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This contains 60 Multiple Choice Questions for IIT JAM Math - 2017 Past Year Paper (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Consider the function f(x, y) = 5 – 4 sin x + y^{2} for 0 < x < 2p and y ∈ R. The set of critical points of f(x, y) consists of

Solution:

QUESTION: 2

Let φ : R → R be a differentiable function such that φ' is strictly increasing with φ(1) = 0. Let a and b denote the minimum and maximum values of φ(x) on the interval [2, 3], respectively.

Then which one of the following is TRUE ?

Solution:

QUESTION: 3

The number of generators of the additive group Z_{36} is equal to

Solution:

QUESTION: 4

Solution:

QUESTION: 5

Let f : R → R be a twice differentiable function. If g(u, v) = f(u^{2} – v^{2}), then

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QUESTION: 6

Solution:

QUESTION: 7

Let f_{1}(x), f_{2}(x), g_{1}(x), g_{2}(x) be differentiable functions on R. be the determinent of the matrix . Then F'(x) is equal to

Solution:

QUESTION: 8

Then which one of the following is TRUE ?

Solution:

QUESTION: 9

Solution:

QUESTION: 10

satisfies the assumptions of Rolle’s theorem in the interval [–1, 1], then the ordered pair (p, q) is

Solution:

QUESTION: 11

The flux of the vector field

along the outward normal, across the ellipse x^{2} + 16y^{2} = 4 is equal to

Solution:

QUESTION: 12

Let M be the set of all invertible 5 × 5 matrices with entries 0 and 1. For each

and n_{0}(M) denote the number of 1’s and 0’s in M, respectively. Then

Solution:

QUESTION: 13

Solution:

QUESTION: 14

Solution:

QUESTION: 15

The line integral of the vector field

along the boundary of the triangle with vertices (1,0,0), (0,1,0) and (0,0,1), oriented anticlockwise, when viewed from the point (2,2,2) is

Solution:

QUESTION: 16

The area of the surface z = xy/3 intercepted by the cylinder x^{2} + y^{2} ≤ 16 lies in the interval

Solution:

QUESTION: 17

be the circle oriented anti- clockwise. Then

Solution:

QUESTION: 18

The flux of along the outward normal, across the surface of the solid is equal to

Solution:

QUESTION: 19

Solution:

QUESTION: 20

Let f : R → [0, ∞) be a continuous function. Then which one of the following is NOT TRUE ?

Solution:

QUESTION: 21

The interval of convergence of the power series

Solution:

QUESTION: 22

Let P_{3 }denote the real vector space of all polynomials with real coefficients of degree at most 3. Consider the map T : P_{3 }→ P_{3} given by

Solution:

QUESTION: 23

Let f(x, y) = for (x, y) ≠ (0, 0). Then

Solution:

QUESTION: 24

Let S be an infinite subset of R such that S\{a} is compact for some α ∈ S. Then which one of the following is TRUE ?

Solution:

QUESTION: 25

Solution:

QUESTION: 26

Then which one of the followings is NOT TRUE ?

Solution:

QUESTION: 27

Solution:

QUESTION: 28

Which one of the following is TRUE ?

Solution:

QUESTION: 29

A particular integral of the differential equation

Solution:

QUESTION: 30

Let y(x) be the solution of the differential equation

satisfying y(0) = 1. Then y(–1) is equal to

Solution:

*Multiple options can be correct

QUESTION: 31

Then which of the following statements is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 32

The volume of the solid is expressible as

Solution:

*Multiple options can be correct

QUESTION: 33

Let be a function. Then which of the following statements is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 34

If X and Y are n × n matrices with real entries, then which of the following is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 35

Let G be a group of order 20 in which the conjugacy classes have sizes 1, 4, 5, 5, 5. Then which of the followings is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 36

Let {x_{n}} be a real sequence such that Then which of the following statements is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 37

Let S be the set of all rational numbers in (0, 1). Then which of the following statements is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 38

Let M be an n × n matrix with real entries such that M^{3 }= I. Suppose that Mv ≠ v for any nonzero vector v. Then which of the following statements is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 39

Let y(x) be the solution of the differential equation

satisfying the condition y(0) = 2. Then which of the following is/are TRUE ?

Solution:

*Multiple options can be correct

QUESTION: 40

Solution:

*Answer can only contain numeric values

QUESTION: 41

Evaluation of 8^{3} × 8^{2} × 8^{-5} is.......

Solution:

*Answer can only contain numeric values

QUESTION: 42

Let G be a subgroup of Then the order of G is -----

Solution:

*Answer can only contain numeric values

QUESTION: 43

Consider the permutations

in S_{8} . The number of η ∈ S_{8} such that

Solution:

*Answer can only contain numeric values

QUESTION: 44

Let P be the point on the surface closet to the point (4,2,0). Then the square of the distance between the origin and P is ______.

Solution:

*Answer can only contain numeric values

QUESTION: 45

Solution:

*Answer can only contain numeric values

QUESTION: 46

Let M be the matrix whose columns are v_{1}, v_{2}, 2v_{1} – v_{2}, v_{1} + 2v_{2} in that order. Then the number of linearly independent solutions of the homogeneous system of linear equations Mx = 0 is __________.

Solution:

*Answer can only contain numeric values

QUESTION: 47

Solution:

*Answer can only contain numeric values

QUESTION: 48

Let P be a 7 × 7 matrix of rank 4 with real entries. Let a ∈ R^{7} be a column vector. Then the rank of P + aa^{T} is at least ________.

Solution:

*Answer can only contain numeric values

QUESTION: 49

For x > 0, let |x| denote the greatest integer less than or equal to x. Then

Solution:

**ANSWER :- 55**

**Solution :- lim x -->0 1/x => 1/0**

**= ∞ i.e Apply L-hospital rule**

**lim x-->0 x[1/x + 2/x + 3/x + 4/x +.......................10/x]**

**lim x→0 x[10*11]/2 * 1/x**

**= [10*11]/2 => 55**

*Answer can only contain numeric values

QUESTION: 50

The number of subgroups of Z_{7} x Z_{7 }of order 7 is _______.

Solution:

*Answer can only contain numeric values

QUESTION: 51

Let y(x), x > 0 be the solution of the differential equation

satisfying the conditions y(1) = 1 and y’(1) = 0. Then the value of e^{2}y(e) is ______

Solution:

*Answer can only contain numeric values

QUESTION: 52

Let T be the smallest positive real number such that the tangent to the helix

at t = T is orthogonal to the tangent at t = 0. Then the line integral of along the section of the helix from t = 0 to t = T is _____

Solution:

*Answer can only contain numeric values

QUESTION: 53

Solution:

*Answer can only contain numeric values

QUESTION: 54

The maximum order of a permutation s in the symmetric group S_{10 }is ____

Solution:

*Answer can only contain numeric values

QUESTION: 55

Solution:

*Answer can only contain numeric values

QUESTION: 56

For a real number x, define [x] to be the smallest integer greater than or equal to x. Then

Solution:

*Answer can only contain numeric values

QUESTION: 57

For x > 1, let

The number of tangents to the curve y = f(x) parallel to the line x + y = 0 is ____

Solution:

*Answer can only contain numeric values

QUESTION: 58

Solution:

*Answer can only contain numeric values

QUESTION: 59

The radius of convergence of the power series

Solution:

*Answer can only contain numeric values

QUESTION: 60

Solution:

### CBSE Past Year Paper Session (2017), Math Class 12

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