This problem involves profit and loss calculations. We are given the total cost price of a certain quantity of rice and the profit in terms of the selling price of a smaller quantity. We need to find the selling price of a specific quantity of rice.
A) The selling price of 5 kg of rice is Rs 285, which matches our calculation.
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(75, 16, 67) (33, 14, 26)
(88, 54, 76)
(28, 72, 64)
(40, 56, 94)
(29, 6, 26)
The problem asks us to identify a set of three numbers that follows the same relationship as the given sets: (75, 16, 67) and (33, 14, 26). We need to find a pattern involving addition, subtraction, multiplication, or division among the numbers in each set.
Let's try to find a relationship between these numbers. A common approach is to look for operations involving the first and third numbers to get the middle number, or vice-versa.
The pattern is \((\text{First number} - \text{Third number}) \times 2 = \text{Middle number}\).
D) (29, 6, 26)
The question asks to identify which institution is NOT part of the three-tier Panchayati Raj system in India. To answer this, one needs to recall the structure of the Panchayati Raj system as established by the 73rd Constitutional Amendment Act.
A) Tehsil Parishad — The term "Tehsil Parishad" is not a recognized tier within the standard three-tier Panchayati Raj system as mandated by the 73rd Constitutional Amendment Act. While "Tehsil" is an administrative division, a "Tehsil Parishad" does not constitute one of the three established tiers of rural local self-government.
The question asks to identify the element that is NOT part of the VIII group and the first series of the fourth period in Mendeleev's periodic table. This requires knowledge of the arrangement of elements in Mendeleev's periodic table, specifically the transition metals of the fourth period.
Correct Option: C) Cu is Copper. In Mendeleev's periodic table, Copper (Cu) belongs to Group IB (or Group 11 in the modern periodic table) of the fourth period, not Group VIII. Group VIII of the fourth period consists of the triad Fe, Co, and Ni.
The question asks for the location of India's first mosque, Cheraman Juma Masjid, which was in the news in 2021 due to its restoration. This requires knowledge of historical religious sites in India.
Correct Option: A) The Cheraman Juma Masjid, India's first mosque, is located in Kodungallur, Thrissur district, Kerala. Its recent restoration in 2021 brought it into the news.
The question asks to identify the financial institution established by the Indian government specifically for promoting sustainable agriculture and rural development. This requires knowledge of the primary mandates of key financial institutions in India.
Correct Option: A) NABARD (National Bank for Agriculture and Rural Development) was established in 1982 by an Act of Parliament (National Bank for Agriculture and Rural Development Act 1981) to facilitate credit for promotion and development of agriculture, small-scale industries, cottage and village industries, handicrafts, and other allied economic activities in rural areas. Its main objective is to promote sustainable and equitable agriculture and rural prosperity through effective credit support, related services, institutional development, and other innovative initiatives.
This problem involves arranging six friends (A, B, C, D, E, F) based on their heights using the given comparative statements. We will deduce their relative heights step-by-step to identify the shortest person.
Statement 1: B is taller than F but shorter than E.
This can be written as: \(E > B > F\).
Statement 2: Only one person is shorter than D.
This means D is the second shortest person among the six friends. If we arrange them from tallest to shortest, D would be the fifth person. Let's denote the positions as 1 (tallest) to 6 (shortest):
\[ \text{_} > \text{_} > \text{_} > \text{_} > D > \text{_} \]
Statement 3: Only three people are taller than C.
This implies that C is the fourth tallest person. In our height order:
\[ \text{_} > \text{_} > \text{_} > C > D > \text{_} \]
Statement 4: F is not the shortest.
From Statement 1, we have \(E > B > F\). Since F is not the shortest, the shortest person must be someone else. The current arrangement is:
\[ \text{_} > \text{_} > \text{_} > C > D > \text{Shortest Person} \]
Combining the information:
We know \(E > B > F\). From the overall order, we have 3 spots before C, and 1 spot after D. The friends are A, B, C, D, E, F.
Let's place C and D:
\[ \text{_} > \text{_} > \text{_} > C > D > \text{_} \]
The people taller than C are E, B, and one more person. Since \(E > B\), E and B must be among the first three positions. Also, F is shorter than B, so F must be at C's position or shorter. But C is already at the 4th position.
Let's refine the order using \(E > B > F\):
Since C is 4th and D is 5th, F cannot be shorter than D (as F is not the shortest, and the shortest position is 6th). F must be taller than D.
If F is taller than D, and \(E > B > F\), then E, B, and F must occupy positions before D. The only way this works is if F is taller than C, which contradicts the current placement of C (4th tallest). This means our initial assumption about F's placement relative to C and D needs re-evaluation.
Let's restart the combined placement carefully:
Now, let's place E, B, F. Since \(E > B > F\), these three people must occupy three consecutive positions in the height order. The available positions before C are \(P_1, P_2, P_3\). So, E, B, F must be \(P_1, P_2, P_3\) in that order:
\[ E > B > F > C > D > P_6 \]
The friends are A, B, C, D, E, F. We have placed E, B, F, C, D. The only remaining friend is A, and the only remaining position is \(P_6\).
Therefore, A must be the shortest person.
\[ E > B > F > C > D > A \]
Let's check all conditions:
All conditions are satisfied.
Identify the shortest person:
Based on our derived order, A is the shortest among all the friends.
Correct Option: C) A is the shortest among all the friends.
The problem states that NCC cadets need to be arranged in a rectangular pattern where the number of rows is equal to the number of columns. This means the total number of cadets participating in the parade must be a perfect square. We are given the total number of cadets who wanted to participate, which is 677. We need to find the minimum number of cadets to be left out, which means we need to find the largest perfect square less than or equal to 677.
Understand the condition: The cadets must be arranged in a rectangular pattern where the number of rows equals the number of columns. If there are \(n\) rows and \(n\) columns, the total number of cadets in the parade will be \(n \times n = n^2\). This means the number of cadets participating in the parade must be a perfect square.
Identify the total number of cadets: The total number of cadets who wanted to participate is 677.
Find the largest perfect square less than or equal to 677: We need to find an integer \(n\) such that \(n^2 \le 677\), and \(n^2\) is as close to 677 as possible.
Determine the number of cadets who can participate: The largest perfect square less than or equal to 677 is 676. This means that \(26 \times 26 = 676\) cadets can be arranged in the desired pattern.
Calculate the minimum number of cadets to be left out: The number of cadets to be left out is the difference between the total number of cadets who wanted to participate and the maximum number of cadets who can participate.
\[ \text{Cadets left out} = \text{Total cadets} - \text{Cadets participating} \] \[ \text{Cadets left out} = 677 - 676 = 1 \]B) 1 is the correct answer. Only 1 cadet needs to be left out for the remaining 676 cadets to form a perfect square arrangement of 26 rows and 26 columns.
A) 4 — If 4 cadets were left out, then \(677 - 4 = 673\) cadets would participate. 673 is not a perfect square (\(25^2 = 625\), \(26^2 = 676\)). This is not the minimum number to be left out.
C) 3 — If 3 cadets were left out, then \(677 - 3 = 674\) cadets would participate. 674 is not a perfect square. This is not the minimum number to be left out.
D) 2 — If 2 cadets were left out, then \(677 - 2 = 675\) cadets would participate. 675 is not a perfect square. This is not the minimum number to be left out.
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then check which conclusions logically follow from these diagrams.
Correct Option: C) Only conclusion III follows
The question asks to identify the major river flowing through the western part of Rajasthan. This requires knowledge of the geography and river systems of Rajasthan.
Correct Option: B) The Luni River is the only major river in the western part of Rajasthan. It originates in the Pushkar Valley of the Aravalli Range, near Ajmer, and flows southwest through the Thar Desert before disappearing into the Rann of Kutch in Gujarat. It is an ephemeral river, meaning its flow is often seasonal.