Sunday, 5 November 2017

HSST Mathematics Solved Paper 36/2016/OL - Part 5

81.       The value of Wronskian W (x, x2, x3) is
(A) 2x2
(B) 2x4
(C) 2x3
(D) x2
Answer: C
82.       The general solution of (∂l2u)/( ∂x2) + (∂2u)/( ∂y2) = 0 is of the form
(A) u= f(x + iy) - g (x - iy)
(B) u = f(x - iy) - g (x - iy)
(C) u = f(x + iy) + g (x - iy)
(D) u = f(x - iy) + g (x + iy)
Answer: C
83.       The partial differential equation formed by eliminating the arbitrary function from z=f((y)/(x)) is
(A) x(∂z)/( ∂x) +(∂z)/( ∂y) = 0
(B) (∂z)/( ∂x) +(∂z)/( ∂y) = 0
(C) (∂z)/( ∂x) + y (∂z)/( ∂y) = 0
(D) x(∂z)/( ∂x) + y (∂z)/( ∂y) = 0
Answer: D
84.       The orthogonal trajectory of the family of curves x2-y2 = k is given by
(A) x2+y2 =c
(B) xy=c
(C) y=c
(D) x=0
Answer: B
85.       The general solution of the wave equation (∂2y)/( ∂t2) = c2 (∂2y)/( ∂x2) is
(A) y (x, t) = Phi (x+ct) + psi (x - ct)
(B) y (x, t) = f (x+ct)
(C) y (x, t) = f (x-ct)
(D) No general solution exists
Answer: A
86.       Stirling's formula is the …………… of Gauss' forward and backward formulae.
(A) Arithmetic mean
(B) Geometric mean
(C) Harmonic mean
(D) None of the above
Answer: A
87.       The interpolating polynomial of the highest degree which corresponds the functional values f (-1) = 9, f(0)=5, f (2) = 3, f (5) = 15 is
(A) x3+x2+2x+5
(B) x2-3x+5
(C) x4+4x3 +5x2+5
(D) x+5
Answer: B
88.       The solution of the integral equation Phi (x) = x+ int_0^x (Xi -x) Phi (Xi) dXi is
(A) cos x
(B) tan x
(C) sin x
(D) sec x
Answer: C
89.       The minimizing curve must satisfy a differential equation called
(A) Lagrange's equation
(B) Euler-Lagrange equation
(C) Gauss equation
(D) None of the above
Answer: B
90.    A solid figure of revolution, for a given surface area, has maximum volume is in the case of
(A) a circle
(B) a sphere
(C) an ellipse
(D) a parabola
Answer: B
91.    A rigid body moving in space with one point fixed has degree of freedom
(A) 3
(B) 1
(C) 6
(D) 9
Answer: A
92.    A particle of unit mass is moving under gravitational field, along the cycloid x = phi - sin phi, y =1 + cos phi.
Then the Lagrangian for motion is
(A) phi^2 (1+cos phi) - g (1- cos phi)
(B) phi^2 (1-cos phi) + g (1+ cos phi)
(C) phi^2 (1-cos phi) - g (1+ cos phi)
(D) 2phi^2 (1-cos phi) - g (1+ cos phi)
Answer: C
93.    L^-1 [(1)/(s (s2+a2))] is
(A) (1)/(a2) (1- cos at)
(B) (2 sin h t)/(t)
(C) (1)/(a2) (e^{at} -1)
(D) (1)/(a2) sin h at
Answer: A
94.    int_0^∞ e^{-x^2}dx is
(A) (1)/(2)
(B) (pi)/(2)
(C) (sqrt(pi))/(2)
(D) -sqrt(pi)
Answer: C
95.    Using Fourier series, representing x in the interval [-pi, pi], the sum of the series
1-(1)/(3)+(1)/(5)-(1)/(7)+... is
(A) 0
(B) 1
(C) (pi)/(2)
(D) (pi)/(4)
Answer: D
96.    The only idempotent t-conorm is
(A) algebraic sum
(B) drastic union
(C) standard fuzzy union
(D) bounded sum
Answer: C
97.    Using fuzzy arithmetic operations on intervals [4,10]/[1,2] is
(A) [4,5]
(B) [2,10]
(C) [2,8]
(D) [4,20]
Answer: B
98.    The language generated by the grammar G = ({S}, {a,b}, S, P) where P is given by is
S -> aSb, S->lambda is
(A) {an bn : n>=0}
(B) {an bn+1 : n>=0}
(C) {an+1 bn : n >= 0}
(D) {an+2 bn : n >= 1}
Answer: A
99.    Which of the following is not true in the derivative of a smooth vector field X ?
(A) grad_v (X+Y) = grad_v X + grad_v Y
(B) grad_v (fX) = (grad_v f) X (p) + f(p) (grad_v X)
(C) grad_v (X * Y) = (grad_v X) * Y (p) + X (p) * (grad_v Y)
(D) grad_v (fX) = f(grad_vX)
Answer: D
100.    Let X be a non-empty compact Hausdorff space. If every point of X is a limit point of X, then
(A) X is disjoint
(B) X is countable
(C) X is uncountable
(D) None of the above
Answer: C

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