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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 .

tan180 cos180 tan90

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

sin90 cot90 tan90

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

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