Math - 2016 Past Year Paper with solutions Attempt Free MCQ Test - IIT

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, x², x² }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 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 {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  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 

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 non-zero vector such that Mx = b for some  x ∈ R³

The value of x^Tb is

The number of group homomorphisms from the cyclic group Z₄ to the cycle group Z₇ is 

In the permutation group S_n (n ≥ 5) , if H  is the smallest subgroup containing all the 3-cycles, then which one of the following is TRUE?  

At x = 0 , the function f is