Q: Which one of the following means closing down a company and selling its assets?
(a)Liquidation
(b)Revitalize
(c)Resurrect
(d)Enliven
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ESE Mathematics Questions
34 previous year questions
Sub-topics
Algebra (21)Geometry (8)Statistics (2)Calculus (2)Number System (1)
Q: The solution of differential equation y′ = (xy² − cos x sin x) / (y(1 − x²)), y(0) = 2 is
(a)y²(1 + x²) − cos²x = 3
(b)y²(1 − x²) + cos²x = 5
(c)y²(1 + x²) + cos²x = 7
(d)y²(1 − x²) − cos²x = 3
Q: The solution of differential equation y″ + 4y′ + 3y = eᵗ; y(0) = 0, y′(0) = 2 is
(a)y(t) = eᵗ/8 − 7e⁻³ᵗ/8 + 3e⁻ᵗ/4
(b)y(t) = eᵗ/8 − 5e⁻³ᵗ/8 + 3e⁻ᵗ/4
(c)y(t) = eᵗ/8 + 7e⁻³ᵗ/8 − 3e⁻ᵗ/4
(d)y(t) = eᵗ/8 + 7e⁻³ᵗ/8 + 3e⁻ᵗ/4
Q: What is the value of ∫₀⁶ 1 / (1 + 3x + x²) dx by applying Simpson's 3/8ᵗʰ rule with h = 1?
(a)0.8145
(b)0.0295
(c)0.5215
(d)0.6315
Q: If yₓ is a polynomial for which the fifth difference is constant and y₁ + y₇ = −496, y₂ + y₆ = 334, y₃ + y₅ = 962, then what is the value of y₄?
(a)571.25
(b)536.75
(c)596.50
(d)597.25
Q: What is the value of ∫ (from y = 0 to a) ∫ (from x = y² ⁄ a to y) [ y ÷ ((a − x)(ax − y²)) ] dx dy by changing the order of integration?
(a)3πa ⁄ 2
(b)5πa ⁄ 4
(c)πa ⁄ 2
(d)πa ⁄ 4
Q: Indicate what will be the letter / numerical in the missing portion in the given figure (circle with letters and numbers).
(a)R/9
(b)P/11
(c)Q/13
(d)P/16
Q: Where were the Fast Patrol Vessels (FPVs) ICGS Ajit and ICGS Aparajit launched?
(a)Cochin Shipyard Limited
(b)Mazagon Dock Shipbuilders
(c)Goa Shipyard Limited
(d)Hindustan Shipyard
Q: The weight of 3 mangoes and 2 apples is 255 grams. The weight of 2 mangoes and 3 apples is 285 grams. Each mango weighs the same and each apple weighs the same. The combined weight of 1 mango and 1 apple will be
(a)98 grams
(b)104 grams
(c)108 grams
(d)114 grams
Q: In a triangle ABC, if the values of a = 3, b = 4 and sin A = 3⁄4, then the angle ∠B will be
(a)30°
(b)45°
(c)60°
(d)90°
Q: Consider the following equation: (x + y + 1) dx + (2x + 2y + 3) dy = 0 Solving the equation will be where: u is (x + y + 1)
(a)u – log(u + 1) = x + c
(b)2u + log(u – 1) = x + c
(c)2u – log(u + 1) = x + c
(d)u + log(u – 1) = x + c
Q: Consider the following matrix: A = [ -2 2 -3 ; 2 1 -6 ; -1 -2 0 ] The Eigen values are
(a)–3, –3 and 5
(b)–3, 3 and –5
(c)3, 3 and –5
(d)3, –3 and 5
Q: An idea, a design, a manuscript, an invention, or a concept which will give rise to a useful product/application, is known as
(a)Intellectual property right
(b)Employees right
(c)Professional right
(d)Recognition right
Q: Which one of the following is an example of discrete random variables?
(a)Triangular Distribution
(b)Normal Distribution
(c)Central Limit Theorem
(d)Negative Binomial Distribution
Q: If X₁ = [1 1]ᵀ, X₂ = [1 0]ᵀ, and X₃ = [0 1]ᵀ are the eigenvectors of the matrix A = [2 1 −1; 3 2 −3; 3 1 −2], then A⁵ =
(a)[32 31 −31; 33 32 −33; 33 31 −32]
(b)[32 31 −33; 33 32 −31; 33 31 −32]
(c)[32 31 −32; 33 32 −33; 33 31 −31]
(d)[32 33 −31; 33 32 −33; 33 31 32]
Q: One side of a rhombus is 10 cm and one of its diagonals is 12 cm. The area of the rhombus is
(a)24 sq. cm
(b)48 sq. cm
(c)72 sq. cm
(d)96 sq. cm
Q: Reduce the matrix A = ⎡1 3 4⎤ ⎢3 2 −1⎥ ⎣4 −1 1⎦ to the tridiagonal form.
(a)⎡ 1 −5 0 ⎤ ⎢ −5 2 1/5 ⎥ ⎣ 0 1/5 13/5⎦
(b)⎡ 1 0 −5 ⎤ ⎢ −5 2/5 −1/5 ⎥ ⎣ 0 −13/5 −1/5⎦
(c)⎡ 1 −5 0 ⎤ ⎢ −5 −2 −13/5 ⎥ ⎣ 0 1/5 1/5⎦
(d)⎡ 1 −5 0 ⎤ ⎢ −5 −2 1/5 ⎥ ⎣ 0 13/5 1/5⎦
Q: What is the shape of the curve represented by x/5 = √[ 1 + ( y/2 )² ] ?
(a)Hyperbola
(b)Rectangular hyperbola
(c)Parabola
(d)Ellipse
Q: What is the particular solution of the differential equation 5 dy/dx + 2x = 3 if the boundary conditions are y = 7/5 and x = 2 ?
(a)y = 3x/5 − x²/5 + 1
(b)y = 3x/5 + x²/5 − 2
(c)y = 5x/3 − x²/3 + 1
(d)y = 5x/3 + x²/3 − 2
Q: The Boston Consulting Group matrix classifies business in four categories as “STAR”, “QUESTION MARK”, “CASH COWS”. Which one of the following is the fourth one?
(a)CATS
(b)HORSES
(c)DOGS
(d)HENS
Q: If A × B means (A² + B²), then the value of 5 × (4 × 3) is
(a)60
(b)300
(c)650
(d)710
Q: The number of triangles in the given figure is
(a)11
(b)13
(c)15
(d)17
Q: The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle is
(a)9 cm
(b)18 cm
(c)20 cm
(d)41 cm
Q: The highest Eigen value of the 2 × 2 matrix [1 2; 4 3] is
(a)−1
(b)−5
(c)5
(d)1
Q: The surface which intersects the surfaces of the system z(x + y) = c(3 z + 1) orthogonally and which passes through the circle x² + y² = 1, z = 1, is given by
(a)x² + y² = 2 z³ + z² − 2
(b)x² − y² = z³ + z + 1
(c)x² − y² = z² + 4
(d)x² + y² = z³ + z² + 4
Q: The sum of all the natural numbers between 1 and 101 which are divisible by 5 is
(a)1000
(b)1050
(c)1500
(d)2550
Q: For the matrix A = [1 4; 2 3] the expression A⁵ − 4A⁴ − 7A³ + 11A² − A − 10I is equivalent to
(a)A² + A + 5I
(b)A + 5I
(c)A² + 5I
(d)A² + 2A + 6I
Q: The solution of the differential equation (1 + y²) dx = (tan⁻¹y − x) dy is
(a)x = tan⁻¹y + 1 + ce^{−tan⁻¹y}
(b)x = tan⁻¹y − 1 + ce^{−tan⁻¹y}
(c)x = ½ tan⁻¹y − 1 + ce^{−tan⁻¹y}
(d)x = ½ tan⁻¹y + 1 + ce^{−tan⁻¹y}
Q: The first moment about origin of binomial distribution is
(a)np
(b)npq
(c)n(1 − p)
(d)n(1 − p)q
Q: For the regression equations y = 0·516x + 33·73 and x = 0·512y + 32·52 the means of x and y are nearly
(a)67·6 and 68·6
(b)68·6 and 68·6
(c)67·6 and 58·6
(d)68·6 and 58·6
Q: In a rectangular hyperbola, if a curve is traced out by a point moving in such a way that the product of its distances from two fixed lines at right angles to each other is a constant, then those fixed lines are called
(a)asymptotes
(b)intercepts
(c)holes
(d)limits
Q: Which one of the following is not the best approach for the prevention of product liability?
(a)Analysis and design
(b)Quality control
(c)Comprehensive testing
(d)Cost
Q: The creative technique applied when the available and required inputs as well as the desired outputs are listed, is
(a)Attribute listing
(b)Direct dreaming
(c)Black box
(d)Delphi
Q: IEEE standard protocol which defines a wireless Personal Area Network (PAN) operable in a room is
(a)Wi-Fi
(b)Bluetooth
(c)Infrared
(d)Wireless LAN
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