1.
Mathematics
If , then
Correct Answer
C. 4
Explanation
The pattern in the given sequence is that each number is obtained by multiplying the previous number by 2. Starting with 2, we multiply it by 2 to get 4, then multiply 4 by 2 to get 8, and finally multiply 8 by 2 to get 16. Therefore, the next number in the sequence would be obtained by multiplying 16 by 2, which equals 32.
2.
Let two complex number and,then
Correct Answer
B. -3
3.
Let z be a complex number, if and , then z=
Correct Answer
B.
4.
If and l,m are negative whereas n is positive then which of the following statement is true?
Correct Answer
C.
Explanation
If l and m are negative while n is positive, it means that both l and m have values less than zero while n has a value greater than zero. In this case, all of the given statements could be true because the "all of these" option implies that all the statements are true. Since we don't have any specific statements provided, we can't determine which ones are true, but we can conclude that it is possible for all of them to be true based on the given information.
5.
Real part of is:
Correct Answer
C. 2035
Explanation
The real part of a complex number is the part that does not involve the imaginary unit. In this case, the correct answer is 2035, as it is the only option that does not involve any imaginary unit. The other options (-2116 and 828) involve the imaginary unit, making them incorrect.
6.
For any two complex numbers, , which of the following is true?
Correct Answer
A.
Explanation
The given correct answer for this question is "The product of two complex numbers is a complex number." This statement is true because when we multiply two complex numbers, we use the distributive property and the fact that the product of two imaginary units is -1. Therefore, the result of the multiplication will always be a complex number with both a real and imaginary part.
7.
=
Correct Answer
A.
8.
If a set A contains 10 entries then no.of distinct functions from A to A is:
Correct Answer
D.
Explanation
The number of distinct functions from set A to set A can be calculated by taking the number of elements in set A (which is 10 in this case) and raising it to the power of the number of elements in set A. In this case, since set A contains 10 entries, the number of distinct functions from A to A would be 10^10.
9.
Each member of a sport club plays at least of soccer, rugby or tennis. The following information is known:
43 members play tennis, 11 play tennis and soccer, 6 play soccer and rugby, 84 play rugby or tennis, 68 play soccer or rugby and 4 play all three sports. How many members are there in sports club?.
Correct Answer
C. 97
10.
Which one of the following statements does represent the Venn Diagram given below:
Correct Answer
D.
11.
Set of residue classes modulo 4 is an abelian group w.r.t '+', then inverse of 3 is:
Correct Answer
C. 1
Explanation
In an abelian group, the inverse of an element is the element that, when added to the original element, results in the identity element (which is usually denoted as 0). In this case, the set of residue classes modulo 4 is an abelian group, so the inverse of 3 would be the element that, when added to 3, gives the identity element 0. The only option that satisfies this condition is 1, as 3 + 1 = 4, which is congruent to 0 modulo 4. Therefore, the correct answer is 1.
12.
Which of the following statements is/are true?
I) Any conditional and its Contrapositive are equivalent
II) Converse and Contrapositive are equivalent
III) Converse and Inverse are equivalent
IV) Inverse and Contrapositive are equivalent
Correct Answer
C. I and III only
Explanation
The correct answer is "I and III only".
Statement I is true because a conditional statement and its contrapositive have the same truth value. The contrapositive is formed by negating both the hypothesis and the conclusion of the conditional statement.
Statement III is also true because the converse and the inverse of a conditional statement have the same truth value. The converse is formed by switching the hypothesis and the conclusion of the conditional statement, while the inverse is formed by negating both the hypothesis and the conclusion.
Therefore, both statements I and III are true, while statements II and IV are not equivalent to the others.
13.
If the matrix AB is a zero matrix, then
Correct Answer
C. It is not necessary that either A=O or B=O or both are zero
Explanation
If the matrix AB is a zero matrix, it means that all the elements in the matrix AB are zero. In order for this to happen, it is not necessary for either matrix A or matrix B to be zero. It is also not necessary for both matrices A and B to be zero. There could be other combinations of non-zero matrices A and B that when multiplied together, result in a zero matrix AB. Therefore, it is not necessary that either A=O or B=O or both are zero.
14.
What must be the matrix X, if
Correct Answer
B. Option 2
15.
Which one do you like?
Correct Answer
A. 10
Explanation
The explanation for the given answer of 10 is not provided.
16.
Which one do you like?
Correct Answer
C. {1,-3}
Explanation
The correct answer is {1,-3} because it is the only option that includes a negative number.
17.
If orders of matrix B and C are and BA=C, then the order of matrix A is:
Correct Answer
B.
18.
The system:
has infinitely many solutions if
Correct Answer
D.
19.
When the polynomial is divided by , then remainder is 5. What is the value of constant k?
Correct Answer
D. 8
Explanation
When a polynomial is divided by a constant, the remainder is equal to the constant. In this case, the remainder is given as 5. Therefore, the value of constant k must be 5.
20.
Equation in which roots are double the roots of is:
Correct Answer
C.
21.
If is the complex cube root of unity then the value of is:
Correct Answer
A. 1
Explanation
The complex cube root of unity is a number that, when raised to the power of 3, equals 1. The possible values for the complex cube root of unity are 1, e^(2Ï€i/3), and e^(4Ï€i/3), where e is Euler's number and i is the imaginary unit. However, the given question does not specify which cube root of unity is being referred to. Since the answer is 1, it can be inferred that the question is referring to the principal cube root of unity, which is 1.
22.
Which of the following systems of equations has as solution set?
Correct Answer
D.
23.
The solution set for the equation is:
Correct Answer
C.
24.
Which of the following statements is/are valid about the degree of polynomial?
I) It cannot be positive and zero
II) It can be rational as well as irrational
III) It can be negative
Correct Answer
D. None of the statements are valid
25.
In partial fraction resolution then:
Correct Answer
B.
26.
There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?
Correct Answer
A.
Explanation
To find the probability, we need to calculate the number of favorable outcomes (selecting 1 girl and 2 boys) divided by the total number of possible outcomes. The number of ways to select 1 girl from 10 is 10C1, and the number of ways to select 2 boys from 15 is 15C2. The total number of ways to select 3 students from 25 is 25C3. Therefore, the probability is (10C1 * 15C2) / 25C3.
27.
Number of diagonals formed in a decagon is:
Correct Answer
B. 35
Explanation
A decagon is a polygon with 10 sides. To find the number of diagonals in a decagon, we can use the formula n(n-3)/2, where n represents the number of sides. Plugging in 10 for n, we get (10(10-3))/2 = 35. Therefore, the correct answer is 35.
28.
If then
Correct Answer
B. 56
Explanation
The given question "If then" does not provide any clear condition or statement to determine the answer. Therefore, it is not possible to generate a meaningful explanation for the given correct answer.
29.
A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two of the civil engineers will sit together?
Correct Answer
C.
Explanation
The total number of engineers is 16. To ensure that no two civil engineers sit together, we can alternate the seating arrangement between software engineers and civil engineers. The number of ways to arrange the software engineers is 10!, and the number of ways to arrange the civil engineers is 6!. Since the table is round, we need to divide the total number of arrangements by the number of engineers (16) to account for rotations. Therefore, the total number of ways to seat them is (10! * 6!) / 16.
30.
Correct Answer
A. 210
31.
Ifthen
Correct Answer
B.
32.
The infinite geometric seriesis a:
Correct Answer
B. Convergent series
Explanation
An infinite geometric series is a convergent series because it has a finite sum when the common ratio is between -1 and 1. In this type of series, each term is obtained by multiplying the previous term by a constant factor called the common ratio. As long as the common ratio is within the specified range, the terms of the series gradually decrease in magnitude and approach zero, resulting in a finite sum.
33.
Sum of the series is:
Correct Answer
B.
34.
How many term of the series :
Correct Answer
C. 8
35.
Which of the following may not be general term of an arithmetic sequence?
Correct Answer
D.
36.
For what value of n,may be A.M between and ?
Correct Answer
A.
37.
The infinite Geometric series
Correct Answer
B. Diverges
Explanation
An infinite geometric series diverges when the absolute value of the common ratio is greater than or equal to 1. In this case, since the series is not specified, we cannot determine the common ratio. Therefore, we cannot determine if the series converges or diverges.
38.
The sum of n terms of will be:
Correct Answer
A.
39.
The term independent of x in is:
Correct Answer
A. 49
Explanation
The term independent of x in the given expression is 49. This means that no matter what value x takes, the term 49 will remain constant and not change. The other options (-1, 84, None of these) are not independent of x as they would vary with different values of x.
40.
Which of the following Muslim scientists did contribute in field of Trigonometry?
Correct Answer
B. Muhammad Ibn Jabir Al-Battani
Explanation
Muhammad Ibn Jabir Al-Battani is the correct answer because he made significant contributions to the field of trigonometry. He developed accurate astronomical tables and improved the measurement of angles and the calculation of trigonometric functions. His work greatly influenced later mathematicians and astronomers, and his name is often mentioned in the context of trigonometry.
41.
The domain of is:
Correct Answer
C.
42.
Approximately equals to:
Correct Answer
B. 0.965
Explanation
The correct answer is 0.965 because it is the closest value to the given approximation of "approximately equals to". The other options are further away from the given value and therefore not the correct answer.
43.
Correct Answer
C.
44.
The angle coterminal with is:
Correct Answer
C.
45.
Is equal to
Correct Answer
C.
46.
Correct Answer
D.
47.
Correct Answer
B.
48.
Which of the following trigonometric function has the graph given below
Correct Answer
C.
49.
Period of is:
Correct Answer
B.
50.
At a point 15 meters away from the base of 15 meters high house, the angle of elevation of the top is:
Correct Answer
C.
Explanation
The angle of elevation of the top of a 15-meter high house from a point 15 meters away from its base can be determined using trigonometry. The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the top of the house. In this case, we have a right triangle with the height of the house as the opposite side and the distance from the base as the adjacent side. Using the tangent function, we can calculate the angle of elevation as the arctan(15/15) which simplifies to 45 degrees.