Q 1- 5 Carry one mark each.
Q.
Choose the appropriate word/ pharase , out of the four options given below, to complete the following sentence:
apparent lifelessness ___________________ dormant life.
Fill in te blank with the correct idiom/ pharase.
That boy from the worn was a ___________________ in the sleepy village.
Choose the statement where underlined word is used correctly.
Tanya is older than Eric.
Cliff is polder than Tanya
Eric is older than cliff.
If the first two statements are true, then the third statement is :
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to completer the league round of matches?
Q No 6 - 10 carry Two marks each
Q.
Select the appropriate option in place of underlined part of the sentnce.
" Increased productivity necessary " reflects greater efforts made by the employee.
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
Statements:
I. No manager is leader.
II All leaders are executives.
Conclusions:
I No manager is an executive
II No executive is a manager.
In the given figure angle is a right angle, PS:QS= 3:1, RT: QT=5:2 and PU: UR = 1:1. if area of triangle QTS is 20 cm2. then the area of triangle PQR in cm2 is ________________.
(Important : you should answer only the numeric value)
Right triangle PQR is to be constructed in the xy- plane so that the right angle is at P and line PR is parallel to the x-axis. The x and y coordinates of P,Q, and R are to be integers that satisfy the inequalities -4x
5 and 6
y
16. How many diffrent triangles could be constructed with these properties ?
A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
Q. 11 – Q. 35 carry one mark each.
Q.
Let T : R4 → R4 be a linear map defined by
Then the rank of T is equal to _________
(Important : you should answer only the numeric value)
Let M be a 3 x 3 matrix and suppose that 1, 2 and 3 are the eigenvalues of M. If
for some scalar α 0, then α is equal to ___________
(Important : you should answer only the numeric value)
Let M be a 3 x 3 singular matrix and suppose that 2 and 3 are eigenvalues of M. Then the number
of linearly independent eigenvectors of M3 + 2 M +I3 is equal to _________
(Important : you should answer only the numeric value)
Let M be a 3 x 3 matrix such that and suppose that
for
some . Then | α| is equal to _______
(Important : you should answer only the numeric value)
Let be defined by
Then the function f is
Consider the power series
The radius of convergence of the series is equal to __________
(Important : you should answer only the numeric value)
Let C={zC : |z-i|=2} . then
is equal to ____________
(Important : you should answer only the numeric value)
Let is equal to ___________
(Important : you should answer only the numeric value)
Let the random variable X have the distribution function
Then P(2X<4) is equal to ___________
(Important : you should answer only the numeric value)
Let X be a random variable having the distribution function
Then E(X) is equal to _________
(Important : you should answer only the numeric value)
In an experiment, a fair die is rolled until two sixes are obtained in succession. The probability that
the experiment will end in the fifth trial is equal to
Let x1 = 2.2, x2 = 4.3, x3 = 3.1, x4 = 4.5, x5 = 1.1 and x6 = 5.7 be the observed values of a
random sample of size 6 from a U(θ - 1, θ + 4) distribution, where θ ∈ (0, ∞) is unknown. Then
a maximum likelihood estimate of θ is equal to
Let be the open unit disc in
with boundary
is the solution of the Dirichlet problem
then u(1/2,0) is equal to
Let c ∈ Z3 be such that is a field. Then c is equal to __________
(Important : you should answer only the numeric value)
Let Then V is
Let be defined by
is equal to __________
(Important : you should answer only the numeric value)
Let 1be the usual topology on R. Let
2 be the topology on R generated by
Let X be a connected topological space such that there exists a non-constant continuous function
f : X → R, where R is equipped with the usual topology. Let f(X) = { f(x): x ∈ X}. Then
Let d1 and d2 denote the usual metric and the discrete metric on R, respectively. Let be defined by f(x) = x, x ∈ R. Then
If the trapezoidal rule with single interval [0, 1] is exact for approximating the integral
then the value of c is equal to ________
(Important : you should answer only the numeric value)
Suppose that the Newton-Raphson method is applied to the equation with an
initial approximation xo sufficiently close to zero. Then, for the root x = 0, the order of convergence of the method is equal to _________
(Important : you should answer only the numeric value)
The minimum possible order of a homogeneous linear ordinary differential equation with real constant coefficients having x2 sin (x) as a solution is equal to _______
(Important : you should answer only the numeric value)
The Lagrangian of a system in terms of polar coordinates (r,θ) is given by
where m is the mass, g is the acceleration due to gravity and denotes the derivative of s with
respect to time. Then the equations of motion are
If y(x) satisfies the initial value problem
then y(2) is equal to __________
(Important : you should answer only the numeric value)
It is known that Bessel functions Jn(x). for n 0, satisfy the identity
for all t > 0 and xR. The value of
is equal to _________
(Important : you should answer only the numeric value)
Q. 36 – Q. 65 carry two marks each.
Q.
Let X and Y be two random variables having the joint probability density function
Then the conditional probability is equal to
Let Ω = (0,1] be the sample space and let be a probability function defined by
Then P({1/2}) is equal to __________
(Important : you should answer only the numeric value)
Let X1, X2 and X3 be independent and identically distributed random variables with E(X1) =0 and is defined through the conditional expectation
then
is equal to __________
(Important : you should answer only the numeric value)
Let X ∼ Poisson(λ), where λ> 0 is unknown. If δ(X) is the unbiased estimator of is equal to ___________
(Important : you should answer only the numeric value)
Let X1,, … , Xn be a random sample from N(μ,1) distribution, where For testing the null
hypothesis Ho :μ=0 against the alternative hypothesis consider the critical region
R
where c is some real constant. If the critical region R has size 0.025 and power 0.7054, then the
value of the sample size n is equal to ___________
(Important : you should answer only the numeric value)
Let X and Y be independently distributed central chi-squared random variables with degrees of
freedom m(3) and n(
3) respectively. If E(X/Y) =3 and m+n =14 then E(Y/X ) is equal to
Let X1, X2, … be a sequence of independent and identically distributed random variables with for n= 1, 2,…,, then
is equal to __________
(Important : you should answer only the numeric value)
Let be a solution of the initial value problem
Then f(1) is equal to
Let be the solution of the initial value problem
Then u(2,2) is equal to ________
(Important : you should answer only the numeric value)
Let be a subspace of the Euclidean space R4. Then the
square of the distance from the point (1,1,1,1) to the subspace W is equal to _______
(Important : you should answer only the numeric value)
Let T : R4 → R4 be a linear map such that the null space of T is
and the rank of (T-4I4) is 3. If the minimal polynomial of T is x(x-4)α. then α is equal to _______
(Important : you should answer only the numeric value)
Let M be an invertible Hermitian matrix and let x,y R be such that x2 <4y. then
Let Then the number
of elements in the center of the group G is equal to
The number of ring homomorphisms from is equal to __________
(Important : you should answer only the numeric value)
Let and
be two polynomials in
Q [x]. Then, over Q,
Consider the linear programming problem
Then the maximum value of the objective function is equal to ______
(Important : you should answer only the numeric value)
Let . Under the usual metric on R2,
Let . Then H
Let V be a closed subspace of be given by f(x) =x and g(x) = x2. if
and pg is the orthogonal projection of g on V, then
Let p(x) be the polynomial of degree at most 3 that passes through the points (-2,12), (-1,1), (0.2) and (2,-8). Then the coefficient of x3 in p(x) is equal to _____________
(Important : you should answer only the numeric value)
If, for some α,β R the integration formula
holds for all polynomials p(x) of degree at most 3, then the value of
3(α-β)2 is equal to _____.
(Important : you should answer only the numeric value)
Let y(t) be a continuous function on (0, ∞) whose Laplace transform exists. If y(t) satisfies
then y(1) is equal to _______
(Important : you should answer only the numeric value)
Consider the initial value problem
if y(x) → 0 as x→ 0+, then α is equal to ______________
(Important : you should answer only the numeric value)
Define by
Then
Consider the unit sphere and the unit normal vector
at each point (x,y,z) on S. The value of the surface integral
is equal to _______
(Important : you should answer only the numeric value)
Let
Define Then the minimum value of f on D is equal to ________
(Important : you should answer only the numeric value)
Let Then there exists a non-constant analytic function f on D such that for all n = 2, 3, 4, …
Let be the Laurent series expansion of
in the annulus 3/2 <|z| <5 . Then a1/a2 is equal to _________
(Important : you should answer only the numeric value)
The value of is equal to __________
(Important : you should answer only the numeric value)
Suppose that among all continuously differentiable functions y(x), x R with y(0) =0 and y(1) = 1/2, the function y0(x) minimizes the functional
then yo (1/2) is equal to
Use Code STAYHOME200 and get INR 200 additional OFF
|
Use Coupon Code |
![]() |
|
![]() |
|
![]() |
|
![]() |
|
|
|
|
|