MATHEMATICS Set 4 Website: https://www.edufever.com Page 10 Answer: Option B Q.44.If five forces are acting on the single particle and having an angle of 72˚ between each and are collinear, then: A. The net force acting on the body is zero and it is stable B. The net force acting on the body is horizontal C. The net force acting on the body is vertical D. The net force acting on the body is at an angle of 45 Answer: Option A Q.45.For stability of equilibrium configuration the net force acting on the body is zero. A. True B. False Answer: Option A Q.46.The net moment of the body is zero that means the distance between the force and the rotational axis is zero thus the stability of equilibrium configuration. A. The first part of the statement is false and other part is true B. The first part of the statement is false and other part is false too C. The first part of the statement is true and other part is false D. The first part of the statement is true and other part is true too Answer: Option C Q.47.For the conditions of the stability of equilibrium configuration of the body, i.e. the body only the external forces defines the equilibrium. Because the internal forces cancels out so not to be considered. A. The first part of the statement is false and other part is true B. The first part of the statement is false and other part is false too C. The first part of the statement is true and other part is false D. The first part of the statement is true and other part is true too Answer: Option C Q.48.The net force of the body is zero that means the force are not being applied to the body at all and hence the body has achieved stability. A. The first part of the statement is false and other part is true B. The first part of the statement is false and other part is false too C. The first part of the statement is true and other part is false D. The first part of the statement is true and other part is true too
MATHEMATICS Set 4 Website: https://www.edufever.com Page 11 Answer: Option C Q.49.Median of 7, 6, 4, 8, 2, 5, 11 is A. 6 B. 12 C. 11 D. 4 Answer: Option A Q.50.Mode of 12, 17, 16, 14, 13, 16, 11, 14 is A. 13 B. 11 C. 14 D. 14 and 16 Answer: Option D **This Question Paper Set brought to you by Edufever.com** For More Question Paper, Placement Paper, Tutorial, Study Materials for job alerts etc. Visit: www.edufever.com Follow Us on:
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MATHEMATICS Set 5 Website: https://www.edufever.com Page 1 Q.1. How is time shifting represented in case of periodic signal? A. If x(t) is shifted to t0, Xn is shifted to t0 B. x(t-t0 ), Yn = Xnn e -njwt0 C. Xn = x(t-t0 ), Yn = Xn e -njwt0 D. Xn = x(-t0 ), Yn = Xn e -njwt0 Answer: Option C Q.2. What are the properties of continuous time fourier series? A. Linearity, time shifting B. Linearity, time shifting, frequency shifting C. Linearity, time shifting, frequency shifting, time reversal, time scaling, periodic convolution D. Linearity, time shifting, frequency shifting, time reversal, time scaling, periodic convolution, multiplication, differentiation Answer: Option D Q.3. How do we represent a pairing of a periodic signal with its fourier series coefficients in case of continuous time fourier series? A. x(t) ↔ Xn B. x(t) ↔ Xn+1 C. x(t) ↔ X D. x(n) ↔ Xn Answer: Option A Q.4. What is the frequency shifting property of continuous time fourier series? A. Multiplication in the time domain by a real sinusoid B. Multiplication in the time domain by a complex sinusoid C. Multiplication in the time domain by a sinusoid D. Addition in the time domain by a complex sinusoid Answer: Option B Q.5. Integration and conjugation are also followed by continuous time fourier series? A. True B. False Answer: Option A Q.6. What is the time reversal property of fourier series coefficients?
MATHEMATICS Set 5 Website: https://www.edufever.com Page 2 A. Time reversal of the corresponding sequence of fourier series B. Time reversal of the last term of fourier series C. Time reversal of the corresponding term of fourier series D. Time reversal of the corresponding sequence Answer: Option A Q.7. If x(t) and y(t) are two periodic signals with coefficients Xn and Yn then the linearity is represented as? A. ax(t) + by(t) = aXn + bYn B. ax (t) + by(t) = Xn + bYn C. ax(t) + by(t) = aXn + Yn D. ax(t) + by(t) = Xn + Yn Answer: Option A Q.8. It does not depend whether the signal is odd or even, it is always reversal of the corresponding sequence of fourier series. A. True B. False Answer: Option B Q.9. What is the period of the signal when it is time shifted? A. Changes according to the situation B. Different in different situation C. Remains the same D. Takes the shifted value Answer: C Q.10. Why does the signal change while time scaling? A. Because the frequency changes B. Time changes C. Length changes D. Both frequency and time changes Answer: Option A Q.11. What is the (, ) entry in the matrix ?
MATHEMATICS Set 5 Website: https://www.edufever.com Page 3 A. 3 B. 4 C. 12 D. 14 Answer: Option B Q.12. Let = − − = − − . What is + ? A. 6 −5 −1 2 21 5 B. 1 −3 4 2 10 7 5 0 −2 11 −3 12 C. 6 −5 1 2 21 5 D. 1 −3 4 2 10 −7 5 −2 −3 5 −2 −3 Answer: Option C Q.13. Consider the four matrices = , = , = = Which of the following products can be made from these matrices? (Zero or more options can be correct) A. B. C. 2 D. E. F. G. H. I. 2 Answer: Option All of these Q.14. Let = − − − = − − Which of the following matrices is equal to the matrix ?
MATHEMATICS Set 5 Website: https://www.edufever.com Page 4 A. −1 15 11 26 −3 12 0 0 B. −1 0 4 26 0 12 0 0 C. −1 15 11 26 −2 11 0 0 D. −1 15 11 26 −2 11 6 0 Answer: Option C Q.15. Let = − − , = − − , = − = Which of the following statements are true? (Zero or more options can be correct) A. − = −2 3 −7 3 4 −7 1 6 −1 B. − = −2 3 −7 3 4 −7 1 6 −1 C. − 2 = 3 −10 −2 −7 D. Both A, B and C Answer: Option D Q.16. If number of columns and rows are not equal in a matrix, then it is said to be a A. Rectangular matrix B. Square matrix C. Diagonal matrix D. Null matrix Answer: Option A Q.17. If sum of two matrices is zero matrixes, then A and B are said to be A. Multiplicative inverse of each other B. Additive inverse of each other C. Transpose of each other
MATHEMATICS Set 5 Website: https://www.edufever.com Page 5 D. Determinant of each other Answer: Option B Q.18. Law which does not hold in multiplication of matrices is known as A. Distributive law B. Inverse law C. Associative law D. Commutative law Answer: Option D Q.19. Methods to solve a pair of simultaneous linear equations are A. 3 B. 2 C. 4 D. 5 Answer: Option B Q.20. Skew symmetric matrix is also called A. Symmetric B. Identical matrix C. Square matrix D. Anti symmetric Answer: Option D Q.21. In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 persons speak both Kannada and English. How many people speak all the three languages? A. 6 B. 7 C. 8 D. 9 Answer: Option A Q.22. If ∶ − − − −> defined by () = + , then values of − () − (−) are respectively A. , 4, −4 B. 3, −3 ,
MATHEMATICS Set 5 Website: https://www.edufever.com Page 6 C. , 3, −3 D. 4, −4 , Answer: Option D Q.23. Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ? A. 2 B. 3 C. 5 D. 9 Answer: Option B Q.24. Let Z denote the set of all integers. Define ∶ —> () = { / ( ) then f is A. Onto but not one-one B. One-one but not onto C. One-one and onto D. Neither one-one nor-onto Answer: Option A Q.25. In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ? A. 18 B. 36 C. 24 D. None of these Answer: Option C Q.26. The set of all Equivalence classes of a set A of cardinality C A. has the same cardinality as A B. forms a partition of A C. is of cardinality 2C D. is of cardinality C2 Answer: Option B Q.27. Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is
MATHEMATICS Set 5 Website: https://www.edufever.com Page 7 A. Symmetric but not transitive B. Partial order C. Equivalence relation D. Anti symmetric and not transitive Answer: Option C Q.28. The set of all real numbers under the usual multiplication operation is not a group since A. Multiplication is not a binary operation B. Multiplication is not associative C. Identity element does not exist D. Zero has no inverse Answer: Option D Q.29. If * is defined on R* as a * b = (/) then identity element in the group (R*, *) is A. 1 B. 2 C. 1/2 D. 1/3 Answer: Option B Q.30. If f: A ---> B is a bijective function, then f -1 of f = A. f o f - 1 B. f C. f - 1 D. IA(Identity map of the set A) Answer: Option D Q.31. In a drawer there are 4 white socks, 3 blue socks and 5 grey socks. Two socks are picked randomly. What is the possibility that both the socks are of same color? A. 4/11 B. 1 C. 2/33 D. 19/66 Answer: Option D Q.32. On rolling a dice 2 times, the sum of 2 numbers that appear on the uppermost face is 8. What is the probability that the first throw of dice yields 4?
MATHEMATICS Set 5 Website: https://www.edufever.com Page 8 A. 2/36 B. 1/36 C. 1/6 D. 1/5 Answer: Option B Q.33. In a drawer there are 5 black socks and 3 green socks. Two socks are picked randomly one after the other without replacement. What is the possibility that both the socks are black? A. 5/14 B. 5/8 C. 3/8 D. 5/16 Answer: Option A Q.34. A box has 5 black and 3 green shirts. One shirt is picked randomly and put in another box. The second box has 3 black and 5 green shirts. Now a shirt is picked from second box. What is the probability of it being a black shirt? A. 4/9 B. 29/72 C. 8/72 D. 3/16 Answer: Option B Q.35. What is the possibility of having 53 Thursdays in a non-leap year? A. 6/7 B. 1/7 C. 1/365 D. 53/365 Answer: Option B Q.36. Number of individuals arriving at boarding counter on an airport is an example of A. Numerical outcome B. Non numerical outcome C. Random outcome D. Simple outcome Answer : Option A
MATHEMATICS Set 5 Website: https://www.edufever.com Page 9 Q.37. Consider two events X and Y, X-bar and Y-bar represents A. Occurrence of Y B. Occurrence of X C. Non-occurrence of X and Y D. Occurrence of X and Y Answer : Option C Q.38. In measuring probability of any certain event, zero represents A. Impossible events B. Possible events C. Certain event D. Sample event Answer : Option A Q.39. If two events X and Y are considered as partially overlapping events then rule of addition can be written as A. P(X or Y) = P(X) - P(Y) + P(X and Y) B. P(X or Y) = P(X) + P(Y) * P(X - Y) C. P(X or Y) = P(X) * P(Y) + P(X - Y) D. P(X or Y) = P(X) + P(Y) - P(X and Y) Answer : Option D Q.40. Variation in which outcomes of experiments are effected by uncontrolled factors is considered as A. Random variation B. Mesokurtic variation C. Platykurtic variation D. Mesokurtic variation Answer: Option A Q.41. If mean of 6 numbers is 17 then sum of numbers is A. 102 B. 103 C. 150 D. 120 Answer: Option A Q.42. Number which occurs most frequently in a set of numbers is
MATHEMATICS Set 5 Website: https://www.edufever.com Page 10 A. Mean B. Median C. Mode D. None of above Answer: Option C Q.43. If mean of 6 numbers is 41 then sum of these numbers is A. 250 B. 246 C. 134 D. 456 Answer: Option B Q.44. Most frequent observation in a data set is called A. Mode B. Median C. Range D. Mean Answer: Option A Q.45. Sum of deviations of values from their mean is always A. 1 B. 0 C. 2 D. 3 Answer: Option B Q.46. Median in set 6, 4, 2, 3, 4, 5, 5, 4 would be A. 3 B. 6 C. 5 D. 4 Answer: Option D Q.47. Summary statistics which measure middle or center of data are called A. Logarithms B. Measures of central tendency
MATHEMATICS Set 5 Website: https://www.edufever.com Page 11 C. Measures of dispersion D. Proportions Answer: Option B Q.48. Average of all observations in a set of data is known as A. Median B. Range C. Mean D. Mode Answer: Option C Q.49. Difference of mode and mean is equal to A. 3(mean-median) B. 2(mean-median) C. 3(mean-mode) D. 2(mode mean) Answer: Option A Q.50 . Distribution in which values of median mean and mode are not equal is considered as A. Experimental distribution B. Asymmetrical distribution C. Symmetrical distribution D. Exploratory distribution Answer: Option B
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MATHEMATICS Set 6 Website: https://www.edufever.com Page 1 Q.1. Can continuous time fourier series undergo periodic convolution? A. They cannot undergo periodic convoluion B. They can undergo in certain situations C. They undergo periodic convolution D. Only even signals undergo periodic convolution Answer: Option C Q.2. What is the fourier series coefficient for n=0? A. Zero B. Unity C. Depends on the situation D. Non zero positive Answer: Option A Q.3. What is the outcome of a periodic convolution of signals in case of continuous time fourier series? A. Division in frequency domain B. Multiplication in frequency domain C. Convolution is easier D. Addition of signals in frequency domain Answer: Option B Q.4. What is the smoothing operation? A. Differentiation property B. Multiplication property C. Integration property D. Conjugation property Answer: Option C Q.5. What is the multiplication property of continuous time fourier series? A. Convolution of the signals B. Multiplication of the elements of the signal C. Division of the frequency domain D. Addition of the signals in frequency domain Answer: Option A
MATHEMATICS Set 6 Website: https://www.edufever.com Page 2 Q.6. If the signal x(t) is odd, what will be the fourier series soeffiients? A. Real and even B. Odd C. Real only D. Real and odd Answer: Option A Q.7. What is the complex conjugate property of a fourier series? A. It leads to convolution B. It leads to time reversal C. It leads to multiplication D. It leads to addition of signals Answer: Option B Q.8. What is the differentiation property of continuous time fourier series? A. Yn = jnwtXn B. Yn = jntXn C. Yn = jnwXn D. Xn = jnwtXn Answer: Option C Q.9. If the signal x(t) is even, what will be the fourier series coefficients? A. Real and even B. Odd C. Real only D. Imaginary and odd Answer: Option D Q.10. What is the integration property of the continuous time fourier series? A. y(t) ↔ Yn = 1/jnwXn B. y(t) ↔ Yn = 1/jwXn C. y(t) ↔ Yn = 1/jnXn D. y(t) ↔ Yn = 1/jnw Answer: A Q.11. In matrices (AB) t equals to
MATHEMATICS Set 6 Website: https://www.edufever.com Page 3 A. b B. a C. a t b t D. b t a t Answer: Option D Q.12. A diagonal matrix having equal elements is called a A. Square matrix B. Identical matrix C. Scalar matrix D. Rectangular matrix Answer: Option C Q.13. If A, B and C matrices are of same order and (A + B) + C = A + (B + C), this law is known as A. Cramer's law B. Distributive law C. Commutative law D. Associative law Answer: Option D Q.14. If determinant of a matrix is not equal to zero, then it is said to be A. Non-singular matrix B. Square matrix C. Singular matrix D. Identical matrix Answer: Option A Q.15. In matrices (A + B) t equals to A. A t B. B t C. A t + B t D. A t B t Answer: Option C Q.16. If = then order of matrix A=?
MATHEMATICS Set 6 Website: https://www.edufever.com Page 4 A. 2 × 2 B. 2 × 3 C. 3 × 2 D. 3 × 3 Anwer: Option B Q.17. What is , if = is a singular matrix? A. 5 B. 6 C. 7 D. 8 Answer: Option D Q.18. If A and B are matrices, then which from the following is true? A. A + B ≠ B + A B. (At ) t ≠ A C. AB ≠ BA D. all are true Answer: Option C Q.19. If = − then =? A. 2 B. 3 C. 4 D. 5 Answer: Option B Q.20. If (G, .) is a group such that (ab)- 1 = b-1 a-1, ∀ a, b ∈ G, then G is a/an A. commutative semi group B. abelian group C. non- abelian group D. None of these Answer: Option B
MATHEMATICS Set 6 Website: https://www.edufever.com Page 5 Q.21. If (G, .) is a group such that a2 = e, ∀ a ∈ G, then G is A. Semi group B. Abelian group C. Non-abelian group D. None of these Answer: Option B Q.22. The set of integers Z with the binary operation "1" defined as a*b =a +b+1 for a, b ∈ Z, is a group. The identity element of this group is A. 0 B. 1 C. -1 D. 12 Answer: Option C Q.23. The identity element in the group given below with respect to matrix {[x x]} multiplication is = : =∈ , ≠ A. 1 0 1 0 B. −1 0 0 −1 C. 1 2 1 2 1 2 1 2 D. 1 1 1 1 Answer: Option C Q.24. In the group (, . ), the value of ( − ) − is A. −1 B. −1 C. −1 D. −1 Answer: Option B Q.25. If (, . ) is a group, such that () = ∀ , ∈ , is a/an A. Commutative semi group B. Abelian group C. Non-abelian group
MATHEMATICS Set 6 Website: https://www.edufever.com Page 6 D. None of these Answer: Option B Q.26. Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an A. Subgroup B. Finite abelian group C. Infinite, non abelian group D. Infinite, abelian Answer: Option C Q.27. If a, b are positive integers, define a * b = α where = (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is A. 3 B. 1 C. 5 D. 4 Answer: Option C Q.28. (Z,*) is a group with a* = + + ∀ , ∈ . The inverse of a is A. 0 B. -2 C. a-2 D. -a-2 Answer: Option D Q.29. Suresh keeps all his socks in a single drawer. He has 24 pairs of white socks and 18 pairs of grey socks. Suresh picks 3 socks randomly. Find the possibility of Suresh choosing a matching pair. A. 1/36 B. 1/108 C. 7/36 D. 1 Answer: Option D
MATHEMATICS Set 6 Website: https://www.edufever.com Page 7 Q.30. A box has 6 black, 4 red, 2 white and 3 blue shirts. Find the probability of drawing 2 black shirts if they are picked randomly? A. 1/8 B. 2/15 C. 6/15 D. 1/7 Answer: Option D Q.31. There are 2 pots. One pot has 5 red and 3 green marbles. Other has 4 red and 2 green marbles. What is the probability of drawing a red marble? A. 9/14 B. 31/48 C. 1 D. 1/2 Answer: Option B Q.32. A pot has 2 white, 6 black, 4 grey and 8 green balls. If one ball is picked randomly from the pot, what is the probability of it being black or green? A. 3/4 B. 7/10 C. 4/3 D. 1/10 Answer: Option B Q.33. In a set of 30 game cards, 17 are white and rest are green. 4 white and 5 green are marked IMPORTANT. If a card is chosen randomly from this set, what is the possibility of choosing a green card or an ‘IMPORTANT’ card? A. 13/30 B. 22/30 C. 17/30 D. 9/13
MATHEMATICS Set 6 Website: https://www.edufever.com Page 8 Answer: Option C Q.34. A box has 6 black, 4 red, 2 white and 3 blue shirts. When 2 shirts are picked randomly, what is the probability that either both are white or both are blue? A. 4/105 B. 1/35 C. 1/105 D. 1/15 Answer: Option A Q.35. Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? A. 8/35 B. 34/35 C. 27/35 D. NONE OF THESE Answer: Option A Q.36. What will be the possibility of drawing a jack or a spade from a well shuffled standard deck of 52 playing cards? A. 4/13 B. 1/26 C. 1/13 D. 17/52 Answer: Option A Q.37. Three unbiased coins are tossed. What is the probability of getting at least 2 tails? A. 0.75 B. 0.5 C. 0.25 D. 0.2
MATHEMATICS Set 6 Website: https://www.edufever.com Page 9 Answer: Option A Q.38. Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7? A. 9/25 B. 9/50 C. 18/25 D. None of these Answer: Option A Q.39. If value of mode is 14 and value of arithmetic mean is 5 then value of median is A. 12 B. 18 C. 8 D. 14 Answer: Option C Q.40. If mean is 11 and median is 13 then value of mode is A. 15 B. 13 C. 11 D. 17 Answer: Option D Q.41. If value of three measures of central tendencies median, mean and mode then distribution is considered as A. Negatively skewed modal B. Triangular model C. Unimodel D. Bimodel Answer: Option C Q.42. In a negative skewed distribution, order of mean, median and mode is as A. Mean<median>mode B. Mean>median>mode C. Mean<median<mode
MATHEMATICS Set 6 Website: https://www.edufever.com Page 10 D. Mean>median<mode Answer: Option C Q.43. Extent to which values are dispersed around central observation is considered as A. Trailing B. Variation C. Extension D. Centralized valuation Answer: Option B Q.44. Mode is best measure of tendency if analysis is A. Descriptive B. Exploratory C. Experimental D. Set of deciles Answer: Option A Q.45. Measure which describes detailed characteristic of whole data set is classified as A. Average or central value B. Positive skewed value C. Negative skewed value D. Positive extended value Answer: Option A Q.46. Manner in which geometric mean, harmonic mean and arithmetic mean are related is as A. A.M>G.M>H.M B. A.M>G.M<H.M C. A.M<G.M<H.M D. A.M<G.M>H.M Answer: Option A Q.47. A numerical value used as a summary measure for a sample, such as sample mean, is known as a A. population parameter B. sample parameter C. sample statistic D. population mean
MATHEMATICS Set 6 Website: https://www.edufever.com Page 11 Answer: Option C Q.48.  is an example of a A. population parameter B. sample statistic C. population variance D. mode Answer: Option A Q.49. If z and w two complex numbers, then A. + = + B. + = − C. + = / D. + = . Answer: Option A Q.50. The square root of the number (-3)2 are A. -3 B. 3 C. 3,-3 D. 3i,-3i Answer: Option C
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MATHEMATICS Set 7 Website: https://www.edufever.com Page 1 Q.1: → is equal to A. 0 B. ∞ C. 1 D. -1 Answer: Option A Q.2:Maxima and Minima occur A. Simultaneously B. once C. Alternately D. Rarely Answer: Option C Q.3:Minimum point of the function f = A. x=1 B. x=-1 C. x=0 D. x= 1/√3 Answer: Option A Q.4:If f (0) = 2 and f (x) = 1 / (5-x2), then lower and upper bound of f(1) estimated by the mean value theorem are A. 1.9, 2.2 B. 2.2, 2.25 C. 2.25, 2.5 D. None of these Answer: Option B Q.5:If x + y = k, x > 0, y > 0, then xy is maximum when A. x = ky B. kx = y C. x = y D. None of these Answer: Option C
MATHEMATICS Set 7 Website: https://www.edufever.com Page 2 Q.6:Let f(x) = , then A. f'(0) = 0 B. f(x) is maximum at x = 0 C. f(x) is minimum at x = 0 D. None of these Answer: Option D Q.7:Limit of the following series as x approaches π/2 is = − ! + ! − ! A. A.2π/3 B. π/2 C. π/3 D. 1 Answer: Option D Q.8:Which of the following is correct? A. f(a) is an extreme value of f(x) if f '(a)=0 B. If f(a) is an extreme value of f(x), then f '(a) = 0 C. If f '(a) = 0, then f (a) is an extreme value of f(x) D. all of these Answer: Option D Q.9:The maxima and minima of the function f(x) = 2x3 - 15x2 + 36x + 10 occur respectively at A. x= 3 and x = 2 B. x = 1 and x = 3 C. x = 2 and x = 3 D. x = 3 and x = 4 Answer: Option C Q.10:Value of 'c' of the mean value theorem for the function f(x) = x(x - 2), when a = 0, b = 3/2, is A. 3/4 B. 1/2 C. 3/2 D. 1/4 Answer: Option A
MATHEMATICS Set 7 Website: https://www.edufever.com Page 3 Q.11:As per properties of real numbers with respect to addition, a + b = b + a and ∀ a, b ∈ R is A. additive inverse B. associative property C. commutative property D. closure property Answer: Option C Q.12:Set of irrational numbers is denoted by A. R B. Q C. R' D. Q' Answer: Option D Q.13:Set consist of positive integers, zero and negative integers is called A. set of even numbers B. set of prime numbers C. set of integers D. set of irrational numbers Answer: Option C Q.14:Set of natural numbers is denoted by A. A B. W C. N D. R Answer: Option C Q.15:Under property of equality of real numbers, a = b and b = c then a = c and ∀ a, b, c ∈ R is called A. reflexive property B. symmetric property C. additive property D. transitive property Answer: Option A Q.16:π is a
MATHEMATICS Set 7 Website: https://www.edufever.com Page 4 A. rational number B. irrational number C. natural number D. whole number Answer: Option A Q.17:Union of set of rational and irrational numbers is known as A. the set of real numbers B. set of irrational numbers C. set of rational numbers D. set of prime numbers Answer: Option A Q Q.18:ι² is equal to A. −1 B. ι C. 1 D. 0 Answer: Option C Q.19:For all a, b, c ∈ R, (a + b) c = ac + bc is said to be A. left multiplicative law B. right multiplicative law C. left distributive law D. right distributive law Answer: Option D Q.20:In a + 0 = a = 0 + a and ∀ a ∈ R then ‘0’ is called A. additive identity B. additive inverse C. associative property D. commutative property Answer: Option A Q.21:If points of straight line are A (1, 2) and B(6, 2) then line AB is A. Horizontal line with equation y = 2 B. Vertical line with equation y = 2
MATHEMATICS Set 7 Website: https://www.edufever.com Page 5 C. Horizontal line with equation x = 6 D. Vertical line with equation x = 6 Answer: Option A Q.22:If y = 5x + c passes through point A (5, 2) then value of 'c' is A. −21 B. −23 C. −25 D. −27 Answer: Option B Q.23:Distance between points (2, 5) and (7, -3) is A. 6.43 B. 9.43 C. 12.43 D. 15.43 Answer: Option B Q.24:If straight line passes through points X (1. 4) and Y (3, 7) then its equation will be A. 2⁄3x + 5⁄2 B. 3⁄2x + 2⁄5 C. 2⁄3x - 2⁄5 D. 3⁄2x + 5⁄2 Answer: Option D Q.25:Straight line equation y = x⁄2 + 1⁄4 has gradient of A. 1⁄2 B. 1⁄4 C. x⁄4 D. x⁄2 Answer: Option A Q.26: Let P and Q be the points on the line joining A(–2 , 5) and B(3 , 1) such that AP = PQ = QB , then the midpoint of PQ is A. (1/2, 3) B. (-1/4,4) C. (2, 3) D. (– 1, 4)
MATHEMATICS Set 7 Website: https://www.edufever.com Page 6 Answer: Option A Q.27:Locus of point of intersection of the perpendicular lines one belonging to (x + y – 2) + λ(2x + 3y – 5) = 0 and other to (2x + y – 11) + λ(x + 2y – 13) = 0 is a A. Circle B. Straight line C. Pair of lines D. None of these Answer: Option A Q.28:The triangle ABC has medians AD, BE, CF. AD lies along the line y = x + 3 , BE lies along the line y = 2x + 4, AB has length 60 and angle C = 90°, then the area of ΔABC is A. 400 B. 200 C. 100 D. none of these Answer: Option A Q.29:The orthocenter of a triangle whose vertices are (0, 0), (√3, 0) and (0, √6) is A. (2, 1) B. (3, 2) C. (4, 1) D. none of these Answer: Option D Q.30:Let ax + by + c = 0 be a variable straight line, where a, b and c are 1st, 3rd and 7th terms of some increasing A.P. Then the variable straight line always passes through a fixed point which lies on A. x² + y2 = 13 B. B) x² + y2 = 5 C. y² = 9x D. 3x+4y=9 Answer: Option A Q.31:Fresenius method extend A. power series method B. logarithmic method C. Laplace method
MATHEMATICS Set 7 Website: https://www.edufever.com Page 7 D. Fourier method Answer: Option A Q.32:In Laplace transform, given ODE is transformed into an algebraic equation called A. linear equation B. subsidiary equation C. random equation D. exponential equation Answer: Option B Q.33:Process of solving ODE using Laplace transform consist of A. two steps B. three steps C. four steps D. five steps Answer: Option B Q.34:If a power series has a positive radius of convergence and sum that is identically zero throughout its interval of convergence, than each coefficient of series must be A. one B. zero C. infinite D. two Answer: Option B Q.35:Study of higher functions not occurring in calculus is called theory of A. logarithmic functions B. exponential functions C. natural functions D. special functions Answer: Option D Q.36:Solution of (y + (x + y)) dx + (y (x + y) dy = 0 is
MATHEMATICS Set 7 Website: https://www.edufever.com Page 8 A. X 2 + y2 = 2 −1 + c B. X 2 + y2 = 4 −1 + c C. X 2 + y2 = −1 + c D. None of these Answer: Option D Q.37:Solution of the differential equation = sin (x + y) + cos (x + y), is A. Log + (+) = y + c B. Log + (+) = x + c C. Log + ( + ) yb + c D. None of these Answer: Option D Q.38:Linear second order ordinary differential equation is non homogeneous if A. there is no constant in equation B. solution is zero C. solution has some value D. independent variable is present Answer: C Q.39:Polynomial ar<sup>2</sup>+br+c=0 is called A. characteristic polynomial B. trivial polynomial C. determinant polynomial D. singular polynomial Answer: Option A Q.40:Current in electrical system is analogues to mechanical system A. mass B. driving force
MATHEMATICS Set 7 Website: https://www.edufever.com Page 9 C. spring module D. displacement Answer: Option D Q.41:Double-sided phase & amplitude spectra _____ A. Possess an odd & even symmetry respectively B. Possess an even & odd symmetry respectively C. Both possess an odd symmetry D. Both possess an even symmetry Answer: Option A Q.42:Which are the only waves that correspond/ support the measurement of phase angle in the line spectra? A. Sine waves B. Cosine waves C. Triangular waves D. Square waves Answer: Option B Q.43:Which type/s of Fourier Series allow/s to represent the negative frequencies by plotting the double-sided spectrum for the analysis of periodic signals ? A. Trigonometric Fourier Series B. Polar Fourier Series C. Exponential Fourier Series D. All of the above Answer: Option C Q.44:What does the first term 'a0' in the below stated expression of a line spectrum indicate ? x(t) = a0 + a1 cos w0 t + a2 cos2 w0 t +......+ b1 sin w0 t + b2 sin w0 t + ..... A. DC component B. Fundamental component C. Second harmonic component D. All of the above
MATHEMATICS Set 7 Website: https://www.edufever.com Page 10 Answer: Option A Q.45:What does the signalling rate in the digital communication system imply ? A. Number of digital pulses transmitted per second B. Number of digital pulses transmitted per minute C. Number of digital pulses received per second D. Number of digital pulses received per minute Answer: Option A Q.46:Which kind of frequency spectrum/spectra is/are obtained from the line spectrum of a continuous signal on the basis of Polar Fourier Series Method? A. Continuous in nature B. Discrete in nature C. Sampled in nature D. All of the above Answer: Option B Q.47:Why are the negative & positive phase shifts introduced for positive & negative frequencies respectively in amplitude and phase spectra? A. To change the symmetry of the phase spectrum B. To maintain the symmetry of the phase spectrum C. Both a & b D. None of the above Answer: Option B Q.48:As the signalling rate increases, _______ A. Width of each pulse increases B. Width of each pulse decreases C. Width of each pulse remains unaffected D. None of the above Answer: Option B Q.49:Duality Theorem / Property of Fourier Transform states that _________ A. Shape of signal in time domain & shape of spectrum can be interchangeable
MATHEMATICS Set 7 Website: https://www.edufever.com Page 11 B. Shape of signal in frequency domain & shape of spectrum can be interchangeable C. Shape of signal in time domain & shape of spectrum can never be interchangeable D. Shape of signal in time domain & shape of spectrum can never be interchangeable Answer: Option A Q.50:Which phenomenon occurs due to an increase in the channel bandwidth during the transmission of narrow pulses in order to avoid any intervention of signal distortion? A. Compression in time domain B. Expansion in time domain C. Compression in frequency domain D. Expansion in frequency domain Answer: Option D
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MATHEMATICS Set 8 Website: https://www.edufever.com Page 1 Q.1: Vector product of two vectors is also known as A. Scalar product B. Dot product C. Point product D. Cross product Answer: Option D Q.2: Cross product of two same vectors is equal to A. 0 B. 1 C. J D. . Answer: Option A Q.3: Scalar product of A.B with angle 180° would produce results equal to A. A.B B. (-AB) C. AB D. B Answer: Option B Q.4: Multiplication of two vectors is of A. 2 types B. 3 types C. 4 types D. 5 types Answer: Option A Q.5: If + = than + : A. 0 B. 1 C. 2a.b D. None of these Answer: Option A Q.6: If , , , are non-coplanar vectors then . × × . + . × . × is equal to:
MATHEMATICS Set 8 Website: https://www.edufever.com Page 2 A. 0 B. 1 C. 3 D. None of these Answer: Option B Q.7: The value of k for which the points A(1, 0, 3) , B(-1, 3,4) ,C(1, 2, 1) and D(k, 2, 5) are coplanar is : A. 1 B. 2 C. 0 D. -1 Answer: Option D Q.8: Let and be two unit vectors such that + two unit vectors such that is also a unit vector. Then the angle between and is: A. 30° B. 60° C. 90° D. 120° Answer: Option D Q.9: Let , unit vectors in the , directions, respectively. Suppose that = − + . What is the magnitude of the vector ? A. 4 B. 12 C. 14 D. 14 Answer: Option C Q.10: Which of the of 3-dimension coordinates axes below are right–handed coordinate systems? (The arrows indicate the positive direction on each axis.) (Zero or more options can be correct) A. Z X
MATHEMATICS Set 8 Website: https://www.edufever.com Page 3 Y Z z y B. x z y C. x D. z x y z E. x y Answer: Option A, D, E Q.11: MCQ: Sec²θ = A. 1 - cos²θ B. 1 - tan²θ C. 1 + tan²θ D. 1 + cot²θ Answer : Option C
MATHEMATICS Set 8 Website: https://www.edufever.com Page 4 Q.12: MCQ: Cos²θ/2 = A. 1 - sin²θ/2 B. 1 - sin²θ C. csc²2θ D. sec²2θ Answer: Option A Q.13: If cosθ = 1/√2, then θ is equal to A. 30° B. 45° C. 60° D. 90° Answer: Option B Q.14: If circumference of a circle is divided into 360 congruent parts, angle subtended by one part at center of circle is called A. Angle B. Radian C. Degree D. Minute Answer : Option C Q.15: MCQ: 16°40′38″ = A. 17° B. 16° C. 60038′ D. 60038″ Answer: Option D Q.16: Question which of the following is not an identity? A. sin2 a+cos2 a = 1 B. sin a = tan a * cos a C. 1 + cot2 a = csc2 a D. 1 - sec2 a = tan2 a Answer: Option D Q.17: Question sin t + cos2 t / sin t =
MATHEMATICS Set 8 Website: https://www.edufever.com Page 5 A. sin t B. csc t C. sec t D. cos t Answer: Option B Q.18: Question which of the following is an identity? A. sin2 u = 1 + cos2 u B. cot u = sin u * cos u C. sin2 u = 1 - 1 / sec2 u D. cos(-u) = - cos u Answer: Option C Q.19: Question sin (x) + sin(x - π) + sin(x + π) = A. -sin(x) B. sin (x) C. C.sec (x) D. cos (x) Answer: Option A Q.20: Question Which of the following is an identity? A. sin (a) cos (a) = (1/2) sin(2 a) B. sin a + cos a = 1 C. sin(-a) = sin a D. tan a = cos a / sin a Answer: Option A Q.21: A Laplace Transform exists when ______ A. The function is piece-wise continuous B. The function is of exponential order C. The function is piecewise discrete D. The function is of differential order A. A & B B. C & D C. A & D D. B & C
MATHEMATICS Set 8 Website: https://www.edufever.com Page 6 Answer:- Option A Q.22: Where is the ROC defined or specified for the signals containing causal as well as anti-causal terms? A. Greater than the largest pole B. Less than the smallest pole C. Between two poles D. Cannot be defined Answer:- Option C Q.23: What should be the value of laplace transform for the time-domain signal equation eat cos ωt.u(t)? A. 1 / s + a with ROC σ > - a B. ω / (s + a) 2 + ω2 with ROC σ > - a C. s + a / (s + a)2 + ω2 with ROC σ > - a D. Aω / s2 + ω2 with ROC σ > 0 Answer:- Option C Q.24: According to the time-shifting property of Laplace Transform, shifting the signal in time domain corresponds to the ______ A. Multiplication by eSt0 in the time domain B. Multiplication by eSt0 in the frequency domain C. Multiplication by est0 in the time domain D. Multiplication by est0 in the frequency domain Answer:- Option B Q.25: Which result is generated/ obtained by the addition of a step to a ramp function ? A. Step Function shifted by an amount equal to ramp B. Ramp Function shifted by an amount equal to step C. Ramp function of zero slope D. Step function of zero slope Answer:- Option B Q.26: Unilateral Laplace Transform is applicable for the determination of linear constant coefficient differential equations with ________ A. Zero initial condition B. Non-zero initial condition
MATHEMATICS Set 8 Website: https://www.edufever.com Page 7 C. Zero final condition D. Non-zero final condition Answer:- Option B Q.27: What should be location of poles corresponding to ROC for bilateral Inverse Laplace Transform especially for determining the nature of time domain signal? A. On L.H.S of ROC B. On R.H.S of ROC C. On both sides of ROC D. None of the above Answer:- Option C Q.28: Generally, the convolution process associated with the Laplace Transform in time domain results into________ A. Simple multiplication in complex frequency domain B. Simple division in complex frequency domain C. Simple multiplication in complex time domain D. Simple division in complex time domain Answer:- Option A Q.29: An impulse response of the system at initially rest condition is basically a response to its input & hence also regarded as, A. Black's function B. Red's function C. Green's function D. None of the above Answer:- Option C Q.30: When is the system said to be causal as well as stable in accordance to pole/zero of ROC specified by system transfer function? A. Only if all the poles of system transfer function lie in left-half of S-plane B. Only if all the poles of system transfer function lie in right-half of S-plane C. Only if all the poles of system transfer function lie at the centre of S-plane D. None of the above Answer:- Option A Q.31: The sum of the percent frequencies for all classes will always equal
MATHEMATICS Set 8 Website: https://www.edufever.com Page 8 A. one B. the number of classes C. the number of items in the study D. 100 Answer: Option D Q.32: Since the mode is the most frequently occurring data value, it A. can never be larger than the mean B. is always larger than the median C. is always larger than the mean D. None of the above answers is correct. Answer: Option D Q.33: Since the population size is always larger than the sample size, then the sample statistic A. can never be larger than the population parameter B. can never be equal to the population parameter C. can never be zero D. None of the above answers is correct. Answer: Option D Q.34: In a five number summary, which of the following is not used for data summarization? A. The smallest value B. The largest value C. The median D. The 25th percentile E. The mean Answer: Option D Q.35: In statistics out of 100, marks of 21 students in final exams are as 90, 95, 95, 94, 90, 85, 84, 83, 85,81, 92, 93, 82, 78, 79, 81, 80, 82, 85, 76, 85 then mode of data is A. 85 B. 95 C. 90 D. 81 Answer: Option A