MATHEMATICS Set 8 Website: https://www.edufever.com Page 9 Q.36: Procedures of descriptive statistics and control charts which are used to improve process are classified as A. Statistical tools B. Parallel tools C. Serial tools D. Behavioral tools Answer: Option A Q.37: Sample statistics are denoted by the A. Upper case Greek letter B. Associated roman alphabets C. Roman letters D. Lower case Greek letter Answer: Option C Q.38: Branches of statistics includes A. Applied statistics B. Mathematical statistics C. Industry statistics D. Both a and b Answer: Option D Q.39: Scale used in statistics which provides difference of proportions as well as magnitude of differences is considered as A. Satisfactory scale B. Ratio scale C. Goodness scale D. Exponential scale Answer: Option B Q.40: 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
MATHEMATICS Set 8 Website: https://www.edufever.com Page 10 Q.41: Consider an event B, non-occurrence of event B is represented by A. Union of A B. Complement of A C. Intersection of A D. A is equal to zero Answer: Option B Q.42: Types of probabilities for independent events must includes A. Joint events B. Marginal events C. Conditional events D. All of above Answer: Option D Q.43: If a person buys a lottery, chance of winning a Toyota car is 60%, chance of winning Hyundai car is 70% and chance of winning both is 40% then chance of winning Toyota or Hyundai is A. 0.6 B. 0.9 C. 0.8 D. 0.5 Answer: Option B Q.44: In a Venn diagram used to represent probabilities, sample space of events is represented by A. Square B. Triangle C. Circle D. Rectangle Answer: Option D Q.45: Outcomes of an experiment are classified as A. Logged events B. Exponential results C. Results D. Events Answer: Option D
MATHEMATICS Set 8 Website: https://www.edufever.com Page 11 Q.46: Joint probability of two statistical dependent events Y and Z can be written as P(Y and Z) = A. P (Z + Y) * P (Y|Z) B. P(Y) * P (Z|Y) C. P(Y) * P (Z|Y) + P (Z) D. P(Y) * P (Z|Y) – P (Z + Y) Answer : Option B Q.47: According to combination rule, if total number of outcomes are 'r' and distinct outcome collection is 'n' then combinations are calculated as A. n! ⁄ r!(n - r)! B. n! ⁄ r!(n + r)! C. r! ⁄ n!(n - r)! D. r! ⁄ n!(n + r)! Answer : Option A Q.48: Marginal probability of independent events and dependent events must be A. Same B. Different C. One D. Two Answer : Option A Q.49: For a random experiment, all possible outcomes are called A. Numerical space B. Event space C. Sample space D. Both b and c Answer : Option D Q.50: Probability without any conditions of occurrence of an event is considered as A. Conditional probability B. Marginal probability C. Non conditional probability D. Occurrence probability Answer: Option B
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MATHEMATICS Set 9 Website: https://www.edufever.com Page 1 Q.1: In both of the diagrams below, the vectors lie in the plane in 3- dimensional space and the angle between them is radians, or 45 degrees. In which direction is the vector × pointing? Z x y y u v x v u (1) (2) A. In the positive direction in both (1) and (2). B. In the negative direction in both (1) and (2). C. In the positive direction in (1) and the negative direction in (2). D. In the positive direction in (2) and the negative direction in (1). Answer: Option C Q.2: What is the approximate angle between if . = , = , = . ? A. 1.25 radians B. 0.87 radians C. 1.32 radians D. 0.96 radians Answer: Option D Q.3: Suppose that is a vector pointing north-west with . = . Which of the following vectors is equal to written in Cartesian form? (Here the unit vector points towards the east and the unit vector points north). A. 12 + 12 B. 6 − 6 C. – 12 + 12 D. − 6 + 6 Anwer: Option D Q.4: Let be two vectors. If the component of in the direction of is negative this means: (Zero or more options can be correct) A. There is an arithmetical error in the calculation.
MATHEMATICS Set 9 Website: https://www.edufever.com Page 2 B. The angle between is obtuse, when the vectors are placed tail to tail. C. The angle between when placed head to tail is acute. D. None of the above. Answer: Option B, C Q.5: If = + + − , find the projection of in the direction of . A. – 1 25 4 − 3 B. 7 25 4 − 3 C. 1 25 4 − 3 D. − 3 25 (4 − 3 Answer: Option C Q.6: Calculate the vector cross product × when = + − − . A. – 2 − 8 − 7 B. – 2 + 8 − 7 C. 2 − 8 + 7 D. 4 + 2 Answer: Option D Q.7: Which of the following symbols represent vectors? A. B. C. D. − E. + F. − Answer: Option A, D, Q.8: Given that is a vector of length 2, s a vector of length 3 and the angle between them when placed tail to tail is 45°, which option is closest to the exact value of . ? A. 4.5 B. 6.2 C. 4.2 D. 5.1 Answer: Option C
MATHEMATICS Set 9 Website: https://www.edufever.com Page 3 Q.9: Find non-zero scalars , such that for all vectors , A. = 2, = 1 B. = −2, = −3 C. = 1, = 3 D. = −2, = 3 Answer: Option B Q.10: A boat sails 5 km south-east then 3 km due west. Approximately how far is it from its starting position? A. 2.7 km B. 4.2 km C. 7.4 km D. 3.6 km Answer: Option D Q.11: 1 + tan²2θ/2 = A. sec²θ B. csc²θ C. csc²2θ D. sec²θ/2 Answer: Option A Q.12: (secθ-tanθ)² = A. 1 + sinθ/1 - sinθ B. (1 - sinθ)/ (1 + sinθ) C. (1 - cosθ)/ (1+cosθ) D. cscθ Answer : Option B Q.13: Csc²θ = A. 1 - cos²θ B. 1 - tan²θ C. 1 + tan²θ D. 1 + cot²θ Answer: Option D Q.14: One second is denoted by
MATHEMATICS Set 9 Website: https://www.edufever.com Page 4 A. 1 rad B. 1′ C. 1″ D. 1° Answer: Option B Q.15: Cosecθ = A. 1/cosθ B. cosθ/sinθ C. sinθ/cosθ D. 1/sinθ Answer : Option D Q.16: If y = cos x, then what is the maximum value of y? A. 1 B. -1 C. π D. 2π Answer : Option A Q.17: What is the amplitude of the function f(x) = -3cos (πx)? A. 3 B. -3 C. π D. 2 Answer : Option A Q.18: What is the range of the function f(x) = - 4 cos(2x - 3)? A. (0, 4) B. [0, 4] C. (-4, 4) D. [-4, 4] Answer : Option D Q.19: What is the range of the function f(x) = - 6 cos(π x - π/2) + 2? A. [-6, 6] B. [-4, 8] C. [0, 8]
MATHEMATICS Set 9 Website: https://www.edufever.com Page 5 D. [-6, 0] Answer : Option B Q.20: What is the amplitude of f(x) = sin(x) + cos(x)? A. √2 B. √2 / 2 C. 2 √2 D. 2 Answer : Option A Q.21: One Dimensional signal is a function of: A. Multiple independent variables. B. Single independent variable. C. Single dependent variable. D. None of the above. Answer: Option B Q.22: The interface between an analog signal and a digital processor is: A. D/A converter. B. Modulator. C. Demodulator. D. None of the above. Answer: Option D Q.23: What are the important block(s) required to process an input analog signal to get an output analog signal? A. A/D converter. B. Digital signal processor. C. D/A converter. D. All of the above. Answer: Option D Q.24: The general form of exponential sequence is: A. () = B. = () C. = cos(ωn + ∅)
MATHEMATICS Set 9 Website: https://www.edufever.com Page 6 D. None of the above. Answer: Option A Q.25: A periodic sequence is a sequence for which: A. = − B. = + C. = cos(ωn + ∅) D. None of the above. Answer: Option B Q.26: A system is said to be invertible if: a) The input signal can be recovered by output signal. b) If it depends only on the past and future values. c) If it is discrete. d) None of the above. Answer: Option A Q.27: The DTFT of a discrete time signal x(n) is defined as: A. B. C. = ∞ = − ∞ − D. None of the above. Answer: Option B Q.28: The Z-Transform X(z) of a discrete time signal X(n) is defined as: A. B. ∞ = − ∞ C. ∞ = − ∞ − D. None of the above. Answer: Option C Q.29: The Fourier transform exists for a discrete time sequence x (n) if and only if the sequence is: A. Absolutely summable
MATHEMATICS Set 9 Website: https://www.edufever.com Page 7 B. Absolutely integrable. C. Not summable D. None of the above Answer: Option A Q.30: The Fourier Transform of the signal = () )is: A. 1 1−− B. 1−− C. 1 1− D. None of the above Answer: Option A Q.31: Which of these represent qualitative data? A. Height of a student B. Liking or disliking of (500) persons of a product C. Income of a government servant in a city D. Yield from a wheat plot Answer: Option B Q.32: The first hand and unorganized form of data is called A. Secondary data B. Organized data C. Primary data D. None of these Answer: Option C Q.34: Census reports used as a source of data is A. Primary source B. Secondary source C. Organized data D. None Answer: Option B Q.35: Questionnaire survey method is used to collect A. Secondary data B. Qualitative variable
MATHEMATICS Set 9 Website: https://www.edufever.com Page 8 C. Primary data D. None of these Answer: Option C Q.36: Population census is conducted through A. Sample survey B. Accounting C. Investigation D. Complete enumeration Answer: Option D Q.37: Given $ = , = , = , = . ₹, $\ = . ₹ ? A. 36 B. 48 C. 41 D. 29 Answer: Option B Q.38: The average of first n natural numbers is A. +1 2 B. None of these C. 2 D. All of these Answer: Option A Q.39: Value of [( + ) ⁄ ] term is formula of A. Variance B. 3rd quartile C. 2nd quartile D. Geometric mean Answer: Option B Q.40: In set 2, 4, 5, 4, 6, 5, 3, 4, 2, mode is A. 2 B. 5 C. 4 D. 3
MATHEMATICS Set 9 Website: https://www.edufever.com Page 9 Answer: Option C Q.41: Table which shows frequency of each score is called a A. Polygon B. Pi chart C. Histogram D. Frequency distribution table Answer: Option D Q.42: Important rules in computation of experimental outcomes includes A. Multiple experiments B. Permutations C. Combinations D. All of above Answer : Option D Q.43: For two events, probability of occurrence of both events at same time or occurrence in series is classified as A. Joint probability B. Dependent probability C. Series probability D. Conditional probability Answer : Option A Q.44: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? A. 1/2 B. 3/4 C. 3/8 D. 5/16 Answer: Option B Q.45: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? A. 1/10 B. B.2/5 C. C.2/7 D. D.5/7
MATHEMATICS Set 9 Website: https://www.edufever.com Page 10 Answer: Option C Q.46: Two dice are tossed. The probability that the total score is a prime number is: A. A.1/6 B. 5/12 C. C.1/2 D. 7/9 Answer: Option B Q.47: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is: A. A.21/46 B. B.25/117 C. C.1/50 D. 3/25 Answer: Option A Q.48: From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? A. A.1/15 B. B.25/57 C. 35/256 D. 1/221 Answer: Option D Q.49: Considering combination rule of counting outcome, value of 5! Is A. 5 B. 120 C. 24 D. 20 Answer : Option B Q.50: If a brown sack consists of 4 white balls and 3 black balls then probability of one randomly drawn ball will be white is A. 4/7 B. 1/7 C. 4/4 D. 4/ 3
MATHEMATICS Set 9 Website: https://www.edufever.com Page 11 Answer : Option A
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MATHEMATICS Set 10 Website: https://www.edufever.com Page 1 Q.1: Consider the following determinant ∆= Which of the following is a factor of Δ ? A. a+b B. a-b C. a+b+c D. abc Answer: Option B Q.2: The determinant of the matrix is determinant 6 −8 0 2 1 1 4 6 0 0 0 0 4 8 0 −1 A. 11 B. -48 C. 0 D. -24 Answer: Option B Q.3: Let A= be an n-rowed square matrix and be the matrix obtained by interchanging the first and second rows of the n-rowed Identify matrix. Then is such that its first A. row is the same as its second row B. row is the same as the second row of A C. column is the same as the second column of A D. row is all zero Answer: Option C Q.4: Let Ax=b be a system of linear equations where A is an m×n matrix and b is a m×1 column vector and X is an n×1 column vector of unknowns. Which of the following is false? A.The system has a solution if and only if, both A and the augmented matrix [Ab] have the same rank B. If m C. If m=n and b is a non-zero vector, then the system has a unique solution
MATHEMATICS Set 10 Website: https://www.edufever.com Page 2 D. The system will have only a trivial solution when m=n, b is the zero vector and rank(A) = n Answer: Option C Q.5: Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of ( −1 ) is _________ [This Question was originally a Fill-in-the-blanks Question] A. 1/8 B. 1 C. ¼ D. 2 Answer: Option A Q.6: If = () then P.I. A. 100 1 +100 () B. 200 1 +200 () C. −100 1 −100 () D. −200 1 −200 () Answer: Option A Q.7: Complementary function of + = A. (2 + 2) B. (2 − 2) C. (ℎ2 + ℎ2) D. (ℎ2 − ℎ2) Answer: Option A Q.8: P.I. of ODE ( + − ) = A. 2 3 B. 2 4 C. 2 5 D. 2 6 Answer: Option A
MATHEMATICS Set 10 Website: https://www.edufever.com Page 3 Q.9: The order and degree of the ODE = = A. Order=4, degree=1 B. Order=3 degree=1 C. Order=4, degree= defined D. Order=4, degree= undefined Answer: Option D Q.10: Which is the linear differential equation? A. + = B. 4 4 = ( + ( ′ ) 2 ) 3 2 C. 4 4 = D. None of these Answer: Option A Q.11: Numbers in form of p⁄q where p, q are integers and q is not zero are called A. irrational numbers B. rational numbers C. whole numbers D. prime numbers Answer: Option B Q.12: Imaginary part of −ι(3ι + 2) is A. −2 B. 2 C. 3 D. −3 Answer: Option A Q.13: Set of all complex numbers is denoted by A. P B. W C. N D. C Answer: Option D
MATHEMATICS Set 10 Website: https://www.edufever.com Page 4 Q.14: In exponential notation an, ‘n’ is called A. radical B. coefficient C. exponent D. base Answer: Option C Q.15: Set of rational numbers is denoted by A. R B. Q C. R' D. Q' Answer: Option B Q.16: The length of the subnormal to the parabola y2 = 4ax at any point is equal to A. 2 B. 2 2a C. a 2 D. 2a Answer: Option D Q.17: If the line x – 1 = 0 is the directrix of the parabola y² – kx + 8 = 0, then one of the values of k is A. 1 8 B. 8 C. 4 D. 1 4 Answer: Option C Q.18: The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax both drawn at the same end of the latus rectum and the axis of the parabola is A. 2 2 a² B. 2a² C. 4a² D. None of these Answer: Option C
MATHEMATICS Set 10 Website: https://www.edufever.com Page 5 Q.19: The equation of the parabola whose vertex and focus lie on the x– axis at distances a and a1 from the origin respectively, is A. Y² = 4(a1 – a)x B. Y² = 4(a1 – a) (x – a) C. Y² = 4(a1 – a) (x – a) D. None of these Answer: Option B Q.20: If the normal’s at t1 and t2 meets on the parabola then A. t2 = – t1 – 2 1 B. t1t2 = 2 C. t1 t2 = – 1 D. None of these Answer: Option B Q.21: Eigenvalues of an orthogonal matrix A are real or complex conjugates in pair and have absolute value A. 0 B. 1 C. infinite D. 0.5 Answer: Option B Q.22: A quantity that is determined by its magnitude is called A. vector B. scalar C. string D. unit Answer: Option B Q.23: In equation y<sup>''</sup>+p(x)y<sup>'</sup>+q(x)y=r(x) , p and q are A. solution B. constants C. functions D. coefficients Answer: Option D
MATHEMATICS Set 10 Website: https://www.edufever.com Page 6 Q.24: Critical point is also called A. stationary point B. minimax point C. center point D. spiral point Answer: Option A Q.25: Resistance in electrical system is analogues to mechanical system A. mass B. damping constant C. spring module D. displacement Answer: Option B Q.26: If Un = and Un = − Un-2 then the value of U4 is: A. 4 B. 3 4 C. 3 8 D. 8 Answer: Option C Q.27: If Un = − dx and n(Un+1 – Un) = sin , the the value of U3 is A. 1 B. 4 C. 1 - 4 D. 1 + 4 Answer: Option D Q.28: If Un = then the value of Un-1 + Un+1 is A. 1 B. n
MATHEMATICS Set 10 Website: https://www.edufever.com Page 7 C. 2/n D. 1/n Answer: Option D Q.29: If Un = dx and Un = Un-1 then the value of U4 is A. 8 B. 16 C. 32 D. 4 Answer: Option C Q.30: If In = = xsinn x dx = + − In-2, the the value of I3 A. 1 9 B. 7 9 C. 6 9 D. 5 9 Answer: Option B Q.31: Find the vector x determined by the given coordinate vector [x]B and the given basis B. = − − , ,[×] = − A. B. − − C. D. − Answer: Option C Q.32: Solve the problem = + + + − − + − − − : , , , , Find the dimension of the subspace H.
MATHEMATICS Set 10 Website: https://www.edufever.com Page 8 A. dim H = 3 B. dim H = 4 C. dim H = 2 D. dim H = 1 Answer: Option C Q.33: Which of the following should be done in order to convert a continuous time signal to a discrete time signal? A. Differentiating B. Integrating C. Sampling D. None of the above Answer: Option C Q.34: Decide whether or not the matrices are inverses of each other. − − A. Yes B. No C. Both A and B D. None of the above Answer: Option B Q.35: If is a × matrix, what is the smallest possible dimension of ? A. 9 B. 7 C. 2 D. 0 Answer: Option C Q.36: Find the vector x determined by the given coordinate vector [x]B and the given basis B. = − − , ,[×] = − A. 2 3 B. −1 −2
MATHEMATICS Set 10 Website: https://www.edufever.com Page 9 C. 2 9 D. −3 9 Answer: Option C Q.37: Solve the problem = + + + − − + − − − : , , , , Find the dimension of the subspace H. A. dim H = 3 B. dim H = 4 C. dim H = 2 D. dim H = 1 Answer: Option C Q.38:The z-transform of a sequence x(n) which is given as = ∞ = − ∞ − , is known as: A. Uni-Lateral Z-transform B. Bi-Lateral Z-transform C. Tri-Lateral Z-transform D. None of the above Answer: Option B Q.39: Decide whether or not the matrices are inverses of each other. − − A. Yes B. No C. Both A and B D. None of the above Answer: Option B Q.40: If is a × matrix, what is the smallest possible dimension of ? A. 9 B. 7 C. 2
MATHEMATICS Set 10 Website: https://www.edufever.com Page 10 D. 0 Answer: Option C Q.41: Which of the following is not a condition of the binomial distribution? A. Only 2 possible outcomes B. Have Constant Probability of Success C. Must Have At Least 3 Trials D. Trials Must Be Independent Answer: Option C Q.42: If the occurrence of one event means that another cannot happen, then the events are A. Independent B. Mutually Exclusive C. Bayesian D. Empirical Answer: Option B Q.43: In a Poisson probability distribution A. The mean and variance of the distribution are same (equal) B. The probability of success is always greater than 5 C. The number of trials is always less than 5 D. It always contains a contingency table Answer: Option A Q.44: Which of the following is not a correct statement about a probability? A. It must have a value between 0 and 1 B. It can be reported as a decimal or a fraction C. A value near 0 means that the event is not likely to occur/happens D. It is the collection of several experiments. Answer: Option D Q.45: If a card is chosen from a standard deck of cards, what is the probability of getting a diamond (♦) or a club (♣)? A. 26/52=1/2 B. 13/52 C. 20/52 D. 12/52
MATHEMATICS Set 10 Website: https://www.edufever.com Page 11 Answer: Option A Q.46: The Fourier Transform of the signal = () )is: A. 1 1−− B. 1−− C. 1 1− D. None of the above Answer: A Q.47: DTFT is a periodic function of ω with period: A. B. 3 2 C. 2 D. None of the above Answer: C Q.48: What is the z-transform of the signal = . () ? A. a) 1 1−0.5−1 ; > 0.5 B. b) 1 1+0.5−1 ; < 0.5 C. c) 1 1−0.5−1 ; > 0.5 D. d) None of the above Answer: A Q.49: The z-transform of a sequence x(n) which is given as = ∞ = − ∞ − , is known as: A. Uni-Lateral Z-transform B. Bi-Lateral Z-transform C. Tri-Lateral Z-transform D. None of the above Answer: B Q.50: Which of the following should be done in order to convert a continuous time signal to a discrete time signal? A. Differentiating B. Integrating
MATHEMATICS Set 10 Website: https://www.edufever.com Page 12 C. Sampling D. None of the above Answer: C
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