \theta) = 2 - \frac{1}{2} \] \[ \text{cosec } \theta + \text{cot } \theta - \text{cosec } \theta + \text{cot } \theta = \frac{4-1}{2} \] \[ 2 \text{cot } \theta = \frac{3}{2} \]Solve for \(\text{cot } \theta\):
\[ \text{cot } \theta = \frac{3}{2 \times 2} \] \[ \text{cot } \theta = \frac{3}{4} \]Convert the fraction to a decimal:
\[ \text{cot } \theta = 0.75 \]Correct Option: D) 0.75
The question asks to identify India's flag bearer at the 2016 Rio Olympics. This requires knowledge of major sporting events and India's representation in them.
Correct Option: B) Abhinav Bindra was the flag bearer for India at the opening ceremony of the 2016 Rio Olympics. He is an Olympic gold medalist in shooting (2008 Beijing Olympics) and a highly respected figure in Indian sports.