Qus : 1
2 The system of linear equations
has
1
unique
solution if λ ≠ 6 2
no
solution if λ = 8
3 Infinitely many solution if λ = 6 4
infinitely
many solution if λ ≠ 8
Go to Discussion
Qus : 4
3 1 is an empty set 2 is a singleton set 3 contains exactly two elements 1 and – 1 4 is equal to R Go to Discussion
Qus : 6
4 1 is not diagonalizable 2 is an independent 3 is nilpotent 4 has different minimal and characteristics polynomial Go to Discussion
Solution Qus : 7
1 The complex number
is the root of the quadratic equation with real coefficients
1 4 2 2 3 4 4 2 Go to Discussion
Qus : 8
2 The locus of the point (α, β) such that the line y = αx + β, become a tangent to the hyperbola 9x2 - 4x2 = 36, is
1 a hyperbola with eccentricity √5/2 2 a hyperbola with eccentricity √5 3 an ellipse with length of semi-major axis 3 4 an ellipse with eccentricity √3/2 Go to Discussion
Qus : 16
3 Which of the following is not correct statement?
1 A non-cyclic group can have all of its proper
subgroups cyclic, 2 Every finite cyclic group has even number of
generators 3 Infinite cyclic group has exactly two generators 4 Every non-trivial group has at least two distinct
subgroups Go to Discussion
Solution Qus : 17
3 Let T = R3 →R3 be a linear transformation defined by T(x,y,x) = (x-y, y-z, z-x). If rank(T) = ρ and nulity(T)=
1 (0,3) 2 (1,2) 3 (2,1) 4 (3,0) Go to Discussion
Solution Qus : 21
4 The area (in squares units) of the quadrilateral
formed by the tangent lines drawn to the ellipse
at the ends of its two latus rectums is
1 125/2 2 125/4 3 75/5 4 75 Go to Discussion
Solution Qus : 22
3 Let V=M2 (R) denote the vector space 2x2 matrices with real entries over the field. Let T:V→V be defined by T(P) = Pt for any P∈V, where Pt is the transpose of P. If E is the matrix representation of T with respect to the standard basis of V the det(E) is equal to
1 1 2 2 3 - 2 4 - 1 Go to Discussion
Solution Qus : 23
1 The equation 2x2 + y2 - 12x - 4y + 16 = 0 represents
1 an ellipse with center (2,3) 2 a hyperbola with eccentricity √2 3 an ellipse with eccentricity
1/√2 4 a hyperbola with center (3,2) Go to Discussion
Solution Qus : 24
5 If f(x) = ax3 + bx2 + x + 1 has a local maxima value 3 at the point of local maxima x = - 2, then f(2) is equal to :
1 19 2 20 3 24 4 25 Go to Discussion
Qus : 25
4 If the Newton-Raphson method is applied to find a
real root of f(x) = 2x2 + x - 2 = 0 with initial approximation x0 = 1. Then the second approximation x2 is
1 56/105 2 82/105 3 84/105 4 24/105 Go to Discussion
Solution Qus : 26
1 The equation of common tangent to the curve y2 = 8x and xy = - 1 is
1 3y = 9x + 2 2 y = 2x+1 3 2y = x + 8 4 y = x + 2 Go to Discussion
Solution Qus : 27
1 The greatest value of the function y = sin x . sin2x on (-∞, +∞)
1 4/(3√3) 2 3/(3√3) 3 2/(3√3) 4 1 Go to Discussion
Solution Qus : 31
1 The area of the plane region by the curves x + 2y2 = 0 and x + 3y2 = 1 above x axis is equal to
1 5/3 2 1/3 3 2/3 4 4/3 Go to Discussion
Qus : 33
2 The perimeter of the loop of the curve 9y2 = (x-y)(x-5)2
1 4√3 2 2√3 3 4 4 3√3 Go to Discussion
Solution Qus : 74
4 1 (a) 2 (b) 3 (c) 4 (d) Go to Discussion
Solution Let U and V be vector spaces.
Then they are isomorphic iff there is a bijection from a basis of U to a basis of V.
The isomorphism is the basis changer function.
This means that if U and V are finite-dimensional vector spaces, they are isomorphic iff dim(U)=dim(V).
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