Compute: 1112 ÷ 139 − 5
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This means we perform division before subtraction.
Correct Option: D) 3
A question and two statements labeled (I), (II) are given. You have to decide which statement(s) is/are sufficient to answer the question.
Gowtham ranks eighteenth in a class. What is his rank from the last?
I. There are 47 students in the class.
II. Jegan who ranks 10th in the same class, ranks 38th from the last.
Statement I alone is sufficient.
Both the statements together are needed.
Statement II alone is sufficient.
Either I or II alone is sufficient.
The problem asks us to find Gowtham's rank from the last, given his rank from the top (18th). We need to determine which of the given statements (I or II) is sufficient to answer this question. The general formula relating rank from top, rank from last, and total number of students is: \(\text{Total students} = \text{Rank from top} + \text{Rank from last} - 1\).
Let Gowtham's rank from the top be \(R_T = 18\).
We need to find Gowtham's rank from the last, let's call it \(R_L\).
The formula connecting these is: \[ \text{Total students} = R_T + R_L - 1 \]
Substituting \(R_T = 18\): \[ \text{Total students} = 18 + R_L - 1 \]
So, \[ \text{Total students} = 17 + R_L \]
From this, we can express \(R_L\) as: \[ R_L = \text{Total students} - 17 \]
To find \(R_L\), we need to know the total number of students in the class.
Since both Statement I alone and Statement II alone are sufficient to answer the question, the correct option is D.
Correct Option: D) Either I or II alone is sufficient.
3 men dig a hole in 10 days. How many days would it take for 5 men to dig the same hole?
This problem involves the concept of work and time, specifically inverse proportionality. The amount of work (digging a hole) is constant. The number of men and the time taken to complete the work are inversely proportional. This means if you increase the number of men, the time taken will decrease, and vice versa. We can use the formula \(M_1 D_1 = M_2 D_2\), where \(M\) is the number of men and \(D\) is the number of days.
The total work done is constant. We can express this as:
\[ M_1 \times D_1 = M_2 \times D_2 \]It would take 5 men 6 days to dig the same hole.
D) 6 — As calculated, 5 men would take 6 days to dig the hole.
The question asks about the location of the United Nations Climate Change Conference held in 2015. This requires knowledge of significant international environmental conferences and their venues.
Correct Option: A) Paris. The 2015 United Nations Climate Change Conference (COP21) was held in Paris, France, where the historic Paris Agreement was adopted.
The question asks to identify which of the given options is NOT a monosaccharide sugar. To answer this, we need to understand the classification of carbohydrates, specifically distinguishing between monosaccharides and other types of sugars.
D) Maltose is a disaccharide, composed of two glucose units. It is not a monosaccharide.
This problem involves set theory, specifically the principle of inclusion-exclusion for two sets. The formula for the number of elements in the union of two sets A and B is given by \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\). We are given the number of elements in set A, set B, and their union, and we need to find the number of elements in their intersection.
Thus, the number of elements in the intersection of A and B is 20.
Correct Option: D) 20
This problem involves set theory, specifically the principle of inclusion-exclusion for two sets. We are given the number of elements in set A, set B, and their union. We need to find the number of elements that are present only in set B.
Correct Option: C) 12
The question asks for the full form of the acronym UNITAR. This is a direct knowledge-based question related to international organizations and their abbreviations. To answer correctly, one needs to know the official name represented by UNITAR.
Correct Option: C) United Nations Institute for Training and Research. UNITAR is a dedicated training arm of the United Nations system, providing training and capacity development activities to assist countries, with a focus on developing countries, to achieve the Sustainable Development Goals.
Which State hosted the 12th National Ice-Skating Championship in India?
Sikkim
Himachal Pradesh
Uttarakhand
Jammu and Kashmir
The question asks to identify the state that hosted the 12th National Ice-Skating Championship in India. This is a factual question related to sports events and their venues. Knowledge of recent national sports events is key to answering this question.
Correct Option: D) The 12th National Ice-Skating Championship was hosted in Gulmarg, Jammu and Kashmir. Gulmarg is a popular winter sports destination known for its natural ice rinks and facilities suitable for such championships.
The question asks about the orbital period of a geostationary satellite. A geostationary satellite is a special type of geosynchronous satellite that orbits the Earth directly above the equator, moving in the same direction as the Earth's rotation and having an orbital period equal to the Earth's rotational period. This allows it to appear stationary from the ground.
B) 24 hours — A geostationary satellite, by definition, completes one orbit in the same time it takes for the Earth to complete one rotation, which is 24 hours. This allows it to maintain a fixed position relative to a point on the Earth's surface.