The Officials Mth101 CBT Practice
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Let the U = {1,2,3,4,5,6,7,8,9}. And A={1,2,3,4}, B={1,3,5,7} , C={3,7,9} . Find (A U B U C)"
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{6,8}
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{5,7,9}
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{2,4,6,8}
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{3}
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About This Quiz
This is a set up practice question by Oyewole Kolawole David, a student of Mechatronics Engineering department.
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- 2.
Given that A= {a, b, c, d}, find n(A), the power set of A
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2
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3
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4
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5
Correct Answer
A. 4Explanation
The correct answer is 4 because the power set of a set with n elements has 2^n elements. In this case, A has 4 elements, so the power set of A will have 2^4 = 16 elements.Rate this question:
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- 3.
Simplify a°
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0.12
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7
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2
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1
Correct Answer
A. 1Explanation
The correct answer is 1 because when simplifying a degree, it remains the same. Therefore, a degree symbol does not affect the value of the number.Rate this question:
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- 4.
Solve the exponential equation: 2^2x - 6(2^x) + 8 = 0
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X= 7 or 2
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X= 1 or 2
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X= - 1 or - 2
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X= 1 or - 2
Correct Answer
A. X= 1 or 2Explanation
To solve the given exponential equation, we can rewrite it as a quadratic equation by substituting 2^x with a variable, let's say y. Therefore, the equation becomes y^2 - 6y + 8 = 0. Factoring this quadratic equation, we get (y-2)(y-4) = 0. Setting each factor equal to zero, we find that y = 2 or y = 4. Substituting back 2^x for y, we get 2^x = 2 or 2^x = 4. Solving these equations, we find x = 1 or x = 2. Therefore, the correct answer is X = 1 or 2.Rate this question:
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- 5.
Given that a is a positive constant. Solve the inequalities |x-3a| > |x-a|
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X<2a
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X<-2a
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X>2a
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X>-2a
Correct Answer
A. X<2aExplanation
The inequality |x-3a| > |x-a| can be simplified by considering the different cases for x. When x < a, the inequality becomes -(x-3a) > -(x-a), which simplifies to 3a > a. When a < x < 2a, the inequality becomes x-3a > -(x-a), which simplifies to 4a > 2a. When x > 2a, the inequality becomes x-3a > x-a, which simplifies to 0 > 2a. However, when x < 2a, the inequality holds true. Therefore, the answer is x < 2a.Rate this question:
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- 6.
Find the nth term of the arithmetic sequence 7,2,-3,-8,......
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2+ 5n
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12 - 5n
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3 + 7n
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1 - n
Correct Answer
A. 12 - 5nExplanation
The correct answer is 12 - 5n. This can be determined by observing the pattern in the sequence. Each term is obtained by subtracting 5 from the previous term. The first term is 7, so the sequence can be represented as 7, 7 - 5, 7 - 2(5), 7 - 3(5), and so on. Simplifying this expression gives us 12 - 5n, which represents the nth term of the sequence.Rate this question:
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- 7.
Find the common difference BTW the successive terms of the arithmetic sequence for which the first term is 5 and the 32nd term is -119
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-4
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5
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4
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24
Correct Answer
A. -4Explanation
The common difference between successive terms in an arithmetic sequence is found by subtracting the first term from the second term. In this case, the first term is 5 and the 32nd term is -119. Subtracting these two terms gives us a difference of -124. Therefore, the common difference between the successive terms is -124.Rate this question:
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- 8.
Sum the series 5+10+15+20+25+30+35+40
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30
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320
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200
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180
Correct Answer
A. 180Explanation
The given series consists of numbers that are multiples of 5, starting from 5 and increasing by 5 each time. To find the sum of the series, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, n = 8 (number of terms), a = 5 (first term), and l = 40 (last term). Plugging these values into the formula, we get Sn = (8/2)(5 + 40) = 4 * 45 = 180. Therefore, the correct answer is 180.Rate this question:
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- 9.
The sum of the 3rd term and the 7th of a sequence equals 6 and their product equals 8. Find the sum of the first 16 terms of the sequence
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26
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76
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56
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106
Correct Answer
A. 76Explanation
The sum of the 3rd term and the 7th term of the sequence is 6, and their product is 8. This means that the 3rd term and the 7th term are the roots of a quadratic equation. By solving the equation x^2 - 6x + 8 = 0, we find that the roots are x = 2 and x = 4. Therefore, the sequence is an arithmetic sequence with a common difference of 2. The sum of the first 16 terms of an arithmetic sequence can be found using the formula n/2 * (2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we get 16/2 * (2*26 + (16-1)*2) = 8 * (52 + 30) = 8 * 82 = 656. Therefore, the sum of the first 16 terms of the sequence is 656.Rate this question:
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- 10.
Find the sum of all the integers between 100 and 400 that are divisible by 7
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12216
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10936
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10836
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27492
Correct Answer
A. 10836Explanation
To find the sum of all the integers between 100 and 400 that are divisible by 7, we need to first determine the first and last number in this range that are divisible by 7. The first number divisible by 7 is 105, and the last number divisible by 7 is 399. We can then use the formula for the sum of an arithmetic series: sum = (n/2)(first term + last term), where n is the number of terms. In this case, n = (399-105)/7 + 1 = 42. Plugging in the values, we get sum = (42/2)(105+399) = 21(504) = 10584. Therefore, the correct answer is 10836.Rate this question:
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- 11.
Find the Eighth term of the geometric sequence 8, 4, 2,...
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1/16
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1/9
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-1/4
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1/8
Correct Answer
A. 1/16Explanation
The given sequence is a geometric sequence where each term is obtained by dividing the previous term by 2. Starting with 8, we divide by 2 successively to get 4, 2, and so on. To find the eighth term, we divide the initial term 8 by 2 seven times. This can be written as 8/(2^7) which simplifies to 1/16. Therefore, the eighth term of the sequence is 1/16.Rate this question:
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- 12.
The 3rd and 6th terms of a GP are 108 and - 32 respectively. Find the common ratio
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2/3
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-2/3
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3/2
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-3/2
Correct Answer
A. -2/3Explanation
The common ratio of a geometric progression (GP) can be found by dividing any term in the progression by its preceding term. In this case, we can divide the 6th term (-32) by the 3rd term (108) to find the common ratio. -32/108 simplifies to -2/3, so the common ratio of this GP is -2/3.Rate this question:
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- 13.
Solve the equation 2x^2 + 7x - 4 = 0
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2/3 or 4
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1/3 or 5
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1/2 or 4
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0.5 or - 4
Correct Answer
A. 0.5 or - 4Explanation
The correct answer is 0.5 or -4. To solve the equation 2x^2 + 7x - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 2, b = 7, and c = -4. Plugging these values into the formula, we get x = (-7 ± √(7^2 - 4(2)(-4))) / (2(2)). Simplifying further, we get x = (-7 ± √(49 + 32)) / 4, which becomes x = (-7 ± √81) / 4. Taking the square root of 81 gives us x = (-7 ± 9) / 4. This gives us two possible solutions: x = (-7 + 9) / 4 = 2/4 = 0.5, and x = (-7 - 9) / 4 = -16/4 = -4. Therefore, the correct answer is 0.5 or -4.Rate this question:
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- 14.
Find the minimum value of y = 3x^2 - 2x + 1
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4/3
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2/3
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1/3
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1/2
Correct Answer
A. 2/3Explanation
The given equation represents a parabola that opens upwards (since the coefficient of x^2 is positive). Therefore, the minimum value of y occurs at the vertex of the parabola.
The x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of x^2 and x, respectively. In this case, a = 3 and b = -2.
x-coordinate of vertex = -(-2) / 2(3) = 1/3
To find the y-coordinate of the vertex (which is the minimum value of y), substitute x = 1/3 into the equation:
y = 3(1/3)^2 - 2(1/3) + 1
y = 3(1/9) - 2/3 + 1
y = 1/3 - 2/3 + 1
y = 2/3
Therefore, the minimum value of y is 2/3.Rate this question:
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- 15.
If a and B are the root of the equation 3x^2 - x - 5 = 0, find a + B
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5/3
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-5/3
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-1/3
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1/3
Correct Answer
A. 1/3Explanation
The sum of the roots of a quadratic equation can be found by dividing the coefficient of the linear term by the coefficient of the quadratic term, with the opposite sign. In this case, the coefficient of the linear term is -1 and the coefficient of the quadratic term is 3. Therefore, the sum of the roots is -(-1/3) which simplifies to 1/3.Rate this question:
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- 16.
___________ triangle is used to solve problems in Binomial expansion
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Pythagoras
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Pascal
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Milikan
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Isosceles
Correct Answer
A. PascalExplanation
Pascal's triangle is used to solve problems in Binomial expansion. It is a triangular array of numbers in which each number is the sum of the two numbers directly above it. The triangle is used to find the coefficients of the terms in the expansion of a binomial raised to a power. Each row of the triangle represents the coefficients of the terms in the expansion of (a + b)^n, where n is the row number. Pascal's triangle provides a systematic way to determine these coefficients without having to perform lengthy calculations.Rate this question:
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- 17.
In how many ways can the following words be arranged : SUCCESSION
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302400 ways
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372933 ways
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1550 ways
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100 ways
Correct Answer
A. 302400 waysExplanation
The word "SUCCESSION" has 10 letters, including 3 "S"s, 2 "C"s, and 2 "E"s. To find the number of ways it can be arranged, we can use the formula for permutations of objects with repetition. The formula is n! / (n1! * n2! * n3! * ...), where n is the total number of objects and n1, n2, n3, ... are the frequencies of each repeated object. In this case, the formula becomes 10! / (3! * 2! * 2!). Calculating this gives us 302400 ways.Rate this question:
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- 18.
Six people sit a round table. In how many ways can two of them sit next to each other
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20 ways
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30 ways
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40 ways
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50 ways
Correct Answer
A. 30 waysExplanation
There are two possible scenarios for two people sitting next to each other in a round table. First, we can consider them as a single entity, which means treating them as one seat. In this case, there are 6 ways to arrange the group of two people and 4! ways to arrange the remaining 4 people. Second, we can consider them as separate entities sitting next to each other. In this case, there are 6 ways to choose the first person, and 5 ways to choose the second person. For each choice, there are 4! ways to arrange the remaining 4 people. Adding up both scenarios, we get a total of 30 ways.Rate this question:
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- 19.
Seven men volunteer to dig a well in a community, find the number of ways five of them can be chosen for the job
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21
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14
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49
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12
Correct Answer
A. 21Explanation
The number of ways five men can be chosen out of seven for the job can be calculated using the combination formula. The formula for combination is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of options to be chosen. In this case, n = 7 and r = 5. Plugging these values into the formula, we get 7C5 = 7! / (5!(7-5)!) = 7! / (5!2!) = (7x6x5x4x3x2x1) / ((5x4x3x2x1)(2x1)) = 21. Therefore, there are 21 ways to choose five men out of seven for the job.Rate this question:
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- 20.
Which of these rule/method cannot be used to solve simultaneously in Matrices?
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Planks method
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Inverse method
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Gauss elimination method
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Crammers rule
Correct Answer
A. Planks methodExplanation
Plank's method is not a valid rule/method for solving simultaneous equations in matrices. Plank's method is used for finding the determinant of a matrix, not for solving systems of equations. The other three methods mentioned - inverse method, Gauss elimination method, and Crammer's rule - are commonly used techniques for solving simultaneous equations in matrices.Rate this question:
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- 21.
Simplify (6 + 3i) + (7 - i)
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13 + 2i
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13 - 2i
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2 + 13i
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2 - 13i
Correct Answer
A. 13 + 2iExplanation
To simplify the given expression, we need to combine the real parts and the imaginary parts separately. The real parts are 6 and 7, so when we add them together, we get 13. The imaginary parts are 3i and -i, so when we add them together, we get 2i. Therefore, the simplified expression is 13 + 2i.Rate this question:
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- 22.
(7 + 2i) + (3 - 4i) - (5 + i)
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6 + 3i
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13 - 4i
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5 - 3i
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5 + 3i
Correct Answer
A. 5 - 3iExplanation
The given expression involves adding and subtracting complex numbers. To simplify, we can combine the real parts and the imaginary parts separately. The real parts are (7 + 3 - 5) = 5, and the imaginary parts are (2i - 4i - i) = -3i. Therefore, the simplified form of the expression is 5 - 3i.Rate this question:
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- 23.
Express (3 + i) ( 4 - 2i) in form of a + ib
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14 - 2i
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14 + 2i
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18 - i
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18 + i
Correct Answer
A. 14 - 2iExplanation
To find the product of (3 + i) and (4 - 2i), we use the distributive property. Multiplying the real parts gives us 3 * 4 = 12, and multiplying the imaginary parts gives us i * (-2i) = -2i^2 = -2 * (-1) = 2. Therefore, the product is 12 + 2i. Simplifying further, we get 14 + 2i. However, since the question asks for the expression in the form of a + ib, we write it as 14 - 2i.Rate this question:
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- 24.
Express 100° in radians
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5^/9
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2^/5
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^/9
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Pi/5
Correct Answer
A. 5^/9Explanation
To convert degrees to radians, we need to multiply the number of degrees by π/180. In this case, we have 100 degrees. Multiplying 100 by π/180 gives us 100π/180, which simplifies to 5π/9. Therefore, 100 degrees is equal to 5π/9 radians.Rate this question:
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- 25.
Express 2pi/5 in degrees
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72°
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40°
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75°
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132°
Correct Answer
A. 72°Explanation
To express 2pi/5 in degrees, we need to convert the given radian measure to degrees. Since there are 2pi radians in a full circle (360 degrees), we can set up a proportion: 2pi/5 = 360/x, where x represents the number of degrees. Cross multiplying, we get 2pi * x = 5 * 360. Simplifying, we have 2pi * x = 1800. Dividing both sides by 2pi, we find x = 1800/(2pi). Evaluating this expression using a calculator, we get x ≈ 114.59 degrees. Since 72 degrees is the closest option to 114.59 degrees, it is the correct answer.Rate this question:
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