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MATHEMATICS Set 1 Page 1 Q.1. Rank of the matrix A = 0 0 0 0 4 2 3 0 1 0 0 0 4 0 3 0 A. 0 B. 1 C. 2 D. 3 Answer: Option D Q.3. Consider the following two statements: (I) The maximum number of linearly independent column vectors of a matrix A is called the rank of A. (II) If A is an n x n square matrix, it will be nonsingular is rank A = n. With reference to the above statements, which of the following applies? A. Both the statements are false B. Both the statements are true C. I is true but II is false. D. I is false but II is true. Answer: Option B Q.3: The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3, is A. 0 B. 1 C. 2 D. 3 Answer: Option B Q.4: Matrix, A = cos sin 0 sin cos 0 0 0 1
MATHEMATICS Set 1 Page 2 A. orthogonal B. non-singular C. have A-1 exists D. both (b) & (c) Answer: Option D Q.5: In the matrix equation Px = q. which of the following is a necessary condition for the existence of at least one solution for the unknown vector x? A. Augmented matrix [Pq] must have the same rank as matrix P B. Vector q must have only non-zero elements C. Matrix P must be singular D. None of these Answer: Option A Q.6: A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is A. A must be invertible B. b must be linearly depended on the columns of A C. b must be linearly independent of the columns of A D. None of these Answer: Option A Q.7: The system of linear equations (4d - 1)x +y + z = 0 - y + z = 0 (4d - 1) z = 0 has a non-trivial solution, if d equals A. ½ B. ¼ C. ¾ D. 1 Answer: Option B Q.8: If, A, B, C are square matrices of the same order, then (ABC)-1 is equal to A. −1 −1 −1
MATHEMATICS Set 1 Page 3 B. −1 −1 −1 C. −1 −1 −1 D. −1 −1 −1 Answer: Option B Q.9: Rank of the matrix 0 0 -3 9 3 5 3 1 1 A. 0 B. 1 C. 2 D. -1 Answer: Option C Q.10: Eigen vector(s) of the matrix 0 0 α 0 0 0 0 0 0 A. (0,0 ,α) B. (α,0,0) C. (0,0,1) D. (0,α,0) Answer: Option D Q.10: Let A = ( aij ) be an n-rowed square matrix and I12 be the matrix obtained by interchanging the first and second rows of the n-rowed identity matrix. Then AJ12 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
MATHEMATICS Set 1 Page 4 Q.11: If functions f and g have domains Df and Dg respectively, then the domain of f / g is given by A. The union of Df and Dg B. The intersection of Df and Dg C. The intersection of Df and Dg without the zeros of function g D. None of the above Answer: Option C Q.12: Let the closed interval [a, b] be the domain of function f. The domain of f(x - 3) is given by A. The open interval (a, b) B. The closed interval [a, b] C. The closed interval [a - 3, b - 3] D. The closed interval [a + 3, b + 3] Answer: Option D Q.13: Let the interval (a, +infinity) be the range of function f. The range of f(x) - 4 is given by A. The interval (a - 4, +infinity) B. The interval (a + 4, +infinity) C. The interval (a, +infinity) D. None of the above Answer: Option A Q.14: If ∅ = , ² then ∅ A. 2x2 B. √x C. C.0 D. D.1 Answer: Option A Q.15: The value of a = − is A. A.>0 B. B.2 C. C.0 - 1 + 100 - 10 + 1 D. undefined Answer: Option A
MATHEMATICS Set 1 Page 5 Q.16: If f(x) = | x |, then for interval [-1, 1], f(x) A. satisfied all the conditions of Role’s Theorem B. satisfied all the conditions of Mean Value Theorem C. does not satisfied the -conditions of Mean Value Theorem D. None of these Answer: Option C Q.17: The function f(x) = x3 - 6x2 + 9x + 25 has A. a maxima at x= 1 and a minima at x = 3 B. a maxima at x = 3 and a minima at x = 1 C. no maxima, but a minima at x = 1 D. a maxima at x = 1, but no minima Answer: Option A Q.18: The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is A. [-3, 3] B. [-2, 2] C. [2, 3] D. [-1, 1] Answer: Option C Q.19: The function = , < − , ≥ A. Is continuous at x = 1 B. Is differentiable at x = 1 C. Is continuous but not differentiable at x = 1 D. None of these Answer: Option C Q.20: If f (x) = [x sin p x] {where [x] denotes greatest integer function}, then f (x) is A. Continuous at x = 0 B. Continuous in (-1, 0) C. Differentiable at x = 1 D. Differentiable in (-1, 1)
MATHEMATICS Set 1 Page 6 Answer: Option A Q.21: If z and w two complex numbers, then A. + = + B. + = − C. + = / D. + = . Answer: Option A Q.22: The square root of the number (-3)2 are A. -3 B. 3 C. 3,-3 D. 3i,-3i Answer: Option C Q.23: The reciprocal of the number is i is: A. -i B. I C. 1 D. -1 Answer: Option A Q.24: If z1 = 2 + ι, z2 = 1 + 3ι, then ι Re ( z1 - z2 ) = A. 1 B. ι C. 2 ι D. 2 Answer: Option B Q.25: A² + b² A. (a + b )(a-b) B. (a + ι b)(a -ι b) C. (a + b )(a- ι b) D. (a + ι b )(a - b) Answer: Option B
MATHEMATICS Set 1 Page 7 Q.26: |z1 - z2 | = A. |Z1| + |Z2| B. ≤|Z1| + |Z2| C. ≤ Z1 + Z2 D. Z1 + Z2 Answer: Option B Q.27: |z1 + z2 | = A. |Z1| + |Z2| B. ≤|Z1| + |Z2| C. ≤ Z1 + Z2 D. Z1 + Z2 Answer: Option B Q.28: Polar form of a complex number is A. r ( tanθ + ιcotθ ) B. r(secθ + ιcosecθ ) C. r(cosθ + ιsinθ ) D. r (sinθ + ιcosθ) Answer: Option C Q.29: Write the following complex number in the form a + bi : 18- − A. 18+ 9i B. 18-9i C. 27+0i D. 0+9i Answer: Option B Q.30: Simplify the following expression: (20-4i)-(6-5i)+(2i-3a) A. 6-3a-23i B. 14-3a+3i C. -3a+18i D. 26-3a-7i
MATHEMATICS Set 1 Page 8 Answer: Option B Q.31: Length of line joining two points (1, 2) and (4, 8) is: A. 3 B. 9 C. C.?45 D. 45 Answer: Option C Q.32: Length of line joining two points (16, 4) and (36, 6) is: A. 22 B. B.?22 C. 404 D. D.?404 Answer: Option D Q.33: Consider a line passing through (16, 4) and (36, 6), gradient of this line is equal to: A. -0.1 B. 0.1 C. -10 D. 10 Answer: Option B Q.34: Coordinates of midpoint of line joining two points (16, 4) and (36, 6) are: A. (26, 5) B. (5, 26) C. (10, 1) D. (1, 10) Answer: Option A Q.35: Consider a line passing through (1, 2) and (4, 8), gradient of this line is equal to: A. 1 ⁄ 2 B. -1 ⁄ 2 C. 2 D. -2 Answer: Option C Q.36: The points (– 1, 1) and ( 1, – 1) are symmetrical about the line
MATHEMATICS Set 1 Page 9 A. Y +x =0 B. Y =x C. X +y =1 D. None of these Answer: Option B Q.37: The equation of straight line which passes through the point (1, 2) and makes an angle cos– 1 with the x– axis is A. X + Y – 2 = 0 B. 2X + Y – = 0 C. X + 2Y – 2 = 0 D. none of these Answer: Option A Q.38: The equation of the line through (3, 4) and parallel to the line y =3x +5 is A. 3X – Y – 5 =0 B. 3X + Y – 5 = 0 C. 3X + Y + 5 = 0 D. 3X – Y + 5 = 0 Answer: Option A Q.39: The quadratic equation whose roots are the x and y intercepts of the line passing through (1, 1) and making a triangle of area A with axes is A. X2 + ax + 2a = 0 B. X2 – 2ax +2a = 0 C. X2 – ax + 2a = 0 D. None of these Answer: Option B Q.40: The incentre of the triangle formed by the lines y = |x| and y = 1 is A. (0, 2 –) B. (2 –, 0) C. (2 +, 0) D. (0, 2 +) Answer: Option A Q.41: Difference equation is used in :
MATHEMATICS Set 1 Page 10 A. Discrete time analysis B. Continuous time analysis C. Digital analysis D. None of the mentioned Answer: Option A Q.42: Difference equation in discrete systems is similar to the _____________ in continuous systems. A. Difference equation B. Differential equation C. Quadratic equation D. None of the mentioned Answer: Option B Q.43: Difference equation model results in: A. Sampled-data systems B. Numerical analysis of continuous time systems C. Continuous time feedback systems D. Both a and b Answer: Option D Q.44: Difference equation technique for higher order systems is used in: A. Laplace transform B. Fourier transform C. Z-transform D. None of the mentioned Answer: Option C Q.45: Difference equation solution yields at the sampling instants only: A. True B. False Answer: Option A Q.46: The poles of a digital filter with linear phase response can lie
MATHEMATICS Set 1 Page 11 A. Only at z =0 B. Only on the unit circle C. Only inside the unit circle but not at z =0 D. On the left side of Real (z) =0 line Answer: Option B Q.47: Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)- 5y(n+1)+6y(n) =x(n) is unstable. Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle. A. Both A and R are true and R is the correct explanation of A B. Both A and R are true but R is NOT the correct explanation of A C. A is true but R is false D. A is false but R is false Answer: Option A Q.48: Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane. Reason (R): For a rational system, ROC is bounded by poles A. Both A and R are true and R is the correct explanation of A B. Both A and R are true bit R is NOT the correct explanation of A C. A is true but R is false D. A is false but R is true Answer: Option B Q.49: If X(z) =(z+z-3)/(z+z-1), then x(n) series has: A. Alternate 0s B. Alternate 1s C. Alternate 2s D. Alternate -1s Answer: Option A Q.50: Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.
MATHEMATICS Set 1 Website: https://www.edufever.com Page 12 Reason (R): For a causal stable system all the poles should be outside the unit circle in the zplane. A. Both A and R are true and R is the correct explanation of A B. Both A and R are true bit R is NOT the correct explanation of A C. A is true but R is false D. A is false but R is true Answer: Option C
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MATHEMATICS Set 2 Website: https://www.edufever.com Page 1 Q.1: Rank of matrix 1 4 8 7 0 0 3 0 4 3 2 1 3 12 24 2 A. 3 B. 1 C. 2 D. 4 Answer: Option D Q.2: Consider the following statements S1: Sum of the two singular n x n matrices may be non-singular S2: Sum of two the non-singular nx n matrices may be singular. Which of the following statements is correct? A. S1 and S2 are both true B. S1 is true, S2 is false C. S1 is false, S2 is true D. S1 and S2 are both false Answer: Option A Q.3: If A and B are square matrices of size n x n, then which of the following statement is not true? A. det. (AB) = det. (A) det. (B) B. det. (kA) = det. (A) C. det. (A + B) = det. (A) + det. (B) D. det. ( ) =1/det. ( −1 ) Answer: Option C Q.4: In the matrix equation Px = q. which of the following is a necessary condition for the existence of at least one solution for the unknown vector x? A. Augmented matrix [Pq] must have the same rank as matrix P B. Vector q must have only non-zero elements C. Matrix P must be singular D. None of these
MATHEMATICS Set 2 Website: https://www.edufever.com Page 2 Answer: Option A Q.5: Rank of the diagonal matrix A. 1 B. 2 C. 3 D. 4 Answer: Option D Q.6: The matrix B = AT, where A is any matrix is A. skew symmetric B. symmetric about the secondary diagonal C. always symmetric D. another general matrix Answer: Option C Q.7: Given: A = 2 0 0 -1 0 1 0 0 0 0 3 0 -1 0 0 4 A. 10 B. -10 C. 24 D. 22 Answer: Option A Q.8: Eigen values of a real symmetric matrix are always A. positive B. real and imaginary
MATHEMATICS Set 2 Website: https://www.edufever.com Page 3 C. negative D. real Answer: Option D Q.9: Determinant of the matrix 1 0 0 0 100 1 0 0 100 200 1 0 100 200 300 1 Is A. 100 B. 200 C. 1 D. 0 Answer: Option C Q.10: The characteristics equation of a matrix A is 2 -t-1=0, then A. −1 does not exist B. −1 exit but cannot be determined from the data C. −1=A+1 D. −1=A-1 Answer: Option D Q.11: Limits Continuity and Differentiability = 0, (n is integer), for A. No value of n B. All value of n C. Only negative value of n D. Only positive value of n Answer: Option B Q.12: → − Equal, where [.] denotes the greatest integer function (a) (b) 0 (c) 1
MATHEMATICS Set 2 Website: https://www.edufever.com Page 4 (d) Does not exist Answer: Option C Q.13: f (x) is a continuous function and takes only rational values. If f (0) = 3, then f (2) equals A. 5 B. 0 C. 1 D. None of these Answer: Option D Q.14: → . − − is equal to A. log2 B. 1 2 log2 C. 2 log2 D. None of these Answer: Option C Q.15: The value of p for which the function = ( −) + , ≠ () , = is continuous at x=0 is A. 1 B. 2 C. 3 D. 4 Answer: Option D Q.16: → −− − is equal to A. 1/2 B. 2 C. −1/2 D. None of these Answer: Option A
MATHEMATICS Set 2 Website: https://www.edufever.com Page 5 Q.17: The number of points where g (f(x)) is discontinuous given that g(x) = +− and f(x) = − is A. 1 B. 2 C. 3 D. 4 Answer: Option C Q.18: →∞ + 2x = A. e-4 B. e-6 C. e-2 D. None of these Answer: Option A Q.19: In order that function f (x) = (x + 1) cot x is continuous at x = 0, f (0) must be defined as A. 0 B. e C. 1/e D. None of these Answer: Option B Q.20: The value of derivative of f (x) = |x –1| + |x –3| at x = 2 is A. –2 B. 0 C. 2 D. Not defined Answer: Option B Q.21: Multiply the following complex numbers: (7-5i)(6+4i) A. 62+2i B. 21-2i C. 21+2i D. 62-2i
MATHEMATICS Set 2 Website: https://www.edufever.com Page 6 Answer: Option D Q.22: Calculate (cos 3Ө+i sin 3Ө)5 A. cos(5Ө)+ i sin(5Ө) B. cos(15Ө)+i sin (15Ө) C. cos53 Ө+ i sin5 3 Ө D. 3(cos5 Ө+ isin5 Ө) Answer: Option B Q.23: Rewrite the following expression: A. he3a Өi B. he3a Ө C. 3he3a Өi D. Ahe3 Ө Answer: Option A Q.24: Write the complex conjucate of 3c-4di A. 3c+4di B. -4di+ 3c C. 3ci-4d D. 3ci+4d Answer: Option A Q.25: Multiply the following complex numbers: 2(cos 4a+ i sin 4a)*7(cos3c+ i sin 3c) A. 14(cos4acos3c+ isin4a sin3c) B. 14(cos(4a+3c)+i sin(4a+3c)) C. 14(cos 4a sin 3c+icos4a sin 3c) D. 14(cos4a sin3c+isin4a cos 3c) Answer: Option B Q.26: Under property of equality of real numbers, a + c = b + c then a = b and ∀ a, b, c ∈ R is called A. cancellation property for addition B. additive property C. cancellation property for multiplication
MATHEMATICS Set 2 Website: https://www.edufever.com Page 7 D. multiplicative property Answer: Option A Q.27: Decimal fraction in which there are finite number of digits in its decimal part is called A. terminating decimal fraction B. non-terminating decimal fraction C. linear fraction D. quadratic fraction Answer: Option A Q.28: ι 10 is equal to A. −1 B. ι C. 1 D. 0 Answer: Option A Q.29: If we include ‘0’ in set of natural number. resulting set is said to be set of A. whole numbers B. natural numbers C. prime numbers D. odd numbers Answer: Option A Q.30: The straight lines of the family x (a+b) + y (a-b) = 2a (a and b being parameters) are A. Not concurrent B. Concurrent at (1, -1) C. Concurrent at (1, 1) D. None of these Answer: Option C Q.31: Points on the line x + y = 4 that lie at a unit distance from the line 4x+ 3y–10=0 are A. (3, 1) AND (–7, 11)
MATHEMATICS Set 2 Website: https://www.edufever.com Page 8 B. (–3, 7) AND (2, 2) C. (–3, 7) AND (–7, 11) D. None of these Answer: Option A Q.32: If the line y = mx meets the lines x + 2y – 1= 0 and 2x – y + 3 = 0 at the same point, then m is equal to A. 1 B. -1 C. 2 D. -2 Answer: Option B Q.33: The member of the family of lines ( p +q)x + (2p +q)y = p + 2q, where p ¹ 0, q ¹0, pass through the point A. (3, – 1) B. – 3 ,1) C. (1, 1) D. None Of These Answer: Option A Q.34: The equation of the line joining the points (– 1, 3) and (4, – 2) is A. x + y – 1 =0 B. x + y +1 =0 C. x + y +2 =0 D. x + y – 2 =0 Answer: Option D Q.35: Locus of the point of intersection of lines x cosa+ y sin a = a and x sin a – y cos a =a (aÎ R ) is A. x2 + y2 =a2 B. x2 + y2 = 2a2 C. x2 + y2 + 2x + 2y = a2 D. None of these Answer: Option B
MATHEMATICS Set 2 Website: https://www.edufever.com Page 9 Q.36: The area of the quadrilateral formed by y = 1 – x, y = 2 – x and the coordinate axes is A. 1 B. 2 C. 3/2 D. None of these Answer: Option C Q.37: If one vertex of an equilateral triangle is at (1, –2) and the base is x + y + 2 = 0, then the length of each side is A. 3 2 B. 2 3 C. 2 3 D. 3 2 Answer: Option B Q.38: The locus of the mid-point of the portion intercepted between the axes by the line x cos a + y sin a = p, where p is a constant is A. X² + y² = 4p² B. 1 ² + 1 ² = 4 ² C. X² + y² = 4 ² D. 1 ² + 1 ² = 2 ² Answer: Option B Q.39: If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is A. Square B. A circle C. Straight line D. Two intersecting lines Answer: Option A Q.40: Solution of the differential equation = sin (x + y) + cos (x + y), is
MATHEMATICS Set 2 Website: https://www.edufever.com Page 10 A. Log + (+) = y + c B. Log + (+) = x + c C. log |1 + tan (x + y)| = y + c D. None of these Answer: Option A Q.41: The equation of the curves, satisfying the differential equation (x2 + 1) = 2x passing through the point (0, 1) and having the slope of tangent at x = 0 as 6 is A. Y 2 = 2x3 + 6x + 1 B. Y = 2x3 + 6x + 1 C. Y 2 = x3 + 6x + 1 D. None of these Answer: Option B Q.42: Solution of + 2xy = y is A. Y = − 2 B. Y = 2 - x C. Y = cex D. Y = − 2 Answer: Option A Q.43: If y = sin ( a sin-1 x), then A. (1 – x 2 ) 2 2 + +a 2 y = 0 B. (1 – x 2 ) 2 2 + −a 2 y = 0 C. (1 – x 2 ) 2 2 − −a 2 y = 0 D. None of these Answer: Option A Q.44: If y = a cos ( log x) + b sin ( log x) , then A. X 2 2 2 + + = 0 B. X 2 2 2 − + = 0
MATHEMATICS Set 2 Website: https://www.edufever.com Page 11 C. X 2 2 2 + − = 0 D. None of these Answer: Option B Q.45: The differential equation y = a – x ( x≠ , ∈ ) represents A. a family of circles with centre on y-axis B. a family of circles with centre at origin C. a family of circles with given radius D. a family of circles with centre on x-axis Answer: Option D Q.46: The differancial equation of the family curves y2 = 4a (x + a) is A. Y 2 = 4 + B. Y 2 2 + 2xy − 2 = 0 C. Y 2 + 4 = 0 D. 2y + 4 = 0 Answer: Option B Q.47: Solution of + = + − dx is A. X – tan-1 B. tan-1 = c C. x tan-1 = c D. none of these Answer: Option C Q.48: A partial, initially at origin moves along x – axis according to the rule = x + 4. The time taken by the practice to traverse a distance of 96 units is A. In 5 B. Log5 e C. 2 In 5 D. 2 log5e Answer: Option C Q.49: If y = cos-1 (Inx), then the value of is
MATHEMATICS Set 2 Website: https://www.edufever.com Page 12 A. 1 1− ( ) 2 B. −1 1− ( ) 2 C. −1 1+ ( ) 2 D. 1 1+ ( ) 2 Answer: Option B Q.50: Under property of equality of real numbers, a = b then b = a and ∀a, b ∈ R is called A. symmetric property B. additive property C. transitive property D. multiplicative property Answer: Option A
MATHEMATICS Set 2 Website: https://www.edufever.com Page 13 **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 3 Website: https://www.edufever.com Page 1 Q.1: Let A and B are square matrices such that AB=I, then zero is an eigen value of A. A but not of B B. but not of A C. both A and B D. neither A nor B Answer: Option D Q.22: The vector is an eigenvector of A = −2 2 −3 2 1 −6 −1 −2 0 one of the eigen values of A is A. 1 B. 2 C. 5 D. -1 Answer: Option C Q.3: Rank of matrix 1 4 8 7 0 0 3 0 4 3 2 1 3 12 24 2 A. 3 B. 1 C. 2 D. 4 Answer: Option D Q.4: If A and B are non-zero square matrices, then AB = 0 implies A. A and B are orthogonal B. A and B are singular 1 2 −1
MATHEMATICS Set 3 Website: https://www.edufever.com Page 2 C. B is singular D. A is singular Answer: Option A Q.5: If A and B be real symmetric matrices of sizen n x n, then A. A = 1 B. A = −1 C. AB = BA D. D.() = BA Answer: Option D Q.6: If AT = A-1, where A is a real matrix, then A is A. normal B. symmetric C. Hermitian D. orthogonal Answer: Option D Q.7: In the matrix equation Px = q. which of the following is a necessary condition for the existence of at least one solution for the unknown vector x? A. Augmented matrix [Pq] must have the same rank as matrix P B. Vector q must have only non-zero elements C. Matrix P must be singular D. None of these Answer: Option A Q.8: Vector which describes total population for each relevant region is classified as. A. migration vector B. selling vector C. buying vector D. population vector Answer: Option D
MATHEMATICS Set 3 Website: https://www.edufever.com Page 3 Q.9: Demand of industry output can come from sources which includes A. demand from different industries B. demand from other than industries C. supply from different industries D. both a and b Answer: Option D Q.10: In inverse and systems of equations, matrix inverse for systems of equation is used to determine A. identified set of equation B. variable set of equation C. solution set of equations D. constant set of equations Answer: Option C Q.11: → + + + − is equal to A. 1 B. −1 C. 2 D. 0 Answer: Option D Q.12: If f(x) = + + + + x Then →∞ is A. e 4 B. e 3 C. e 2 D. None of these Answer: Option A Q.13: → (+) + − is equal to A. a 2 cosa + a sina B. a 2 cosa + 2a sina C. 2a2 cosa + a cosa D. None of these
MATHEMATICS Set 3 Website: https://www.edufever.com Page 4 Answer: Option B Q.14: The value the limit → ( − − ) ( + − ) , a > 0 is A. 0 B. 1 C. Infinity D. Does not exist Answer: Option D Q.15: The value of → + + 1/x² is A. e 2 B. e 3 C. e 5 D. None of these Answer: Option A Q.16: The minimum value of | x2 _ 5x + 21 | is A. -5 B. 0 C. -1 D. -2 Answer: Option B Q.17: Value of the definite integral + − is A. -2ln2 B. 2 C. 0 D. (ln2)2 Answer: Option D Q.18: What is the derivative of f(x) = | x | at x = 0 A. 1 B. -1 C. 0 D. Does not exist
MATHEMATICS Set 3 Website: https://www.edufever.com Page 5 Answer: Option D Q.19: The value of the improper integral A. A.1/4 B. 0 C. -1/4 D. 1 Answer: Option C Q.20: The function f(x) = 3x(x - 2) has a A. Minimum at x = 1 B. Maximum at x = 1 C. Minimum at x = 2 D. Maximum at x = 2 Answer: Option A Q.21: → + + + − is equal to A. 1 B. −1 C. 2 D. 0 Answer: Option D Q.22: If f(x) = + + + + x Then →∞ is A. e 4 B. e 3 C. e 2 D. None of these Answer: Option A Q.23: → (+) + − is equal to A. a 2 cosa + a sina B. a 2 cosa + 2a sina C. 2a2 cosa + a cosa D. None of these Answer: Option B
MATHEMATICS Set 3 Website: https://www.edufever.com Page 6 Q.24: The value the limit → ( − − ) ( + − ) , a > 0 is A. 0 B. 1 C. Infinity D. Does not exist Answer: Option D Q.25: The value of → + + 1/x² is A. e 2 B. e 3 C. e 5 D. None of these Answer: Option A Q.26: The minimum value of | x2 _ 5x + 21 | is A. -5 B. 0 C. -1 D. -2 Answer: Option B Q.27: Value of the definite integral + − is A. -2ln2 B. 2 C. 0 D. (ln2)2 Answer: Option D Q.28: What is the derivative of f(x) = | x | at x = 0 A. 1 B. -1 C. 0 D. Does not exist Answer: Option D
MATHEMATICS Set 3 Website: https://www.edufever.com Page 7 Q.29: The value of the improper integral A. A.1/4 B. 0 C. -1/4 D. 1 Answer: Option C Q.30: The function f(x) = 3x(x - 2) has a A. Minimum at x = 1 B. Maximum at x = 1 C. Minimum at x = 2 D. Maximum at x = 2 Answer: Option A Q.31: → + + + − is equal to A. 1 B. −1 C. 2 D. 0 Answer: Option D Q.32: If f(x) = + + + + x Then →∞ is A. e 4 B. e 3 C. e 2 D. None of these Answer: Option A Q.33: → (+) + − is equal to A. a 2 cosa + a sina B. a 2 cosa + 2a sina C. 2a2 cosa + a cosa D. None of these Answer: Option B
MATHEMATICS Set 3 Website: https://www.edufever.com Page 8 Q.34: The value the limit → ( − − ) ( + − ) , a > 0 is A. 0 B. 1 C. Infinity D. Does not exist Answer: Option D Q.35: The value of → + + 1/x² is A. e 2 B. e 3 C. e 5 D. None of these Answer: Option A Q.36: The minimum value of | x2 _ 5x + 21 | is A. -5 B. 0 C. -1 D. -2 Answer: Option B Q.37: Value of the definite integral + − is A. -2ln2 B. 2 C. 0 D. (ln2)2 Answer: Option D Q.38: What is the derivative of f(x) = | x | at x = 0 A. 1 B. -1 C. 0 D. Does not exist Answer: Option D
MATHEMATICS Set 3 Website: https://www.edufever.com Page 9 Q.39: The value of the improper integral A. A.1/4 B. 0 C. -1/4 D. 1 Answer: Option C Q.40: The function f(x) = 3x(x - 2) has a A. Minimum at x = 1 B. Maximum at x = 1 C. Minimum at x = 2 D. Maximum at x = 2 Answer: Option A Q.41: The solution of the differential equation = + is A. = kx B. = k C. = ky D. = k Answer: Option A Q.42: Solution of the differential equation In = ax + by is A. 1 e -by = 1 e ax + C B. 1 e -by = 1 e ax + C C. 1 e -by = - 1 e ax + C D. 1 e -by = - 1 e ax + C Answer: Option A Q.43: If x = 2 In cot t and y = tan t + cot t, the value of is A. Cot 2t B. tan 2t
MATHEMATICS Set 3 Website: https://www.edufever.com Page 10 C. cos 2t D. sec 2t Answer: Option A Q.44: Solution of (x2 sin3 y – y 2 cos x) dx + (x3 cos y sin2 y – 2y sin x) dy = 0 is A. 3 3 3 B. X 3 sin3 y = y2 sin x + c C. 3 3 3 = y2 sin x + c D. None of these Answer: Option C Q.45: If the general solutions of a differential equation is (y + c)2= cx, where c is an arbitrary constant, then the order and degree of differential equation is A. 1, 2 B. 2, 1 C. 1, 3 D. None of these Answer: Option A Q.46: Wronskian is a A. difference B. integration C. determinant D. differentiation Answer: Option C Q.47: A technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems is called A. static calculus B. dynamic calculus C. operational calculus D. integral Answer: Option C Q.48: Wronskin in a set of solution represent its A. superposition B. linear independency
MATHEMATICS Set 3 Website: https://www.edufever.com Page 11 C. combinations D. integrations Answer: Option B Q.49: Operational calculus is also known as A. operational analysis B. operational amplification C. logical analysis D. integration Answer: Option A Q.50: Mass in mechanical system is analogues to electrical system A. inductance B. resistance C. capacitance D. reciprocal of capacitance Answer: Option A
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MATHEMATICS Set 4 Website: https://www.edufever.com Page 1 Q.1. Who discovered Fourier series? A. Jean Baptiste de Fourier B. Jean Baptiste Joseph Fourier C. Fourier Joseph D. Jean Fourier Answer: Option B Q.2. What is Fourier series? A. The representation of periodic signals in a mathematical manner is called a Fourier series B. The representation of non periodic signals in a mathematical manner is called a Fourier series C. The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier series D. The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier series Answer: Option D Q.3. What are the two types of Fourier series? A. Trigonometric and exponential B. Trigonometric and logarithmic C. Exponential and logarithmic D. Trigonometric only Answer: Option A Q.4. Fourier series representation can be used in case of Non-periodic signals too. True or false? A. True B. False Answer: Option B Q.5. Choose the condition from below that is not a part of Dirichlet’s conditions? A. If it is continuous then there are a finite number of discontinuities in the period T1 B. It has a finite average value over the period T C. It has a finite number of positive and negative maxima in the period T D. It is a periodic signal Answer: Option D
MATHEMATICS Set 4 Website: https://www.edufever.com Page 2 Q.6. What are the conditions called which are required for a signal to fulfil to be represented as Fourier series? A. Dirichlet’s conditions B. Gibbs phenomenon C. Fourier conditions D. Fourier phenomenon Answer: Option A Q.7. How is the exponential Fourier series represented? A. X(t) = ∑Xn ejnwt + wt B. X(t) = 1/T∑Xnejnwt C. X(t) = ∑Xn ejnwt D. X(t) = T*∑Xn ejnwt Answer: Option C Q.8. How is a trigonometric Fourier series represented? A. A0 +∑*ancos(w0 t)+ ansin(w0 t)] B. ∑*ancos(w0 t)+ ansin(w0 t)] C. A0 *∑*ancos(w0 t)+ ansin(w0 t)] D. A0 +∑*ancos(w0 t)+ ansin(w0 t)] + sinwt Answer: Option A Q.9. What is the equation – Xn =1/T∫x(t) ejnwt called? A. Synthesis equation B. Analysis equation C. Frequency domain equation D. Discrete equation Answer: Option B Q.10. What is the equation – X(t)=∑Xnejnwt called? A. Synthesis equation B. Analysis equation C. Frequency domain equation D. Discrete equation Answer: Option A
MATHEMATICS Set 4 Website: https://www.edufever.com Page 3 Q.11.If determinant of a matrix is equal to zero, then it is said to be A. Square matrix B. Singular matrix C. Non-singular matrix D. Identical matrix Answer: Option B Q.12.If matrices are of same order and + = + , this law is known as A. Distributive law B. Commutative law C. Associative law D. Cramer's law Answer: Option B Q.13. We can add two matrices having real numbers A and B if their A. Order is same B. Rows are same C. Columns are same D. Elements are same Answer: Option A Q.14.If a matrix has equal number of columns and rows then it is said to be a A. Row matrix B. Identical matrix C. Square matrix D. Rectangular matrix Answer: Option C Q.15.A pair of equations to determine value of 2 variables is called A. Simultaneous linear equations B. Paired equations C. Quadratic equations D. Simple equations Answer: Option A
MATHEMATICS Set 4 Website: https://www.edufever.com Page 4 Q.16.What is the size of the matrix = ? A. 2 × 3 B. 3 × 2 C. 3 × 4 D. 4 × 3 Answer: Option C Q.17.Which sums can be made from the following matrices? = , = , = , = (Zero or more options can be correct) A. + B. + C. + D. + E. + F. + G. + H. + Answer: Option A, B, C, D, E, F Q.18.If = − find the matrix 7A. A. 7 0 21 2 −1 2 0 2 1 B. 1 0 3 4 −7 14 0 2 1 C. 1 0 3 2 −1 2 0 14 7 D. 7 0 21 14 −7 14 0 14 7 Answer: Option D Q.19.If is a × matrix, and B is a × matrix, how many columns does have?
MATHEMATICS Set 4 Website: https://www.edufever.com Page 5 A. 4 B. 2 C. 6 D. 1 Answer: Option A Q.20.Let = , = − = − which of the following statements are correct? (Zero or more option can be correct) A. + = 5 5 5 5 B. = 0 1 2 −3 −4 10 C. + = 2 5 3 0 D. = 3 2 1 13 6 −1 E. = −8 20 −8 13 Answer: Option A, B, D Q.21.Sum of products can be done using A. Demorgan's theorem B. Algebraic theorem C. Demorgan's postulate D. Algebraic postulate Answer: Option A Q.22.The number of elements in the Power set P(S) of the set = [ [ ɸ] , ,[ , ]] is A. 2 B. 4 C. 8 D. None of these Answer: Option C Q.23. Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then A. At least one of the sets Si is a finite set B. Not more than one of the set Si can be inite
MATHEMATICS Set 4 Website: https://www.edufever.com Page 6 C. At least one of the sets Si is an ininite set D. None of these Answer: Option C Q.24.If f : −> and , ⊆ , then f ( ∩ ) is equal to A. ( ∩ ) B. ( ∪ ) C. ( → ) Answer: Option C Q.25.If A and B are sets and A∪ B= A ∩ B, then A. A = φ B. B = φ C. A = b D. None of these Answer: Option C Q.26.If X and Y are two sets, then X ∩ (Y ∪ X) C equals A. X B. Y C. Ø D. None of these Answer: Option C Q.27.The number of elements in the power set of the set {{a, b}, c} is A. 8 B. 4 C. 3 D. 7 Answer: Option B Q.28.If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R? A. 5 B. 8 C. 9 D. 5
MATHEMATICS Set 4 Website: https://www.edufever.com Page 7 Answer: Option D Q.29.Order of the power set of a set of order n is A. B. 2 C. 2 D. 2 Answer: Option D Q.30.In a language survey of students it is found that 80 students know English, 60 know French, 50 know German, 30 known English and French, 20 know French and German, 15 know English and German and 10 students know all the three languages. How many students know at least one language? A. 135 B. 30 C. 10 D. 45 Answer: Option A Q.31.Joint probability of independent events J and K is equal to A. P (J) * P (K) B. P (J) + P (K) C. P (J) * P (K) + P (J-K) D. P (J) * P (K) – P (J * K) Answer: Option C Q.32.Way of getting information from measuring observation whose outcomes occurrence is on chance is called A. Beta experiment B. Random experiment C. Alpha experiment D. Gamma experiment Answer: Option B Q.33.Probability which is based on self-beliefs of persons involved in experiment is classified as A. Subjective approach B. Objective approach
MATHEMATICS Set 4 Website: https://www.edufever.com Page 8 C. Intuitive approach D. Sample approach Answer : Option A Q.34.Probability of second event in situation if first event has been occurred is classified as A. Series probability B. Conditional probability C. Joint probability D. Dependent probability Answer : Option B Q.35.In probability theories, events which can never occur together are classified as A. Collectively exclusive events B. Mutually exhaustive events C. Mutually exclusive events D. Collectively exhaustive events Answer : Option C Q.36. What are the chances that no two boys are sitting together for a photograph if there are 5 girls and 2 boys? A. 1/21 B. 4/7 C. 2/7 D. 5/7 Answer: Option D Q.37. A box has 6 black, 4 red, 2 white and 3 blue shirts. What is the probability that 2 red shirts and 1 blue shirt get chosen during a random selection of 3 shirts from the box? A. 18/455 B. 7/15 C. 7/435 D. 7/2730 Answer: Option A Q.38.What is probability of drawing two clubs from a well shuffled pack of 52 cards? A. 13/51 B. 1/17
MATHEMATICS Set 4 Website: https://www.edufever.com Page 9 C. 1/26 D. 13/17 Answer: Option B Q.39.When two coins are tossed simultaneously, what are the chances of getting at least one tail? A. 3/4 B. 1/5 C. 4/5 D. 1/4 Answer: Option A Q.40.A box has 6 black, 4 red, 2 white and 3 blue shirts. What is probability of picking at least 1 red shirt in 4 shirts that are randomly picked? A. 4/15 B. 24/455 C. 69/91 D. 22/91 Answer: Option C Q.41.Which of the following is correct for stability of equilibrium configuration? A. The application of the conditions of the equilibrium of the body is valid only in the 2D B. The application of the conditions of the equilibrium of the body is valid only in the 3D C. The application of the conditions of the equilibrium of the body is valid only in the 1D D. The application of the conditions of the equilibrium of the body is valid throughout Answer: Option D Q.42.For stability of equilibrium configuration the net moment acting on the body by various forces is zero. A. True B. False Answer: Option A Q.43.Free body diagrams don’t play any role in making the calculations on the conditions of stability of equilibrium configuration. A. True B. False