errata prayaas mathematics

ERRATA FOR PRAYAAS/MATHEMATICS

Mathematics Mock JEE MAINS - 2 JEE-2014

2. Number of ways in which 19 indistinguishable books be packaged into 3 numbered boxes such that no

box be empty, is :

(A) 306 (B) 243 (C) 171 (D) 153

25. If A.M. between andth thp q terms of an A.P. be equal to A.M. between andth thr s

terms of same A.P.,

then p q is equal to :

(A) r s (B) r s

r s

(C)

r s

r s

(D) 1r s


18. If 2

11 1 1 1 1 1

/ x / xy

x x x x x x

, then dy

dx is :

(A) yx x x

(B)

1 1 1y

x / x / x / x

(C) 1 1 1

y/ x / x / x

(D) 1 1 1

y / x / x / x

x / x / x / x


16. If f a b x f x , then

b

a

x f x dx is equal to :

(A) 2

b

a

a bf b x dx

(B) 2

b

a

a bf x dx

(C) 2

b

a

b af x dx

(D) 2

b

a

b af b x dx


6. A point P is selected inside an equilateral triangle. If sum of lengths of perpendiculars dropped on to

three sides from P is 10 cm, then the length of altitude of triangle is (in cm) :

(A) 5 (B) 5 3

2 (C) 10 3 (D) 10


19. The solution for x of the equation 2

221

xdt

t t

, is :

(A) 2 (B) 2 (C) 2 (D) None of these


1. Which of the following statement is correct for the following function

1f x n

cosx sin x

(where denote greatest integer function)?

(A) f x is not injective mapping

(B) f x is not continuous in its domain

(C) f x is not derivable at all points in its domain

(D) f x is non-derivable at two points in its domain exhibits sharp corner


7. Complex numbers, z1, z2, z3 and z4 represent vertices A, B, C, D of a square ABCD (in order) of area

1 sq. units. If z is a point on or inside the square such that 3 1

2 4

and6 4

z z z zarg arg

z z z z.

The possible number of such complex numbers z is :

(A) 1 (B) 2 (C) 4 (D) 0

13. The integral

22

0

x

x

e xdx x

x x e

is equal to :

(A) 2

1xe

ln cx

(B)

2

1

2

xeln c

x

(C) 2

2xe

ln cx

(D)

2

xeln x c

x


12. If the equation of the plane passing through the point 1 2 0, , and parallel to the lines

1 2

3 0 1

x y z

and

1 2 1 1

1 2 1

x y z

is 1ax by cz , then the value of a b c , is :

(A) 3 (B) 4 (C) 5 (D) 2


1. If a, b, c are three complex numbers selected randomly (without repetition) from the set

{1, 2, 3..2013), then the probability that 0

a barg

a c is :

(A) 1

3 (B)

2

3 (C)

3

2013 (D) None of these

Paragraph for Questions 13 - 14

There are three different lots of Mathematics, Physics

and Chemistry books arranged in three different lots as

shown in the following diagram.

13. The number of distinct ways in which we can pile up these books in a single lot without any restriction is:

(A) 12!

3! (B) 12! (C)

12!

4! (D)

12!

5!

14. The number of distinct ways in which we can pile up 12 books such that at time of piling up all these

books in a single lot we always pickup the book from the top of respective lots is :

(A) 12!

3! 5! (B)

12!

4! 5! (C)

12!

3!4!5! (D)

12!

3!4!

19. If a, b, c are non-zero real numbers and the equation 2 0ax bx c i has one imaginary root, then :

(A) a = bc (B) a = b2c (C) if 0a bc b (D) None of these


26. Let p be the statement '7 is not greater than 4 and q be the statement 'Paris is in France'.

Then p q is the statement

(A) 7 is greater than 4 or Paris is not in France

(B) 7 is not greater than 4 and Paris is not in France

(C) 7 is greater than 4 and Paris is in France

(D) 7 is greater than 4 and Paris is not in France


2. Let f be a continuous function in [1, 4] and differentiable in (1, 4), f (1) = 5 and f (4) = 8

and 1 1 4f x x , . Then the value of f (3) is equal to :

(A) 5 (B) 6 (C) 7 (D) 4

M3

M2

M1

P4

P3

P2

P1

C4

C3

C2

C1

C5

24. If 2010 2 2010

0 1 2 20101 x C C x C x . . . . . . . C x

then the sum of series 2 5 8 2009 C C C ............. C is equal to :

(A) 20101 2 12

(B) 20101 2 13

(C) 20091 2 12

(D) 20091 2 13

26. If 4 5y x is a tangent to the curve 2 3y px q at (2, 3) then :

(A) p = 2, q = 7 (B) p = 2, q = 7

(C) p = 2, q = 7 (D) p = 2, q = 7


21. The x co-ordinate of the point on the curve y x which is closest to the point (2, 1) is :

(A) 2 (B) 3 (C) 1

2 (D) 1

22. A man walk from the point A (1, 1) toward (NE) after walking 2 unit from this point he take turn

toward (NW) direction and walks 3 units then the reaches at point B, then from B point he takes turn

toward (NE) and walks about 2 units distance from B point then reaches at point C then C is :

(A) 42 3 1i /i e i (B) 42 2 3 1i /i e i

(C) 41 i /i e (D) None of these

errata prayaas mathematics

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