The question asks to identify a plant known for its stinging hairs that cause pain upon accidental touch. We need to evaluate each option based on this characteristic.
Based on this evaluation, Nettle is the only plant that fits the description.
Correct Option: A) Nettle is a plant famous for its stinging hairs (trichomes) that inject irritants when touched, causing a painful sensation.
The problem asks for the product of 987 and 999. This can be solved by direct multiplication or by using a simplification technique where 999 is expressed as \(1000 - 1\).
We can rewrite 999 as \(1000 - 1\). This makes the multiplication easier.
\[ 987 \times 999 = 987 \times (1000 - 1) \]Multiply 987 by each term inside the parenthesis.
\[ 987 \times (1000 - 1) = (987 \times 1000) - (987 \times 1) \]First, multiply 987 by 1000.
\[ 987 \times 1000 = 987000 \]Next, multiply 987 by 1.
\[ 987 \times 1 = 987 \]Subtract the second result from the first result.
\[ 987000 - 987 \] 987000
- 987
--------
986013
Alternatively, direct multiplication:
987
x 999
-----
8883 (\(987 \times 9\))
88830 (\(987 \times 90\))
888300 (\(987 \times 900\))
------
986013
A) 986013 is the correct product of 987 and 999.
The question asks to identify the UN specialized agency responsible for directing and coordinating international health-related matters. This requires knowledge of the functions of various UN agencies.
Correct Option: B) WHO is the United Nations specialized agency responsible for international public health. It directs and coordinates health-related matters globally, providing leadership, setting standards, and offering technical support.
Find the area of an equilateral triangle whose perimeter is 24 cm.
144 cm²
24\(\sqrt{3}\) cm²
16\(\sqrt{3}\) cm²
16 cm²
To find the area of an equilateral triangle, we first need to determine the length of its side. Since the perimeter is given, we can find the side length. Once the side length is known, we can use the standard formula for the area of an equilateral triangle.
An equilateral triangle has all three sides equal in length. Let the side length be \(a\).
The perimeter of an equilateral triangle is given by:
\[ \text{Perimeter} = 3 \times \text{side} = 3a \]Given perimeter is 24 cm.
\[ 3a = 24 \text{ cm} \]Divide by 3 to find \(a\):
\[ a = \frac{24}{3} = 8 \text{ cm} \]So, the side length of the equilateral triangle is 8 cm.
The formula for the area of an equilateral triangle with side length \(a\) is:
\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]Substitute the value of \(a = 8\) cm into the formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} (8)^2 \] \[ \text{Area} = \frac{\sqrt{3}}{4} \times 64 \]Simplify the expression:
\[ \text{Area} = 16\sqrt{3} \text{ cm}^2 \]Correct Option: C) 16\(\sqrt{3}\) cm²
This question is based on a circular seating arrangement involving eight persons: A, B, C, D, E, F, G, and H. All eight persons are facing away from the centre of the table. We need to arrange them according to the given conditions and determine which pair can occupy the positions immediately adjacent to A. Since everyone faces outward, the right side of a person is anticlockwise and the left side is clockwise.
All eight persons are sitting around a circular table facing away from the centre.
In a circular seating arrangement, we can fix A at any position because rotating the entire arrangement does not change the relationships.
B is fourth to the right of A.
Since there are eight persons, moving four positions in either direction leads to the opposite seat.
Therefore, A and B sit opposite each other.
B is an immediate neighbour of E.
Exactly two persons sit between E and F, so their positions differ by three seats around the circle.
We can place E next to B and then position F three seats away from E.
Exactly three persons sit between G and H.
Therefore, G and H must sit opposite each other.
Also, B must not be adjacent to G.
These conditions restrict the available positions for G and H.
D is third to the left of C.
Since all persons face outward, the left direction is clockwise.
Therefore, D must be three positions clockwise from C.
One valid arrangement, written clockwise starting from A, is:
A → D → F → H → B → E → C → G → A
Verify the conditions:
Thus, this arrangement satisfies all the conditions.
In the clockwise arrangement:
G → A → D
Therefore, the two immediate neighbours of A are G and D.
Hence, option B is correct.
Correct Option: B) G and D
A valid clockwise seating arrangement is A → D → F → H → B → E → C → G. In this arrangement, D sits immediately clockwise from A and G sits immediately anticlockwise from A. Therefore, G and D can be the neighbours of A, making option B correct.
A salesman has to cover 6 km in \( \frac{3}{4} \) h. If he covers \( \frac{1}{2} \) of the distance in \( \frac{2}{3} \) of the total time, then what must be his speed (in km/h) to cover the remaining distance in the remaining time?
To find the required speed, we need to determine the remaining distance and the remaining time. We will calculate the distance covered and time elapsed in the first part of the journey, then subtract these from the total distance and total time, respectively. Finally, we will use the formula Speed = Distance / Time to find the speed for the remaining part.
Identify total distance and total time:
Total distance \(D = 6 \text{ km}\)
Total time \(T = \frac{3}{4} \text{ h}\)
Calculate distance covered in the first part:
The salesman covers \(\frac{1}{2}\) of the total distance.
\[ D_1 = \frac{1}{2} \times D = \frac{1}{2} \times 6 \text{ km} = 3 \text{ km} \]Calculate time elapsed in the first part:
The salesman covers this distance in \(\frac{2}{3}\) of the total time.
\[ T_1 = \frac{2}{3} \times T = \frac{2}{3} \times \frac{3}{4} \text{ h} = \frac{2}{4} \text{ h} = \frac{1}{2} \text{ h} \]Calculate the remaining distance:
Remaining distance \(D_R = D - D_1 = 6 \text{ km} - 3 \text{ km} = 3 \text{ km}\)
Calculate the remaining time:
Remaining time \[T_R = T - T_1 = \frac{3}{4} \text{ h} - \frac{1}{2} \text{ h}\]
To subtract, find a common denominator:
\[ T_R = \frac{3}{4} \text{ h} - \frac{2}{4} \text{ h} = \frac{1}{4} \text{ h} \]Calculate the required speed for the remaining part:
Speed \[S_R = \frac{\text{Remaining Distance}}{\text{Remaining Time}}\]
\[ S_R = \frac{D_R}{T_R} = \frac{3 \text{ km}}{\frac{1}{4} \text{ h}} = 3 \times 4 \text{ km/h} = 12 \text{ km/h} \]Correct Option: D) 12
The salesman must travel at a speed of 12 km/h to cover the remaining 3 km in the remaining 1/4 hour.
The cost price of 19 pens is equal to the selling price of 16 pens. Percentage gain is:
18 \( \frac{3}{4} \) %
12.5%
15%
15 \( \frac{3}{4} \) %
To find the percentage gain, we need to establish a relationship between the cost price (CP) and the selling price (SP) of a single pen based on the given information. We can then use the formula for percentage gain: \[\text{Percentage Gain} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100\%\].
Formulate the equation from the given problem statement:
Let the cost price of one pen be \(\text{CP}\) and the selling price of one pen be \(\text{SP}\).
According to the problem, the cost price of 19 pens is equal to the selling price of 16 pens.
Express SP in terms of CP (or vice versa):
From the equation above, we can write:
Calculate the gain:
Gain is the difference between the selling price and the cost price.
Substitute the expression for SP:
\[ \text{Gain} = \frac{19}{16} \text{CP} - \text{CP} \] \[ \text{Gain} = \left( \frac{19}{16} - 1 \right) \text{CP} \] \[ \text{Gain} = \left( \frac{19 - 16}{16} \right) \text{CP} \] \[ \text{Gain} = \frac{3}{16} \text{CP} \]Calculate the percentage gain:
The formula for percentage gain is:
Substitute the value of Gain:
\[ \text{Percentage Gain} = \frac{\frac{3}{16} \text{CP}}{\text{CP}} \times 100\% \] \[ \text{Percentage Gain} = \frac{3}{16} \times 100\% \]Simplify the percentage gain:
\[ \text{Percentage Gain} = \frac{300}{16}\% \]Divide 300 by 16:
\[ \frac{300}{16} = \frac{150}{8} = \frac{75}{4} \]Convert the improper fraction to a mixed number:
\[ \frac{75}{4} = 18 \frac{3}{4}\% \]Correct Option: A) \(18 \frac{3}{4}\) %
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
The expression is \(4 \times 36 - 6[3 + 2(216 \div 6) - 51]\).
First, calculate the division inside the innermost parenthesis:
\[ 216 \div 6 = 36 \]Substitute this back into the expression:
\[ 4 \times 36 - 6[3 + 2(36) - 51] \]Next, perform the multiplication inside the square bracket:
\[ 2(36) = 72 \]Substitute this back:
\[ 4 \times 36 - 6[3 + 72 - 51] \]Now, perform addition and subtraction from left to right inside the square bracket:
\[ 3 + 72 = 75 \] \[ 75 - 51 = 24 \]So the expression becomes:
\[ 4 \times 36 - 6[24] \]Now, perform the multiplications from left to right:
\[ 4 \times 36 = 144 \] \[ 6 \times 24 = 144 \]Substitute these values back:
\[ 144 - 144 \]Correct Option: B) 0
The question asks to identify the Ministry responsible for the "Startup India" initiative. This requires knowledge of major government schemes and their associated ministries.
Correct Option: D) Commerce and Industry
This is a coding-decoding question where words are given new names. The task is to identify the actual item being referred to and then find its new name according to the given code.
Correct Option: A) Rose