Examine the following statements:
1. George attends Music classes on Monday.
2. He attends Mathematics classes on Wednesdays.
3. His Literature classes are not on Friday.
4. He attends History classes on the day following the day of his Mathematics classes.
5. On Tuesday, he attends his Sports classes.
If he attends just one subject in a day and his Sunday is free, than he is also free on
UPSC - 2014
This is a logical reasoning problem that requires us to deduce George's schedule for the week based on the given statements. We need to assign one subject to each day from Monday to Saturday, as Sunday is free and he attends only one subject per day. We will build a day-wise schedule step-by-step.
D) Friday. Based on the step-by-step deduction, Friday is the only day left unassigned to any class, meaning George is free on Friday.
Directions for the following 3 items given below (Questions 8-10)
A, B, C, D, E, F are members of a family. They are engineer, Stenographer, doctor, draughtsman, lawyer and judge(not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family.
What is the profession of B?
UPSC - 2014
This is a blood relation and profession-based puzzle. We need to deduce the profession of each family member, especially B, by systematically using the given clues. We will build a family tree and assign professions and genders where possible.
Identify Members and Professions:
Process Clues and Deduce Relationships/Professions:
Consolidate Information:
Identify Remaining Member and Profession:
Which of the following is/are a couple/couples?
UPSC - 2014
The question asks to identify which pairs of forces constitute a 'couple'. In physics, a couple is defined as a pair of forces that are equal in magnitude, opposite in direction, and separated by a perpendicular distance, resulting in a pure rotational effect (torque) without any translational motion.
Without a diagram, we must assume a standard representation where A, B, C, D refer to individual forces. In typical problems of this nature, forces A and D are often depicted as acting in opposite directions, parallel to each other, and with equal magnitudes. Similarly, forces B and C are often depicted as acting in opposite directions, parallel to each other, and with equal magnitudes. If this is the case, then both AD and BC would form couples.
For example, imagine a square ABCD. If force A acts upwards at corner A, and force D acts downwards at corner D, with equal magnitudes and parallel lines of action, they form a couple. Similarly, if force B acts to the right at corner B, and force C acts to the left at corner C, with equal magnitudes and parallel lines of action, they form a couple.
Given the options, the question implies that 'AD' refers to the pair of forces A and D, and 'BC' refers to the pair of forces B and C. In the context of competitive exams, when such a question is asked without a diagram, it usually refers to forces that are inherently designed to form couples based on their labels.
Assuming the standard interpretation where A and D are equal and opposite, and B and C are equal and opposite, and they act along different lines of action:
Therefore, both AD and BC would be couples.
C) Both AD and BC. This option is correct because, in the absence of a diagram, the standard interpretation of such a question in competitive exams is that the pairs mentioned (AD and BC) are intended to represent forces that meet the criteria of a couple (equal magnitude, opposite direction, parallel lines of action, separated by a distance).
What is the profession of D?
UPSC - 2014
Consider the following matrix: 
What is the missing number at "?" in the matrix?
UPSC - 2015
To find the missing number in the matrix, we need to identify the pattern or rule applied to the numbers in the rows.
Correct Option: A) 5
A group of 630 children is seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?
UPSC - 2014
The problem describes a scenario where children are seated in rows, and each subsequent row has 3 fewer children than the one in front of it. This forms an arithmetic progression. We are given the total number of children and need to find which number of rows is not possible. We will set up an equation for the sum of an arithmetic progression and test each given option.
Let \(n\) be the number of rows. Let \(a\) be the number of children in the first row. The common difference \(d\) is \(-3\) because each subsequent row has 3 less children.
The number of children in the rows will be \(a, a-3, a-6, \dots, a-(n-1)3\). For the number of children to be positive, we must have \(a-(n-1)3 > 0\), which implies \(a > 3(n-1)\).
The sum of an arithmetic progression is given by the formula:
\[ S_n = \frac{n}{2} [2a + (n-1)d] \]In this case, \(S_n = 630\) and \(d = -3\). So, the equation becomes:
\[ 630 = \frac{n}{2} [2a + (n-1)(-3)] \]\[ 1260 = n [2a - 3(n-1)] \]We need to check which value of \(n\) (number of rows) from the options does not yield an integer value for \(a\) (number of children in the first row) that also satisfies \(a > 3(n-1)\).
Test Option A: \(n = 3\)
\[ 1260 = 3 [2a - 3(3-1)] \]\[ 1260 = 3 [2a - 3(2)] \]\[ 1260 = 3 [2a - 6] \]\[ 420 = 2a - 6 \]\[ 426 = 2a \]\[ a = 213 \] Check condition: \(a > 3(n-1) \implies 213 > 3(3-1) \implies 213 > 3(2) \implies 213 > 6\). This is possible.Test Option B: \(n = 4\)
\[ 1260 = 4 [2a - 3(4-1)] \]\[ 1260 = 4 [2a - 3(3)] \]\[ 1260 = 4 [2a - 9] \]\[ 315 = 2a - 9 \]\[ 324 = 2a \]\[ a = 162 \] Check condition: \(a > 3(n-1) \implies 162 > 3(4-1) \implies 162 > 3(3) \implies 162 > 9\). This is possible.Test Option C: \(n = 5\)
\[ 1260 = 5 [2a - 3(5-1)] \]\[ 1260 = 5 [2a - 3(4)] \]\[ 1260 = 5 [2a - 12] \]\[ 252 = 2a - 12 \]\[ 264 = 2a \]\[ a = 132 \] Check condition: \(a > 3(n-1) \implies 132 > 3(5-1) \implies 132 > 3(4) \implies 132 > 12\). This is possible.Test Option D: \(n = 6\)
\[ 1260 = 6 [2a - 3(6-1)] \]\[ 1260 = 6 [2a - 3(5)] \]\[ 1260 = 6 [2a - 15] \]\[ 210 = 2a - 15 \]\[ 225 = 2a \]\[ a = \frac{225}{2} = 112.5 \] Since \(a\) must be an integer (number of children), \(n=6\) is not possible.D) 6 — When \(n=6\), the calculated number of children in the first row, \(a\), is \(112.5\). Since the number of children must be an integer, 6 rows is not a possible arrangement.
