Who was the first British Viceroy of India?
Lord Canning
Lord Wellesley
William Bentinck
Robert Clive
The question asks to identify the first British Viceroy of India. This requires knowledge of the administrative changes implemented by the British in India, specifically after the Revolt of 1857.
Correct Option: A) Lord Canning was the Governor-General of India during the Revolt of 1857 and subsequently became the first Viceroy of India under the Government of India Act of 1858.
What is the difference between the compound interest and the simple interest on a sum of Rs 4,500 for 3 years at the rate of 8% per annum?
To find the difference between compound interest (CI) and simple interest (SI) for a given principal amount, rate, and time, we will calculate SI and CI separately and then find their difference. Alternatively, for 3 years, there's a direct formula for the difference between CI and SI.
Given:
Calculate Simple Interest (SI):
The formula for Simple Interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]Substitute the given values:
\[ \text{SI} = \frac{4500 \times 8 \times 3}{100} = 45 \times 8 \times 3 = 360 \times 3 = \text{Rs } 1080 \]Calculate Compound Interest (CI):
The formula for the amount (A) under compound interest is:
\[ \text{A} = \text{P} \left(1 + \frac{\text{R}}{100}\right)^\text{T} \]Substitute the given values:
\[ \text{A} = 4500 \left(1 + \frac{8}{100}\right)^3 = 4500 \left(1 + 0.08\right)^3 = 4500 (1.08)^3 \]Calculate \((1.08)^3\):
\[ (1.08)^3 = 1.08 \times 1.08 \times 1.08 = 1.1664 \times 1.08 = 1.259712 \]Now, calculate the Amount (A):
\[ \text{A} = 4500 \times 1.259712 = \text{Rs } 5668.704 \]Compound Interest (CI) is Amount - Principal:
\[ \text{CI} = \text{A} - \text{P} = 5668.704 - 4500 = \text{Rs } 1168.704 \]Calculate the difference between CI and SI:
\[ \text{Difference} = \text{CI} - \text{SI} = 1168.704 - 1080 = \text{Rs } 88.704 \]Rounding to two decimal places, the difference is Rs 88.70.
Alternative Method (Direct Formula for CI - SI for 3 years):
The formula for the difference between CI and SI for 3 years is:
\[ \text{CI} - \text{SI} = \text{P} \left(\frac{\text{R}}{100}\right)^2 \left(3 + \frac{\text{R}}{100}\right) \]Substitute the given values:
\[ \text{CI} - \text{SI} = 4500 \left(\frac{8}{100}\right)^2 \left(3 + \frac{8}{100}\right) \] \[ \text{CI} - \text{SI} = 4500 \left(0.08\right)^2 \left(3 + 0.08\right) \] \[ \text{CI} - \text{SI} = 4500 \times 0.0064 \times 3.08 \] \[ \text{CI} - \text{SI} = 28.8 \times 3.08 \] \[ \text{CI} - \text{SI} = 88.704 \]Rounding to two decimal places, the difference is Rs 88.70.
Correct Option: D) Rs 88.70
To determine the type of triangle, we need to calculate the lengths of all three sides using the distance formula. Once we have the side lengths, we can check for equality of sides (for isosceles or equilateral) and apply the Pythagorean theorem to check for a right angle.
Let the vertices of the triangle be \(A=(4,1)\), \(B=(1,1)\), and \(C=(3,5)\).
We will use the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\), which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]Step 1: Calculate the length of side AB.
\[ AB = \sqrt{(1 - 4)^2 + (1 - 1)^2} = \sqrt{(-3)^2 + (0)^2} = \sqrt{9 + 0} = \sqrt{9} = 3 \]Step 2: Calculate the length of side BC.
\[ BC = \sqrt{(3 - 1)^2 + (5 - 1)^2} = \sqrt{(2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20} \]Step 3: Calculate the length of side AC.
\[ AC = \sqrt{(3 - 4)^2 + (5 - 1)^2} = \sqrt{(-1)^2 + (4)^2} = \sqrt{1 + 16} = \sqrt{17} \]Step 4: Analyze the side lengths.
The lengths of the sides are \(AB=3\), \(BC=\sqrt{20}\), and \(AC=\sqrt{17}\). Since all three side lengths are different (\(3 \neq \sqrt{20} \neq \sqrt{17}\)), the triangle is a scalene triangle.
Step 5: Check for a right angle using the Pythagorean theorem.
For a right-angled triangle, the square of the longest side must be equal to the sum of the squares of the other two sides. The longest side is \(BC=\sqrt{20}\).
\[ (BC)^2 = (\sqrt{20})^2 = 20 \]Sum of the squares of the other two sides:
\[ (AB)^2 + (AC)^2 = (3)^2 + (\sqrt{17})^2 = 9 + 17 = 26 \]Since \(20 \neq 26\), the triangle is not a right-angled triangle.
B) Scalene triangle
Since all three sides have different lengths (\(3\), \(\sqrt{20}\), \(\sqrt{17}\)), the triangle is a scalene triangle. Also, it is not a right-angled triangle as it does not satisfy the Pythagorean theorem.
On 7th June 1984 it was a Thursday. What day was it on 7th June 1983?
To determine the day of the week for a previous year, we need to calculate the number of odd days between the two given dates. An ordinary year has 365 days, which is 52 weeks and 1 odd day. A leap year has 366 days, which is 52 weeks and 2 odd days. When moving backward in time, we subtract the odd days.
Number of odd days \[= \frac{\text{Total number of days}}{7}\]
Number of odd days \[= \frac{366}{7} = 52 \text{ weeks and } 2 \text{ days remainder}\]
So, there are 2 odd days between 7th June 1983 and 7th June 1984.
Day on 7th June 1983 \( = \) Day on 7th June 1984 \( - \) Number of odd days
Day on 7th June 1983 \( = \) Thursday \( - \) 2 days
Counting backward from Thursday: Wednesday (1 day back), Tuesday (2 days back).
Therefore, 7th June 1983 was a Tuesday.
Correct Option: A) Tuesday
The question asks for the year Apple introduced the iPad as a multimedia device. This is a factual question related to technology history, specifically Apple product launches. To answer this, one needs to recall the launch date of the first-generation iPad.
Correct Option: C) 2010 is the correct answer because Apple introduced the first iPad in January 2010, with sales beginning in April of the same year.
The question asks to identify the physical quantity that is defined as the product of force and displacement. We need to recall the definitions of the given options in physics.
A) Work — Work is defined as the product of force and displacement in the direction of the force. It is a scalar quantity and represents the energy transferred by a force.
The question asks to identify which option is NOT a part of the 5-Kingdom classification system proposed by R.H. Whittaker. To answer this, we need to recall the five kingdoms defined by Whittaker.
Correct Option: D) Protozoa is not one of the five kingdoms in Whittaker's classification. Protozoa is a subgroup within the Kingdom Protista, comprising unicellular eukaryotic organisms that exhibit animal-like characteristics, such as motility and heterotrophic nutrition. It is not a separate kingdom itself.
If ‘+’ is denoted as ‘–’ and ‘×’ is denoted as ‘÷’ then what is the value of ((25 + 30) × 5) × 10?
This problem involves substituting new operators for existing ones and then evaluating the expression following the order of operations (BODMAS/PEMDAS).
The original expression is: \((25 + 30) \times 5) \times 10\)
Applying the given changes:
The modified expression becomes:
\[ ((25 - 30) \div 5) \div 10 \]Now, evaluate the expression step-by-step:
B) The calculated value of the expression is \(-0.1\).
Which of the fractions given below, when added to \( \frac{5}{16} \), gives 1?
\( \frac{6}{8} \)
\( \frac{11}{32} \)
\( \frac{22}{32} \)
\( \frac{13}{2} \)
To find the fraction that, when added to \( \frac{5}{16} \), gives 1, we need to determine the difference between 1 and \( \frac{5}{16} \). This can be done by subtracting \( \frac{5}{16} \) from 1. We will then compare the result with the given options.
C) \( \frac{22}{32} \)
Let's simplify option C: \( \frac{22}{32} \). Both the numerator and the denominator are divisible by 2. Dividing both by 2, we get:
This matches our calculated value for \( x \).
The question asks for the date when the first 'Persons of Indian Origin (PIO) Parliamentarian Conference' was held. This is a factual question related to current events and international relations concerning India's diaspora.
Correct Option: C) 9 January 2018