The surface area (in cm²) of a sphere of radius 14 cm is:
Take π = \( \frac{22}{7} \)
To find the surface area of a sphere, we use the standard formula for the surface area of a sphere, which is \(4 \pi r^2\), where \(r\) is the radius. We are given the radius and the value of \(\pi\), so we can directly substitute these values into the formula and calculate the result.
The surface area of the sphere is \(2464 \text{ cm}^2\).
Correct Option: D) 2464
To solve this problem, we need to apply the given operations to each digit in the number. We will identify odd and even digits, perform the specified additions or subtractions, and then form the new number. Finally, we will identify the third digit from the right in the modified number.
Therefore, the third digit from the right is 2.
Correct Option: D) 2
The question asks about the specific region where the Sixth Schedule of the Indian Constitution applies. This schedule is a constitutional provision designed to protect the rights of tribal populations through the formation of autonomous administrative divisions.
D) North-East India — The Sixth Schedule of the Indian Constitution deals with the administration of tribal areas in the states of Assam, Meghalaya, Tripura, and Mizoram, all of which are located in North-East India. It provides for the formation of Autonomous District Councils and Regional Councils with powers over land, forest, water, shifting cultivation, village administration, inheritance of property, marriage and divorce, social customs, etc., to protect the tribal culture and identity.
The problem presents an analogy based on letter clusters. We need to identify the pattern or relationship between the letters in the given pair (XTR) and then apply the same pattern to find the missing letter clusters (# and %). This involves analyzing the alphabetical positions of the letters and the operations (addition/subtraction) performed on them.
B) # = DZX, % = FBZ. The pattern is that each letter in the first cluster is shifted backward by 6 positions in the alphabet to get the corresponding letter in the second cluster. Applying this to DZX gives XTR, and applying it to LHF gives FBZ.
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 a consistent pattern emerges.
So, the missing number is 69.
Correct Option: C) 69
The area of a quadrilateral can be calculated by dividing it into two triangles using one of its diagonals. The area of the quadrilateral is the sum of the areas of these two triangles. We are given the total area of the quadrilateral and the lengths of the perpendiculars from two vertices to a common diagonal. We can use the formula for the area of a triangle (\(0.5 \times \text{base} \times \text{height}\)) to find the length of the diagonal.
Correct Option: A) 24
To simplify \(10.1^3\) using a suitable identity, we can express \(10.1\) as a sum of two numbers, one of which is an integer, making the calculation easier. The most suitable identity here is the binomial expansion for \((a+b)^3\).
Correct Option: B) 1030.301
To solve this problem, we need to apply the given rules to each digit of the original number. First, identify whether each digit is odd or even. Then, perform the specified addition or subtraction. Finally, count how many distinct digits appear more than once in the new number formed.
A) Two. The digits 3 and 5 appear more than once in the new number 9375315.
This problem involves tracking a person's movement in different directions and calculating the final displacement from the starting point. We can solve this by breaking down the movement into horizontal (East-West) and vertical (North-South) components, or by visualizing the path on a coordinate plane.
So, Point P is at \((4, 0)\) relative to Point A, which is at \((0, 0)\).
To reach Point A from Point P, Mr. HIJ needs to move from \((4, 0)\) to \((0, 0)\).
The change in position required is:
\[ \Delta x = 0 - 4 = -4 \text{ km} \]\[ \Delta y = 0 - 0 = 0 \text{ km} \]A negative change in the x-coordinate means moving west. The distance is \(4\) km.
Therefore, he needs to drive 4 km to the west to reach Point A.
D) 4 km to the west — As calculated, the final position P is 4 km to the east of A. To return to A, he must drive 4 km to the west.
This problem involves calculating the final income after a percentage increase applied annually for a certain number of years. This can be solved using the compound interest formula or by calculating the increase year by year.
The income increases by 15% of the initial income.
\[ \text{Income after 1st year} = \text{Initial Income} + (\text{Initial Income} \times \text{Rate}) \]\[ = 70,000 + (70,000 \times 0.15) \]\[ = 70,000 + 10,500 \]\[ = 80,500 \]The increase for the second year is based on the income at the end of the first year.
\[ \text{Income after 2nd year} = \text{Income after 1st year} + (\text{Income after 1st year} \times \text{Rate}) \]\[ = 80,500 + (80,500 \times 0.15) \]\[ = 80,500 + 12,075 \]\[ = 92,575 \]The formula for compound growth is:
\[ \text{Final Income} = P \left(1 + \frac{r}{100}\right)^n \]\[ \text{Final Income} = 70,000 \left(1 + \frac{15}{100}\right)^2 \]\[ = 70,000 (1 + 0.15)^2 \]\[ = 70,000 (1.15)^2 \]\[ = 70,000 \times 1.3225 \]\[ = 92,575 \]The income after 2 years is ₹92,575.
C) ₹92,575 is the correct income after 2 years, calculated by applying a 15% annual increase compounded over two years.