DPP-1..pdf iit maths

MATHE THEMATIC TI CS

Q U A N T U M C L A S SE S  

Target arget IIT J EE 2014 CLASS : XI (ALL)

D a i l y Pra c t ic ic e Pr o b l e m s  

DATE : 21-08/2012

TIME : 40 to 50 Min.

Q.1

State State wheth whether er th the fol follo lowi wing ng statem statemen ents ts are are True or False.

(i)

If x, y, y, z are are al all dif differen erentt real real numbe umbers rs,, th then

  1 1 1       =    x  y y  z z  x  (x  y) 2 (y  z) 2 (z  x )2 1

1

[Sol.

RHS =

=

1

1 (x  y) 2 1 (x  y) 2

 

1 (y  z) 2 1 ( y  z) 2

 

1 (z  x) 2 1 (z  x) 2

 +

 +

DPP. NO.-1

2

2 ( x  y)( y  z )

 +

2 ( y  z )(z  x )

2[ z  x  x  y  y  z ] ( x  t )( z  x )

 = LHS

 +

tan2 · sin sin2 = tan2 – sin2.

[Ans. True]

(iii)

1  102 1  99·101  = 101.

[Ans. True]

sin(1) – cos(1) < 0

(v)

Ther Theree exi exist nat natur ural al numb umbers, ers, m & n such that

( x  t )(z  x )

  True

(ii)

(iv)

2

[Ans. False] 2 2 m  = n  +

2002 .

[ Ans. False]

 Fi ll in th e b lank la nk s .

tan180    cos180    tan90   

Q.2

The expression

Q.3

[ Ans.  1 ] If 2 cos2 ( + x) + 3 sin( sin ( + x) vanishes then th thee values of x lying lying in the interval from 0 to 2 are _____. 2 2 [Hint : 2cos 2cos x – 3sinx = 0  2(1 – sin x) – 3 sinx = 0] [ Ans. : x = /6 or 5/6 ]

Q.4 1

sin90    cot90   tan90  

If tan 25º = a then the value of

tan 20 5  tan11 5 ta n 245  ta n 335

wherever it it is defined, defined, is equal to ______.

 in  in terms of ‘a’ is _____.

[Ans:

1  a2 1 a

[Hi [Hint : tan205° = tan(180° + 25°) ; tan115° = tan(90° + 25°) and simil similarly arly]]

Select the correct alternative : (Only one is correct)

Q.5

The numbe numberr of real real soluti solution on(s) (s) of the the equati equation, on, sin sin (2x) = x +  x is : (A*) 0

(B) 1

(C) 2

(D) none of these

[Hint [Hint : LHS (maximum (maximum value) value) = 1 or RHS (minim (minimum um value) value) = 2. which which is is not possible] possible]

(M.P.) Ph. 0755-4078104, 0755-4078104, 9827745800 9827745800 QUANTUM CLASSES S: R-26, M.P. Nagar zone- II, Bhopal (M.P.)

2

]

   

tan x  Q.6

The expression

(A) (1 + cos2x) Q.7

(B*) sin2x

(C) – (1 + cos2x)

Number of values of ‘x’  (–2,2) satisfying the equation 2sin (A) 8 [Hint:

Q.8

   3     3  7  x  . cos  x   sin  2    2     2   simplifies to      3    x cos x   . tan 2 2        

(B) 6





 , 

2

3 2

(C*) 4

2x

 6 is

(D) 2

]

m & n both are positive

(B) m & n both are negative

(C) m is positive and n is negative

Let

 y

1

=

2

3  ..... (B)

2 1

y= 2

If tan =

a

is

1

13  3

[Hint:

 y

1

3

(A)

(D*) m is negative and n is positive.

, then the value of

1

2

Q.10

 4.2cos

Let m = tan 3 and n = sec 6, then which one of the following statement holds good? (A)

Q.9

2x

(D) cos2x

1

 =

13  3 2

3 y 7  2y

15  3

(C)

(D*)

2

 7y + 2y2 = 3 + y

or

15  3 2

2y2 + 6y – 3 = 0  (D)

3 y

 where a, b are positive reals and   1st quadrant then the value of 

b sin sec7 + cos cosec7 is

(A*)

(C)

(a  b) 3 (a 4  b 4 ) (ab) 7 / 2

(a  b)3 ( b 4  a 4 ) (ab) 7 / 2

(B)

(a  b) 3 (a 4  b 4 )

(D) 

(ab) 7 / 2 (a  b) 3 (a 4  b 4 ) (ab) 7 / 2

QUANTUM CLASSES S: R-26, M.P. Nagar zone-II, Bhopal (M.P.) Ph. 0755-4078104, 9827745800