The sequence {S_{n}} of real numbers given by
Let be the vector space (over R) of all polynomials of degree ≤ 3 with real coefficients. Consider the linear transformation T: P → P defined by
Then the matrix representation M of T with respect to the ordered basis {1, x, x^{2}, x^{2} }satisfies
Let f : [1,1] → R be a continuous function. Then the integral
is equal to
Let σ be an element of the permutation group S_{5 } Then the maximum possible order of σ is
Let f be a strictly monotonic continuous real valued function defined on [a,b] such that f(a) < a and f(b) >b Then which one of the following is TRUE?
The nonzero value of n for which the differential equation
becomes exact is
One of the points which lies on the solution curve of the differential equation
with the given condition y(0) = 1, is
Let S be a closed set of R, T a compact set of R such that S ∩ T ≠ Ø. Then S ∩ T is
Let S be the series
and T be the series
of real numbers. Then which one of the following is TRUE?
Let {a_{n}} be a sequence of positive real numbers satisfying
Then all the terms of the sequence lie in
The largest eigenvalue of the matrix
The value of the integral
If the triple integral over the region bounded by the planes 2x + y + z = 4, x = 0 , y = 0, z = 0
is given by then the function
The surface area of the portion of the plane y + 2z = 2 within the cylinder x^{2} + y^{2} = 3 is
The function f(x,y) = 3x^{2}y + 4y^{3} 3x^{2}  12y^{2} + 1 has a saddle point at
Let y(x) be the solution of the differential equation
Then y(2) is
The general solution of the differential equation with constant coefficients
approaches zero as x → ∞ if
of S. Then which one of the following is FALSE?
The sum of the series
is
Then which one of the following is TRUE?
The matrix is a unitary matrix when α is
a nonzero vector such that Mx = b for some x ∈ R^{3}
The value of x^{T}b is
The number of group homomorphisms from the cyclic group Z_{4} to the cycle group Z_{7} is
In the permutation group S_{n }(n ≥ 5) , if H is the smallest subgroup containing all the 3cycles, then which one of the following is TRUE?
At x = 0 , the function f is
be a sequence of positive real numbers satisfying
If α and β are the roots of the equation
then which of the following statement(s) is(are) TRUE ?
The value(s) of the integral
. is
Then at the point (0, 0) which of the following statement(s) is(are) TRUE ?
Consider the differential equation
Then which of the following statement(s) is(are) TRUE?
Which of the following statement(s) is(are) TRUE?
Then which of the following statement(s) is(are)
TRUE?
Let G be a finite group and o(G) denotes its order. Then which of the following statement(s) is(are) TRUE?
Consider the set For which of the following choice(s) the set V becomes a two dimensional subspace of R^{3} over R ?
Then which of the following statement(s) is(are) TRUE?
Let {S_{n}} be a sequence of real numbers given by
Then the least upper bound of the sequence {S_{n}} is ____
Let {S_{k}} be a sequence of real numbers, where
then is
Let be a nonzero vector and Then the dimension of the vector space over R is
Let f be a real valued function defined by
Then the value of at any point (x,y) where x > 0, y > 0, is _____
Then the value of integral from (0, 0) to (1, 1) along the path
is expressed as
where ξ lies between 2 and x , then the value of c is ____
Let y_{1}(x) , y_{2}(x), y_{2}(x) be linearly independent solutions of the differential equation
If the Wronskian W(y_{1 },y_{2 },y_{3}) is of the form ke^{bx} for some constant k, then the value of b is____________
The radius of convergence of the power series
Let f : (0,∝ ) → R be a continuous function such that
Then the value of
Let G be a cyclic group of order 12. Then the number of nonisomorphic subgroups of G is ____________
The value of is equal to
Let R be the region enclosed by and . Then the value of
Let
Then Mx = 0 has infinitely many solutions if trace(M) is
Let C be the boundary of the region enclosed by y = x^{2} ,y = x + 2, and x = 0. Then the value of the line integral
where C is traversed in the counter clockwise direction, is _____
Let S be the closed surface forming the boundary of the region V bounded by x^{2} + y^{2} = 3,
z = 0, z = 6, Then the value of
where n^{^} is the unit outward drawn normal to the surface S, is ______
Let y(x) be the solution of the differential equation
Then y(x) attains its maximum value at x = ____________
The value of the double integral
is
Let H denote the group of all 2x 2 invertible matrices over Z_{5} under usual matrix multiplication. Then the order of the matrix in H is 
N(A) the null space of A and R(B) the range space of B. Then the dimension of N(A )∩ R(B)over R is __
The maximum value of f(x,y) = x^{2} + 2y^{2} subject to the constraint y  x^{2} + 1 = 0 is ___________
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