Consider the above figure. The figure which does not belong to the group is:
The task is to identify the figure that does not belong to the group based on a common pattern or characteristic shared by the other figures.
Correct Option: C) The arrangement in option C includes a plane instead of a boat, which makes it different from the other options.
To find the correct mean, we first need to calculate the incorrect sum of the terms. Then, we will adjust this sum by subtracting the incorrectly read values and adding the correct values. Finally, we will divide the corrected sum by the total number of terms to get the correct mean.
Given that the mean of 10 terms is 49.
The formula for mean is:
\[ \text{Mean} = \frac{\text{Sum of terms}}{\text{Number of terms}} \]So, the incorrect sum of the 10 terms is:
\[ \text{Incorrect Sum} = \text{Mean} \times \text{Number of terms} \] \[ \text{Incorrect Sum} = 49 \times 10 = 490 \]To get the corrected sum, we subtract the sum of incorrect values from the incorrect sum and add the sum of correct values.
\[ \text{Corrected Sum} = \text{Incorrect Sum} - \text{Sum of Incorrect Values} + \text{Sum of Correct Values} \] \[ \text{Corrected Sum} = 490 - 60 + 120 \] \[ \text{Corrected Sum} = 430 + 120 = 550 \]The number of terms remains 10.
\[ \text{Correct Mean} = \frac{\text{Corrected Sum}}{\text{Number of terms}} \] \[ \text{Correct Mean} = \frac{550}{10} = 55 \]C) 55 is the correct mean after adjusting for the mistakenly read terms.
The given diagram shows the number of students who play football (F), hockey (H) and basketball (B) in the class. What is the number of students who play basketball in the class?
To find the number of students who play basketball, we need to analyze the Venn diagram provided, which shows the distribution of students playing football (F), hockey (H), and basketball (B).
Correct Option: B) 62
The question asks about the primary chemical composition of tooth enamel. To answer this, one needs to recall basic biological chemistry related to human body structures, specifically teeth.
Correct Option: B) Calcium phosphate
The cost of installing a paved floor in a circular room at the rate of Rs 10 per sqm is Rs 1,540. What will be the cost of fencing this floor at the rate of Rs 6 per metre?
To find the cost of fencing, we first need to determine the radius of the circular room. We can do this by using the given total cost of paving and the rate per square meter to calculate the area of the floor. Once the area is known, we can find the radius. With the radius, we can calculate the circumference of the floor, which represents the length of fencing required. Finally, we multiply the circumference by the fencing rate to get the total cost of fencing.
The total cost of paving is Rs 1,540, and the rate is Rs 10 per square meter.
\[ \text{Area} = \frac{\text{Total Cost}}{\text{Rate per sqm}} = \frac{1540}{10} = 154 \text{ sqm} \]The area of a circle is given by the formula \(A = \pi r^2\). We know the area is 154 sqm and we'll use \(\pi = \frac{22}{7}\).
\[ 154 = \frac{22}{7} \times r^2 \]\[ r^2 = \frac{154 \times 7}{22} \]\[ r^2 = 7 \times 7 \]\[ r^2 = 49 \]\[ r = \sqrt{49} \]\[ r = 7 \text{ meters} \]The circumference of a circle is given by the formula \(C = 2\pi r\).
\[ C = 2 \times \frac{22}{7} \times 7 \]\[ C = 2 \times 22 \]\[ C = 44 \text{ meters} \]The circumference is 44 meters, and the rate of fencing is Rs 6 per meter.
\[ \text{Cost of Fencing} = \text{Circumference} \times \text{Rate per meter} \]\[ \text{Cost of Fencing} = 44 \times 6 \]\[ \text{Cost of Fencing} = 264 \text{ Rs} \]B) Rs 264 is the correct cost of fencing the floor.
The question asks about the fundamental force responsible for the Moon's orbit around the Earth. This involves understanding the nature of forces that govern celestial motion.
A) Gravitational force — The gravitational force between the Earth and the Moon provides the necessary centripetal force that keeps the Moon in its orbit around the Earth.
The question asks about the fundamental nature of gravitational force. We need to recall Newton's Law of Universal Gravitation, which describes how gravity acts between objects.
B) Each and Every — Gravitational force is a universal force, meaning it acts between any two objects that possess mass. The magnitude of this force depends on the masses involved, making it noticeable only for massive objects like planets.
The question asks for the location of Sanjay Gandhi National Park. This requires knowledge of the geographical distribution of important national parks in India.
Correct Option: B) Sanjay Gandhi National Park is located in Mumbai, which is in the state of Maharashtra. It is one of the most visited national parks in Asia, known for its rich biodiversity and the ancient Kanheri Caves located within its boundaries.
Study the given statements and conclusions carefully and decide which of the conclusions logically follow(s) from the statements.
Statements:
Some girls are doctors.
All doctors are sisters.
Conclusions:
I. Some girls are sisters.
II. All sisters are girls.
Only II follows
Either I or II follows
Only I follows
Both I and II follow
This is a syllogism problem. We need to determine which conclusions logically follow from the given statements. We can use Venn diagrams or logical deduction to solve this.
C) Only I follows. Conclusion I is a direct logical deduction from combining both statements. If some girls are doctors, and all doctors are sisters, then it must be true that some girls are sisters.
The question asks for the atomicity of phosphorus. Atomicity refers to the number of atoms present in one molecule of an element. We need to recall the common molecular form of phosphorus.
D) Tetratomic. Phosphorus commonly exists as \(P_4\) molecules, meaning each molecule is composed of four phosphorus atoms, making it tetratomic.