How many triangles are present in the given figure?
To find the total number of triangles in the given figure, we need to identify and count all possible triangles formed by the intersecting lines.
In this figure, the total number of triangles is 18.
Correct Option: C) 18
The question asks to identify the Chief Editor of Times Now as of 2018. This requires knowledge of prominent Indian news anchors and their affiliations during that specific period.
A) Rahul Shivshankar was indeed the Chief Editor of Times Now in 2018. He took over the role after Arnab Goswami's departure.
Jayant covers a certain distance in 2\( \frac{1}{2} \) hours at a speed of 54 km/h. How much time will Prabhu take to cover the same distance at a speed of 72 km/h?
2\( \frac{1}{2} \) hours
2\( \frac{1}{5} \) hours
1\( \frac{7}{8} \) hours
3 hours
To solve this problem, we first need to calculate the total distance covered by Jayant using his speed and time. Once we have the distance, we can then calculate the time Prabhu will take to cover the same distance using his given speed.
Given:
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]So, the distance \(D\) covered is:
\[ D = S_J \times T_J = 54 \text{ km/h} \times 2.5 \text{ h} = 135 \text{ km} \]Prabhu needs to cover the same distance \(D = 135\) km.
Given:
The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]So, the time \(T_P\) taken by Prabhu is:
\[ T_P = \frac{D}{S_P} = \frac{135 \text{ km}}{72 \text{ km/h}} \]Now, simplify the fraction:
\[ T_P = \frac{135}{72} = \frac{15 \times 9}{8 \times 9} = \frac{15}{8} \text{ hours} \]Convert the improper fraction to a mixed number:
\[ \frac{15}{8} = 1 \frac{7}{8} \text{ hours} \]Correct Option: C) 1\( \frac{7}{8} \) hours
The given series is a geometric progression (GP). We need to identify the first term, the common ratio, and then use the formula for the sum of the first \(n\) terms of a GP.
The given series is 16, 32, 64, 128, \(\dots\)
Let's check the ratio between consecutive terms:
Since the ratio is constant, this is a geometric progression (GP).
The sum of the first \(n\) terms of a GP is given by the formula:
\[ S_n = a \frac{(r^n - 1)}{(r - 1)} \quad \text{if } r > 1 \]Substitute the values:
\[ S_{10} = 16 \frac{(2^{10} - 1)}{(2 - 1)} \]First, calculate \(2^{10}\):
\[ 2^{10} = 1024 \]Now substitute this back into the sum formula:
\[ S_{10} = 16 \frac{(1024 - 1)}{(1)} \] \[ S_{10} = 16 \times 1023 \]Perform the multiplication:
\[ 16 \times 1023 = 16368 \]C) 16368 is the sum of the first 10 numbers in the series.
The problem asks us to decode a word based on a given coding pattern. We need to identify the rule used to transform "TREE" into "USFF" and then apply the same rule to "MANGO".
Let's compare the letters of "TREE" with "USFF":
The pattern is clear: each letter in the original word is shifted one position forward in the English alphabet.
Now, we apply the same "+1" rule to each letter of "MANGO":
Combining these, the coded word for MANGO is NBOHP.
Correct Option: D) NBOHP
This question tests general knowledge about international cricket events and their locations. Specifically, it asks about the host country for the Sano Cricket Curry Festival organized by the ICC in 2018.
Correct Option: B) Japan
Select the figure that is different from the other three.
To identify the figure that is different from the others, we need to analyze the orientation and arrangement of the arrows and circles within each diagram. The goal is to find a pattern or characteristic that sets one figure apart.
Correct Option: D) The circle is at the intersection of the arrows, unlike the other options where it is at the end.
The question asks to identify the specific type of motion when a body moves in a circular path with constant speed. This requires understanding the definitions of various types of motion, particularly those related to circular paths.
D) Uniform circular motion is precisely defined as the motion of a body along a circular path at a constant speed. While the speed is constant, the velocity vector is continuously changing direction, which implies there is an acceleration (centripetal acceleration) directed towards the center of the circle.
To find the thickness of the circular ring, we need to determine the radii of both the inner and outer circles. The circumference of a circle is given by the formula \(C = 2\pi r\). We can use the given circumferences to find the inner and outer radii, and then subtract the inner radius from the outer radius to get the thickness.
Correct Option: D) 3.5 cm
Select the option that groups together the following figures logically.
1, 2; 3, 4; 5, 6
1, 6; 2, 5; 3, 4
1, 5; 2, 6; 3, 4
1, 4; 2, 5; 3, 6
To solve this problem, we need to identify a logical grouping of the figures based on their visual characteristics. The key is to observe the relationship between shapes within each figure.
Now, identify the logical grouping:
Thus, the logical grouping is 1, 6; 2, 5; 3, 4.
Correct Option: B) 1, 6; 2, 5; 3, 4
