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, x2, x2 }satisfies
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Let f : [-1,1] → R be a continuous function. Then the integral
is equal to
Let σ be an element of the permutation group S5 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 {an} be a sequence of positive real numbers satisfying
Then all the terms of the sequence lie in
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 x2 + y2 = 3 is
The function f(x,y) = 3x2y + 4y3 -3x2 - 12y2 + 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
a non-zero vector such that Mx = b for some x ∈ R3
The value of xTb is
The number of group homomorphisms from the cyclic group Z4 to the cycle group Z7 is
In the permutation group Sn (n ≥ 5) , if H is the smallest subgroup containing all the 3-cycles, then which one of the following is TRUE?