This is a syllogism problem. We need to analyze the given statements and determine which conclusions logically follow. We can use Venn diagrams or logical deduction to solve this.
A) Only conclusion 2 follows.
The given series is an alternating series, meaning it consists of two interleaved sub-series. We need to identify the pattern in each sub-series to find the missing number.
Correct Option: C) 10
The problem requires us to rearrange the digits of a given number in ascending order and then find the sum of two specific digits from the new arrangement: the second digit from the left and the second digit from the right.
C) 10 is the sum of the second digit from the left (3) and the second digit from the right (7) in the new number.
This problem involves calculating the principal amount (sum borrowed) when a loan is repaid in equal annual installments under compound interest. We need to find the present value of each installment and sum them up to get the total principal borrowed.
Understand the formula for Present Value of an Installment:
If an installment \(X\) is paid at the end of \(n\) years at an interest rate \(R\) compounded annually, its present value (PV) is given by:
Identify the given values:
Calculate the present value of the first installment:
The first installment is paid at the end of 1 year. So, \(n=1\).
So, the present value of the first installment is Rs 840.
Calculate the present value of the second installment:
The second installment is paid at the end of 2 years. So, \(n=2\).
So, the present value of the second installment is Rs 800.
Calculate the total sum borrowed:
The total sum borrowed is the sum of the present values of all installments.
Therefore, the sum borrowed is Rs 1,640.
Correct Option: C) Rs 1,640
Match the columns.
| Group-I | Group-II |
| I. Mechanical barrier | A. Copper-T |
| II. Chemical method | B. Vasectomy |
| III. Device | C. Condom |
| IV. Surgical method | D. Pill |
I-C; II-D; III-A; IV-B
I-C; II-A; III-B; IV-D
I-C; II-B; III-D; IV-A
I-C; II-A; III-D; IV-B
The question asks to match different contraceptive methods (Group-II) with their respective categories (Group-I). We need to identify the type of contraceptive method for each item in Group-II and then match it correctly with Group-I.
A) I-C; II-D; III-A; IV-B
This combination correctly matches all the items.
This problem involves setting up equations based on the given age ratios at different points in time (past and future). We will use variables to represent the current ages of the son and father, then form equations based on the given ratios. Solving these equations will give us their current ages, from which we can find the positive difference.
Let the current age of the son be \(S\) years and the current age of the father be \(F\) years.
Four years ago: Their ages were \(S-4\) and \(F-4\). The ratio was 2:7.
\[ \frac{S-4}{F-4} = \frac{2}{7} \] Cross-multiplying gives: \[ 7(S-4) = 2(F-4) \] \[ 7S - 28 = 2F - 8 \] \[ 7S - 2F = 20 \quad \text{(Equation 1)} \]Ten years hence (from now): Their ages will be \(S+10\) and \(F+10\). The ratio will be 3:7.
\[ \frac{S+10}{F+10} = \frac{3}{7} \] Cross-multiplying gives: \[ 7(S+10) = 3(F+10) \] \[ 7S + 70 = 3F + 30 \] \[ 7S - 3F = 30 - 70 \] \[ 7S - 3F = -40 \quad \text{(Equation 2)} \]Solve the system of equations: We have two linear equations:
Equation 1: \(7S - 2F = 20\)
Equation 2: \(7S - 3F = -40\)
Subtract Equation 2 from Equation 1:
\[ (7S - 2F) - (7S - 3F) = 20 - (-40) \] \[ 7S - 2F - 7S + 3F = 20 + 40 \] \[ F = 60 \]So, the father's current age is 60 years.
Substitute \(F=60\) into Equation 1 to find \(S\):
\[ 7S - 2(60) = 20 \] \[ 7S - 120 = 20 \] \[ 7S = 140 \] \[ S = \frac{140}{7} \] \[ S = 20 \]So, the son's current age is 20 years.
Calculate the positive difference between their ages:
\[ \text{Difference} = F - S = 60 - 20 = 40 \]The positive difference between their ages is 40 years.
A) 40 years is the correct difference calculated from the current ages of the father (60 years) and the son (20 years).
The question asks for the launch year of the SVAMITVA Scheme. This requires knowledge of current affairs and government schemes, specifically their initiation dates.
D) 2020 — The SVAMITVA Scheme was launched on April 24, 2020, by the Prime Minister of India, Narendra Modi, on the occasion of National Panchayati Raj Day. It is a Central Sector Scheme of the Ministry of Panchayati Raj.
This problem involves ordering six friends based on their ages using a series of comparative statements. We will deduce the relative ages of the friends step-by-step to determine who is the youngest.
The complete order from oldest to youngest is: Moni > Arjun > (Bindi/Himesh) > (Bindi/Himesh/Saya) > Saya > Pankaj (or Moni > Arjun > Bindi > Saya > Himesh > Pankaj or Moni > Arjun > Himesh > Bindi > Saya > Pankaj, etc. The exact order of Bindi, Saya, and Himesh among themselves isn't fully determined, but Pankaj is definitely the youngest).
Correct Option: B) Pankaj is the youngest.
This question tests the understanding of Faraday's Law of Electromagnetic Induction and Ohm's Law. We need to analyze how the induced electromotive force (EMF) and induced current depend on the resistance (R) of the coil.
C) induced EMF does not depend on R but induced current does. This statement accurately reflects the principles of electromagnetic induction and Ohm's Law.
The question asks to identify the cricket team that achieved the historic milestone of playing 1000 One Day International (ODI) matches in February 2022. This is a factual question related to cricket history and current affairs.
Correct Option: C) India