Adv Mock 3 Paper 2 Mat

8/12/2019 Adv Mock 3 Paper 2 Mat

1/6

manishkumarphysics.in

Space for rough work

MATHEMATICS

SECTION ISingle Correct Choice Type

This section contains 9 single correct choice type questions. Each question has 4 choices: (a),(b), (c) and (d) for its answer, out of which ONLY ONE is correct.

1. Complete set of values of real k such that equation k x x = 11 costan has a real solution is

(a)

2,

2 (b)

2

,2

5

(c)

4,

4 (d)

4

,4

5

2. The plane containing the line5

2

4

1

2

3 == z y x is rotated through an angle2

about this

line to contain the point (4, 3, 7). The equation of plane before rotation is(a) 4884 =++ z y x (b) 4884 = z y x (c) 4884 =+ z y x (d) 4884 =+ z y x

3. The largest power of 2 that divides ( ) ]113[ 12 ++ n is (where [ .] is greatest integer function)(a) n (b) n + 1(c) n 1 (d) none of these

4. Let S be the focus of x y 42

= and a point P is moving on the curve such that its abscissa isincreasing at the rate of 4 units/sec, then the rate of increase of projection of SP on 1=+ y x when P is at (4, 4), is

(a) 3 (b) 1

(c) 2 (d)2

3


2/6



5. If ( )222

2 14

111

+

+

+=

cbc

ab

aS , where 41 cba , then minimum

value of S is

(a) 2812 (b) 212 (c) 2810 + (d) 2216

6. If A and B are two square matrices such that O AB B A =++ , then AB is equal to(a) BA (b) A(c) B (d) none of these

7. dx x

0

][cot is equal to (where [ .] denotes greatest integer function)

(a) 2

(b) 2

(c) (d)

8. A variable line L is drawn through origin to meet the lines 010:1 = x y L and020 = x y at the point A and B respectively. A point P is taken on L such that

222

111OBOAOP

+= . Locus of P is

(a) ( ) 802 = x y (b) ( ) 1002 = x y

(c) 433 = y x (d) 1033 = y x

9. Line 111

=+b y

a x

and 122

=+b y

a x

are not meeting co-ordinate axis on concyclinc points. If

2121 bbaa = , then

(a) 2121 bbaa = (b) 2121 bbaa =

(c) 2121 bbaa = (d) 2121 bbaa = is not possible


3/6



SECTION IIMultiple Correct Choice Type

This section contains 4 multiple correct choice type questions. Each question has4 choices: (a), (b), (c) and (d) for its answer, out of which ONE OR MORE is/ are correct.

10. If ( )( ) ,sinsinsinsin 21111 =++ z yw x then N N N N N w z

y x N N

N N

4321 ,,,;43

21

(a) has a maximum value 2 (b) has a minimum value 2(c) is independent of 1 N (d) none of these

11. The function f is continuous and has the property x x f f = 1))(( for all ].1 ,0[ x Whichof the following is/are true?

(a) 143

41 =

+

f f (b) =1

0 2

1)( dx x f

(c)21

)(lim21

=

x f x

(d) none of these

12. From a variable point on a fixed normal to a parabola, two other normals are drawn to parabola. Line joining their feet is(a) parallel to a fixed line(b) making acute angle with x-axis if slope of fixed normal is positive(c) diameter to a parabola of fixed axis(d) none of these

13. a , b, c are the sides of a scalene triangle such that 011

1

32

32

32

=

cccbbb

aaa

.

Which of following is/are not true?(a) maximum value of the perimeter of the triangle is 3.(b) minimum value of )1)(1)(1( cba +++ is 8.

(c) maximum value of ))()(( csbsas is81

.

(d) minimum value ofcba111 ++ is 3.


4/6


5/6



SECTION IVMatrix Match Type

This section contains 2 questions. Each question contains statements given in two columns,which have to be matched. The statements in Column I are labelled A, B, C and D, while thestatements in Column II are labelled 1, 2, 3, 4 and 5. Any given statement in Column I canhave correct matching with ONE OR MORE statement(s) in Column II . The appropriate

bubbles corresponding to the answers to these questions have to be darkened as illustrated inthe following example:If the correct matches are A 1, 4 and 5; B 2 and 3; C 1 and 2; and D 4 and 5; then thecorrect darkening of bubbles will look like the following.

A 1 2 3 4 1 2 3 4

1 2 3 4

1 2 3 4

B C D

1 2 3 4 5

5

5

5

5

1. Let S be the set of n students. The students plan to visit two institute next month. Any studentcan accompany or withdraw from the visit. So on both occasions any subset of S can go.

Column I Column II

(A) Probability that number of students in first trip aregreater than number of students in 2 nd 1. trip is 12

2

2 4

+

n

nnn C

(B) Probability that each student goes in one trip isexactly 2. n

sn

r n

nsr C C

4

.0


6/6



2. ( ) ( )4

32

1

4tanln5sin

2cos)(

nnn

n x

x x x

x f

= where N nnnn 4321 ,,,

Column-I Column-II

(A) If 31 , nn are even and 42 , nn are odd 1. 1= x is point of maxima(B) If 41 , nn are even and 32 , nn are odd 2. 1= x is point of minima

(C) 321 ,, nnn are even and 4n is odd 3. 1= x is a neither point of maxima norminima

(D) 21 , nn are odd and 43 , nn are even 4. 5= x is point of maxima

5. 5= x is neither point of minima normaxima

Documents

Adv Mock 3 Paper 2 Mat