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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 .
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 ______.