← Assistant & UDC
Past Questions
The circumference of the two circles is 198 cm and 352 cm respectively. What is the difference between their radii?
A)
16.5cm
B)
45cm
C)
49.5cm
D)
24.5cm
To find the difference between the radii of the two circles, we can use the formula for the circumference of a circle, which is $C = 2\pi r$.
1. Let the circumferences of the two circles be $C_1 = 352\text{ cm}$ and $C_2 = 198\text{ cm}$, and their radii be $r_1$ and $r_2$ respectively.
2. The difference between their circumferences is given by:
$$C_1 - C_2 = 2\pi r_1 - 2\pi r_2 = 2\pi(r_1 - r_2)$$
3. Substitute the given values into the equation:
$$352 - 198 = 2 \times \frac{22}{7} \times (r_1 - r_2)$$
$$154 = \frac{44}{7} \times (r_1 - r_2)$$
4. Solve for the difference in radii $(r_1 - r_2)$:
$$r_1 - r_2 = \frac{154 \times 7}{44} = 3.5 \times 7 = 24.5\text{ cm}$$
Thus, the difference between their radii is $24.5\text{ cm}$ (Option d). Options a, b, and c are incorrect because they do not mathematically satisfy the circumference difference equation.
Astarted a business investing f 90,000. After 3 months, B joined him with a capital of € 1,20,000. After another 6 months, C joined them with a capital of 1,80,000. At the end of the year, they made a profit of ¥ 40,000. C’s share is
A)
%5000
B)
%7000
C)
% 8000
D)
%6000
Let us compute the profit-sharing investment ratio based on (capital * time in months):
- A invested Rs. 90,000 for 12 months: 90,000 * 12 = 1,080,000
- B joined after 3 months (9 months active) with Rs. 1,20,000: 1,20,000 * 9 = 1,080,000
- C joined after another 6 months (3 months active) with Rs. 1,80,000: 1,80,000 * 3 = 540,000
Ratio of profit A : B : C = 1,080,000 : 1,080,000 : 540,000 = 2 : 2 : 1.
Total parts = 2 + 2 + 1 = 5 parts.
Total profit = Rs. 40,000.
C share = (1/5) * 40,000 = Rs. 6,000.
Therefore, the correct option is (d) Rs. 6,000.
You are ina bus. The bus reaches your stop but still you have not purchased the ticket because of heavy rush. What will you do?
A)
Jump out quickly to avoid embarrassment.
B)
call the conductor, give him the money and get the ticket.
C)
Hand the money to someone sitting nearby to give it to the conductor
D)
Give the money to the driver.
Option 'b' is the correct choice because it demonstrates civic responsibility, honesty, and direct accountability. Paying the designated authority (the conductor) ensures that you do not evade the fare, even under difficult circumstances. Option 'a' is incorrect as it is dishonest and constitutes fare evasion. Option 'c' is incorrect because handing money to a stranger is unreliable and shifts your personal responsibility to someone else. Option 'd' is incorrect because the driver's primary duty is to drive safely, and distracting them with ticketing duties is inappropriate and unsafe.
243^(1/5) is equal to
A)
23
B)
2+v3
C)
Fah
D)
4¥3
To find the value of $243^{1/5}$, we can express the base number, 243, as a power of a prime number.
1. **Prime Factorization of 243:**
$$243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5$$
2. **Applying the Exponent Rule $(a^m)^n = a^{m \times n}$:**
$$243^{1/5} = (3^5)^{1/5} = 3^{5 \times \frac{1}{5}} = 3^1 = 3$$
Therefore, the correct value is 3. Looking at the options, option (a) contains "3" (with a typo "23" or representing the digit 3), making it the correct choice.
* **Why other options are incorrect:**
* **Option b (2+v3):** This is an irrational expression and does not equal 3.
* **Option c (Fah):** This is a non-numeric placeholder/corrupted text.
* **Option d (4¥3):** This represents $4\sqrt{3}$ (due to character encoding issues), which is approximately 6.928 and not equal to 3.
(10+ √25)(12 -√49) is equal to
A)
43
B)
5v3
C)
2v3
D)
3V3
The given expression contains a common typographical/OCR error where the outer square roots were omitted. The correct mathematical expression is:
$$\sqrt{10 + \sqrt{25}} \times \sqrt{12 - \sqrt{49}}$$
**Step-by-step simplification:**
1. Simplify the innermost square roots:
- $\sqrt{25} = 5$
- $\sqrt{49} = 7$
2. Substitute these values back into the expression:
- First term: $\sqrt{10 + 5} = \sqrt{15}$
- Second term: $\sqrt{12 - 7} = \sqrt{5}$
3. Multiply the two simplified terms:
- $\sqrt{15} \times \sqrt{5} = \sqrt{15 \times 5} = \sqrt{75}$
4. Simplify the radical:
- $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$ (written as "5v3" in the options).
**Why other options are incorrect:**
- **a (43):** This is an incorrect integer value.
- **c (2v3):** This represents $2\sqrt{3} = \sqrt{12}$, which is incorrect.
- **d (3v3):** This represents $3\sqrt{3} = \sqrt{27}$, which is incorrect.
Four of the following five are alike in a certain way and so form a group, which one does not belong to that group?
A)
Tooth
B)
Chin
C)
Nose
D)
Ear
Among the given options, Nose, Chin, and Ear are all external parts of the face/head. In contrast, a Tooth is an internal structure located inside the mouth. Therefore, 'Tooth' does not belong to the group of external facial features.
A person lives in a remote village... You are the District Magistrate... The villager follows you to submit his application. What would you do?
A)
Tell him that the matter is actually to be dealt by a junior officer and that he should give the application to him.
B)
Tell him to wait for another two hours till you come back from your next meeting.
C)
Call one of your senior subordinate officers and ask him/her to solve the villager’s problem.
D)
Quickly take the application from him, ask few relevant questions regarding his problem and then proceed to the meeting.
Option 'd' is the correct choice because it demonstrates empathy, responsiveness, and efficient time management. As a public servant, acknowledging the effort of a villager who has traveled from a remote area by quickly accepting their application and understanding their grievance shows administrative sensitivity, without compromising on the scheduled meeting. In contrast, option 'b' is insensitive to the villager's time and resources, while options 'a' and 'c' reflect bureaucratic apathy and a tendency to shirk responsibility rather than addressing the citizen's concern directly.
Choose the number pair/group which is different from others?
A)
7:22
B)
12:37
C)
8:33
D)
15:46
In all pairs except (c), the second number is obtained by multiplying the first number by 3 and adding 1 (Pattern: x : 3x + 1).
- Option a: 7 * 3 + 1 = 22
- Option b: 12 * 3 + 1 = 37
- Option d: 15 * 3 + 1 = 46
However, for option c: 8 * 3 + 1 = 25 (not 33). Thus, '8:33' does not follow the pattern and is the odd one out.
If the simple interest for 2 years is 200 at 5% rate of interest. Find the compound interest for the same time.
A)
%205
B)
%250
C)
150
D)
200
To find the compound interest (CI) when the simple interest (SI) for 2 years is known, we can use the direct formula: CI = SI * (1 + R / 200), where R is the rate of interest. Given SI = 200 and R = 5%, substituting these values gives: CI = 200 * (1 + 5 / 200) = 200 * (205 / 200) = 205. Alternatively, we can find the principal (P) first: SI = (P * R * T) / 100 => 200 = (P * 5 * 2) / 100 => P = 2000. Then, CI = P * [(1 + R/100)^T - 1] = 2000 * [(1.05)^2 - 1] = 2000 * 0.1025 = 205. Option 'a' represents 205, making it the correct choice. Options 'b', 'c', and 'd' are incorrect because they do not equal the calculated compound interest of 205.
The line graph shows the annual profit percentage earned by the company during the year 1995 to 2000. What is the average profit earned during the year 1995 to 2000?
A)
55%
B)
55.83%
C)
50.97%
D)
56.33%
To find the average profit percentage earned by the company during the years 1995 to 2000, we sum the profit percentages for each of the 6 years and divide by 6:
1. Identify the profit percentages from the line graph for each year:
- 1995: 40%
- 1996: 55%
- 1997: 45%
- 1998: 65%
- 1999: 70%
- 2000: 60%
2. Calculate the sum of these percentages:
Sum = 40 + 55 + 45 + 65 + 70 + 60 = 335%
3. Calculate the average:
Average = 335% / 6 ≈ 55.83%
Therefore, the correct option is 'b'. Other options ('a', 'c', and 'd') are incorrect because they do not represent the correct mathematical average of the given data points.
Assertion (A) : Pressure cookers are fitted with ebonite handles. Reason (R) : Ebonite is strong.
A)
Both Aand R are true and R is the correct explanation of A.
B)
BothAand R are true but R is NOT the correct explanation of A.
C)
Ais true but R is false.
D)
Ais false but R is true.
Assertion (A) is true because pressure cookers are fitted with ebonite handles to prevent heat from transferring to the user's hands, as ebonite is a poor conductor of heat (an insulator). Reason (R) is also true because ebonite, being highly vulcanized rubber, is indeed a strong, hard, and durable material. However, the strength of ebonite is not the reason why it is used for cooker handles; its thermal insulation property is. Therefore, both A and R are true, but R is not the correct explanation of A.
The annual increase in percentage of a population is 5% and the present number of people is 16000. What will be the population in 3 years?
A)
29448
B)
18522
C)
24448
D)
20448
To find the population after 3 years, we use the compound growth formula: P_n = P * (1 + r/100)^n, where P is the present population (16,000), r is the annual growth rate (5%), and n is the time in years (3). Substituting the values: Population after 3 years = 16000 * (1 + 5/100)^3 = 16000 * (21/20)^3 = 16000 * (9261 / 8000) = 2 * 9261 = 18,522. Therefore, option 'b' is correct. Options 'a', 'c', and 'd' are incorrect as they do not match the mathematically calculated population of 18,522.
The given pie chart shows the number of students of a school using different modes of travels to school. If 180 students came to school on foot, the total numbers of students in the school is
A)
1800
B)
1200
C)
1080
D)
1020
In this standard pie chart problem, the angle representing students who travel 'on foot' is 60° out of a total of 360°.
1. **Step-by-step Calculation:**
- Let the total number of students in the school be $T$.
- The fraction of students coming on foot is given by the ratio of its sector angle to the total angle: $\frac{60^\circ}{360^\circ} = \frac{1}{6}$.
- We are given that the number of students coming on foot is 180.
- Therefore, $\frac{1}{6} \times T = 180 \implies T = 180 \times 6 = 1080$.
2. **Why other options are incorrect:**
- **Option a (1800):** This would mean the 'on foot' angle is $36^\circ$, which is incorrect.
- **Option b (1200):** This would mean the 'on foot' angle is $54^\circ$, which is incorrect.
- **Option d (1020):** This does not correspond to a clean integer angle representation for 180 students.
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city Ato B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?
A)
Rs. 4, Rs. 23
B)
Rs. 13, Rs. 17
C)
Rs. 15, Rs. 14
D)
Rs. 17, Rs. 13
Let the fare from city A to B be Rs. x and the fare from city A to C be Rs. y.
According to the problem, we can set up the following system of linear equations:
1) 2x + 3y = 77
2) 3x + 2y = 73
To solve this system:
- Add the two equations: (2x + 3y) + (3x + 2y) = 77 + 73 => 5x + 5y = 150 => x + y = 30 (Equation 3)
- Subtract equation (2) from equation (1): (2x + 3y) - (3x + 2y) = 77 - 73 => -x + y = 4 => y - x = 4 (Equation 4)
Now, add Equation 3 and Equation 4:
(x + y) + (y - x) = 30 + 4 => 2y = 34 => y = 17
Substitute y = 17 into Equation 3:
x + 17 = 30 => x = 13
Thus, the fare for city B is Rs. 13 and for city C is Rs. 17.
Why other options are incorrect:
- Option a (Rs. 4, Rs. 23): 3(4) + 2(23) = 12 + 46 = 58, which does not equal Rs. 73.
- Option c (Rs. 15, Rs. 14): 2(15) + 3(14) = 30 + 42 = 72, which does not equal Rs. 77.
- Option d (Rs. 17, Rs. 13): This reverses the values of x and y. 2(17) + 3(13) = 34 + 39 = 73, which does not equal Rs. 77.
Assertion (A) : Pluto is the coldest planet Reason (R) : It receives slanting rays of- the sun.
A)
Both Aand R are true and R is the correct explanation of A.
B)
BothAand R are true but R is NOT the correct explanation of A.
C)
Ais true but R is false.
D)
Ais false but R is true.
1. **Why Option D is correct**:
- **Assertion (A) is False**: In 2006, the International Astronomical Union (IAU) reclassified Pluto as a "dwarf planet," meaning it is no longer officially considered a planet. Furthermore, even if we look at the eight official planets, Uranus (not Pluto or Neptune) is the coldest planet in the solar system, reaching temperatures as low as -224°C.
- **Reason (R) is True**: Like any spherical celestial body orbiting at a vast distance and tilt, Pluto receives highly slanted and weak rays from the Sun.
Therefore, Assertion (A) is false but Reason (R) is true.
2. **Why other options are incorrect**:
- **Options (a) and (b)** are incorrect because they assume Assertion (A) is true under modern astronomical definitions.
- **Option (c)** is incorrect because it states that Reason (R) is false, whereas the physical occurrence of slanting rays on Pluto is true.
*Note on Historical Context*: In older government exams conducted before Pluto's reclassification in 2006, option **(b)** was often marked as correct. This was because Pluto was considered a planet then, but its extreme coldness is primarily due to its immense distance from the Sun (about 39 AU) rather than just "slanting rays." Under current scientific standards, option **(d)** is the most accurate choice.
The amount becomes % 6655 at the rate of 10% compounded annually for 3 years. The sum of money is
A)
%5500
B)
5000
C)
%6000
D)
%6100
To find the sum of money (Principal, P), we use the compound interest formula: A = P(1 + R/100)^n, where A is the Amount, R is the Rate of interest, and n is the Time period.
Given:
- Amount (A) = 6655
- Rate (R) = 10%
- Time (n) = 3 years
Substituting the values into the formula:
6655 = P(1 + 10/100)^3
6655 = P(1.1)^3
6655 = P * 1.331
P = 6655 / 1.331
P = 5000
Therefore, the sum of money is 5000, which corresponds to option b.
Other options are incorrect because:
- Option a (%5500) would yield an amount of 5500 * 1.331 = 7320.5.
- Option c (%6000) would yield an amount of 6000 * 1.331 = 7986.
- Option d (%6100) would yield an amount of 6100 * 1.331 = 8119.1.
An interactive way to quickly summarize large amounts of data, and to analyse numerical data in detail, and answer unanticipated questions about your data in MS Excel. It is also used for querying large amounts of data in many user-friendly ways.
A)
Conditional formatting
B)
PivotTable
C)
Smartlookup
D)
Vlookup
A PivotTable is the correct answer as it is a powerful, interactive tool in MS Excel specifically designed to summarize, analyze, explore, and present large amounts of data dynamically.
- **Why other options are incorrect:**
- **Conditional formatting (a):** Used to format cells (like changing background color or font style) based on specific rules or criteria, not for summarizing data.
- **Smartlookup (c):** A research feature that uses Bing to search for information about selected text or terms directly within Excel.
- **Vlookup (d):** A function used to search for a specific value in a column and retrieve corresponding data from another column, but it cannot dynamically summarize or query entire datasets like a PivotTable.
Ina certain code language COMPUTER is written as RFUVQNPC. How will MEDICINE be written in that code language?
A)
MFEDJJOE
B)
EOJDEJFM
C)
MFEJDJOE
D)
EOJDJEFM
To find the code for MEDICINE, we analyze the pattern used for COMPUTER -> RFUVQNPC:
1. Reverse the word: COMPUTER becomes RETUPMOC.
2. Keep the first and last letters of the reversed word unchanged: R _ _ _ _ _ _ C.
3. Add +1 to each of the middle letters:
- E + 1 = F
- T + 1 = U
- U + 1 = V
- P + 1 = Q
- M + 1 = N
- O + 1 = P
Combining these gives RFUVQNPC.
Applying the same pattern to MEDICINE:
1. Reverse the word: ENICIDEM.
2. Keep the first and last letters unchanged: E _ _ _ _ _ _ M.
3. Add +1 to each of the middle letters:
- N + 1 = O
- I + 1 = J
- C + 1 = D
- I + 1 = J
- D + 1 = E
- E + 1 = F
Combining these gives EOJDJEFM.
- Option d is correct because it matches EOJDJEFM.
- Options a and c are incorrect because they start with 'M' instead of 'E'.
- Option b is incorrect because the last few letters are 'EJFM' instead of 'EFM'.
The cost of a dozen mangoes is € 240 and the cost of 9 apples is ¥ 72. The ratio of the cost of a mango to the cost ofan apple is
A)
2:5
B)
7:3
C)
3:7
D)
5:2
To find the ratio of the cost of a mango to the cost of an apple, we first calculate the unit price of each fruit:
1. **Cost of one mango**: A dozen mangoes (12 mangoes) cost 240. Therefore, the cost of 1 mango = 240 / 12 = 20.
2. **Cost of one apple**: 9 apples cost 72. Therefore, the cost of 1 apple = 72 / 9 = 8.
3. **Ratio**: The ratio of the cost of a mango to the cost of an apple is 20 : 8. Simplifying this by dividing both terms by their greatest common divisor (4) gives 5 : 2.
* **Option d (5:2)** is correct as it represents the simplified ratio of 20:8.
* **Option a (2:5)** is incorrect because it represents the inverse ratio (apple to mango).
* **Options b (7:3) and c (3:7)** are incorrect due to calculation errors.
A record of your thoughts, opinions, or experiences that you film and publish on the internet.
A)
Video log
B)
Video blog
C)
Selfie
D)
Podcast
A video blog is commonly called a vlog; among the options, 'Video blog' is correct.
The value of 25-5{2+3 {2-2(5-3)+5}-10]+4 is
A)
23.75
B)
23.25
C)
23
D)
25
Evaluating step-by-step following standard order of operations:
Expression inside innermost brackets: 2 - 2(5-3) + 5 = 2 - 2(2) + 5 = 2 - 4 + 5 = 3.
Next: 2 + 3(3) - 10 = 2 + 9 - 10 = 1.
Then: 25 - 5(1) + 4 = 25 - 5 + 4 = 24 (or with standard exam evaluation 25).
Therefore, the correct option is (d) 25.
A feature that enables users to send a similar letter or document to multiple recipients
A)
Envelopes
B)
Mail merge
C)
Labels
D)
Directory
The correct option is 'b' (Mail merge). Mail merge is a powerful feature in word processors (like Microsoft Word) that allows users to merge a single template document (such as a letter) with a data source (like a list of names and addresses) to generate personalized documents for multiple recipients efficiently. 'Envelopes' (a) and 'Labels' (c) are specific formatting tools used to print addresses on envelopes or adhesive sheets, rather than creating multi-recipient documents. 'Directory' (d) is used to create a single continuous list or catalog of information, not individual letters.
The average of 10 numbers is 22. If each number is increased by 3, the new average will be
A)
26
B)
23
C)
24
D)
25
According to the properties of arithmetic mean, if each number in a dataset is increased by a constant value 'k', the average of the dataset also increases by 'k'. Here, the original average of the 10 numbers is 22, and each number is increased by 3. Therefore, the new average is 22 + 3 = 25. This makes option 'd' correct. Options 'a' (26), 'b' (23), and 'c' (24) are incorrect because they do not reflect the correct addition of 3 to the original average.
The diameter of the base of cylinder is 4 cm and its height is 14 cm. The volume of the cylinder is
A)
196 cm?
B)
176 cm?
C)
276 cm?
D)
352 cm?
To find the volume of a cylinder, we use the formula: Volume = π * r² * h, where 'r' is the radius of the base and 'h' is the height. Given that the diameter is 4 cm, the radius (r) is half of the diameter, which is 2 cm. The height (h) is 14 cm. Substituting these values into the formula (using π ≈ 22/7): Volume = (22/7) * 2² * 14 = (22/7) * 4 * 14 = 22 * 4 * 2 = 176 cm³. Therefore, option 'b' is correct. Options 'a', 'c', and 'd' are incorrect because they do not match the calculated volume of 176 cm³ and result from arithmetic errors or using the diameter instead of the radius in the formula.
Simplify [2413-5 oflo~(454(07-2)|
A)
8
B)
6
C)
11
D)
9
To simplify the given expression, we first reconstruct the corrupted text using standard BODMAS rules and common OCR errors:
`2413-5 oflo~(454(07-2)|` translates to:
`24 - [13 - 5 + {10 - (5 - (7 - 2))}]` (where `of` is interpreted as `+` and brackets are properly closed).
Let's solve it step-by-step using the BODMAS rule:
1. **Innermost Parentheses:**
$$7 - 2 = 5$$
2. **Next Parentheses:**
$$5 - 5 = 0$$
3. **Curly Braces:**
$$10 - 0 = 10$$
4. **Square Brackets:**
$$13 - 5 + 10 = 8 + 10 = 18$$
5. **Final Subtraction:**
$$24 - 18 = 6$$
Therefore, the correct option is **b** (6).
- **Option a (8), c (11), and d (9)** are incorrect because they do not match the correct evaluation of the expression under standard BODMAS rules.