To find the number of moles of oxygen gas from its given mass, we need to use the formula relating mass, molar mass, and moles. First, determine the molar mass of oxygen gas (\(\text{O}_2\)), then apply the formula: \[\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}}\].
Thus, 12 g of oxygen gas contains 0.375 mole.
Correct Option: B) 0.375
The question asks to identify the country with which India signed three agreements in March 2018, specifically aimed at fostering an open, independent, and prosperous Indo-Pacific region. This is a current affairs question related to international relations and India's foreign policy.
D) Vietnam: In March 2018, India and Vietnam signed three agreements during the visit of the Indian President to Vietnam. These agreements were part of strengthening their comprehensive strategic partnership and working towards an open, independent, and prosperous Indo-Pacific region.
The angle of depression to the foot of a building from the top of an 88\(\sqrt{3}\) m high tower is 60°. How far is the tower located from the building?
This problem involves trigonometry, specifically the concept of the angle of depression. We can visualize the situation as a right-angled triangle where the height of the tower is one side, the distance from the tower to the building is the other side, and the line of sight from the top of the tower to the foot of the building forms the hypotenuse. We will use the tangent function to relate the angle of depression to the height of the tower and the unknown distance.
Understand the setup: Let the height of the tower be \(h\) and the distance from the tower to the building be \(x\). The angle of depression from the top of the tower to the foot of the building is given as \(60^\circ\).
Draw a diagram: Imagine a right-angled triangle. Let A be the top of the tower, B be the base of the tower, and C be the foot of the building. Then AB is the height of the tower, BC is the distance from the tower to the building, and AC is the line of sight. The angle of depression is the angle between the horizontal line from A and the line AC. Due to alternate interior angles, the angle \(\angle ACB\) (angle at the foot of the building looking up to the top of the tower) will also be \(60^\circ\).
Identify knowns and unknowns:
Apply trigonometric ratio: In the right-angled triangle \(\triangle ABC\), we have the opposite side (height of the tower) and the adjacent side (distance from the tower to the building) relative to the angle \(\theta = 60^\circ\). The tangent function relates these:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]\[ \tan(60^\circ) = \frac{AB}{BC} \]Substitute values and solve for \(x\):
\[ \sqrt{3} = \frac{88\sqrt{3}}{x} \]Isolate \(x\):
\[ x = \frac{88\sqrt{3}}{\sqrt{3}} \]\[ x = 88 \text{ m} \]A) 88 m is the correct answer. The calculation shows that the distance from the tower to the building is 88 meters.
Choose the correct picture which comes next in the sequence of the above pictures:
To solve this problem, we need to identify the pattern in the given sequence of shapes and determine which option logically follows.
Correct Option: B) The diamond shape follows the logical progression of the sequence.
This is an element belonging to the 16th group of the periodic table that is used in the manufacturing of vulcanised rubber. This element reacts with hot and conc. HNO3 to form sulphuric acid. Which element is it?
The question describes an element based on three key properties: its group in the periodic table, its use in vulcanised rubber manufacturing, and its reaction with hot concentrated nitric acid to form sulphuric acid. We need to identify the element that matches all these characteristics.
Correct Option: C) Sulphur
This problem can be solved by forming a system of two equations based on the given information: one for the sum of ages and one for the product of ages. We can then solve these equations to find their current ages and subsequently their ages one year hence.
Let Navya's current age be \(N\) years and Kavya's current age be \(K\) years.
From the problem statement, the sum of their ages is 35 years:
\[ N + K = 35 \quad \text{(Equation 1)} \]The product of their ages is 300:
\[ N \times K = 300 \quad \text{(Equation 2)} \]From Equation 1, we can express \(K\) in terms of \(N\):
\[ K = 35 - N \]Substitute this expression for \(K\) into Equation 2:
\[ N \times (35 - N) = 300 \] \[ 35N - N^2 = 300 \]Rearrange the equation into a standard quadratic form \(aN^2 + bN + c = 0\):
\[ N^2 - 35N + 300 = 0 \]Solve the quadratic equation. We need two numbers that multiply to 300 and add up to 35. These numbers are 15 and 20.
\[ N^2 - 20N - 15N + 300 = 0 \] \[ N(N - 20) - 15(N - 20) = 0 \] \[ (N - 20)(N - 15) = 0 \]This gives two possible values for \(N\): \(N = 20\) or \(N = 15\).
If \(N = 20\), then from Equation 1, \(K = 35 - 20 = 15\).
If \(N = 15\), then from Equation 1, \(K = 35 - 15 = 20\).
So, their current ages are 20 years and 15 years.
The question asks for their ages 1 year hence. We need to add 1 to each of their current ages.
Correct Option: C) 21 years and 16 years
Choose the correct picture from the below options which fits the blank space(?) above.
The question involves identifying the correct piece that fits into the blank space in a given pattern. The pattern is divided into four sections, and each section has a specific design that complements the others.
Correct Option: B) The piece fits perfectly into the blank space, maintaining the symmetry and continuity of the pattern.
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the second pair to find the missing term.
Correct Option: C) Baby — A caterpillar develops into a butterfly. Similarly, a mother gives birth to a baby, and a baby grows up to be an adult. The relationship is one of offspring or earlier developmental stage.
To find the number of years it takes for a sum of money to double itself at a given simple interest rate, we can use the formula for simple interest. When the sum doubles, the simple interest earned will be equal to the principal amount.
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]Since \(SI = P\), we have:
\[ P = \frac{P \times 10 \times T}{100} \]We can cancel \(P\) from both sides (assuming \(P \neq 0\)):
\[ 1 = \frac{10 \times T}{100} \]Simplify the fraction:
\[ 1 = \frac{T}{10} \]Multiply both sides by 10:
\[ T = 10 \text{ years} \]Correct Option: C) 10 years
The question asks to identify the Indian state where Madhubani painting, practiced in the Mithila region, originates. This requires knowledge of the geographical distribution of traditional Indian art forms.
Correct Option: D) Bihar is the correct answer. Madhubani painting, also known as Mithila painting, is a famous folk art form that originated and is primarily practiced in the Mithila region of Bihar, India.
