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ARCHIVE(17 18) JEE(ADVANCE! ome
/18}JEE (ADVANCED) QUESTION BANK me a
jotric Ratio:
Integer Type/Fill in the Blanks
1 W(x) Sin sin (+3) coaxcoe( 6% 4) and of) <1 men go 09 = __ (1996, 2)
2 WA>0,B> ie
O.and A + 8 = 7/3, then the maximum value of tana tanB is. (1993, 2)
3 Wk sin( 5) sin( 2) sin( 7), then the numerical value otkis—(* =10"). (1993, 2)
4 The value of si) in( Paes Fz s(n (Se an( st sin( 12s (1991, 2)
5 The larger of coslog and logeosa if e°*/? <0 t
B)Urwrheh rare
Ay > b> b> by
Oiotenet O) b> b> trl
4 cos(a=p) #1 and cos (a + f)= 1, where a, Rela, m}, Pars of a, which satisty both the
equations is/ are on
2 (04 (2005)
4 The maximum value of (cos cs) » (COS ta) «» (COS ns under the restrictions 0 < c, ca, » nS
w2 and (Cot c14) + (COL cg) -.- (COL an) = 1 15
a) et
“oi $
: (2001)
5 D) 1 Y
Ox ©
8 Was t= 52 and i+ y=
My =a, then tan a equals
ean tan _ (8) tan p+ tany
eo tany (0) 2tan B +e
6. Utne.
Woe “a4 integer. sino = 3b, sin’ @, for every value
One Sa os Mathematics-156 Fimaee Aner
The value of cos112° 30! is
(2-2)
A -
(1998, 2)
© ee) (D) None of these
Let Ay Ay Az As AyAs be a regular hexagon inscribed in a circle of unit radius. Then the product of
8.
the lengths of the line segments Ay Ay, Ao Ap and Ao Ac iS:
(a) 34 (8) 3v3
3
@s o 28 (1998, 2)
9. Which of the following number (s) is/are rational ?
(A) sin? (8) cos15°
(C) sin15°cos15® (D) sin15°cos75° (1998, 2)
10, seco =—*9_istrue and only it
(x+y)
Axtys0 (B)x=y,x20
(C)x=y (O)x#0,y20 (1996, 1)
11, The value of the expression /3cosec20° — seo 20° is equal to
ot (8) 2 sin 20°/sin 40°
(0)4 sin 20°/sin 40° (1988, 2)
12. The expression 3/sin*/ 25a) sint
"° ( 2 a}ssin Grte) ~2fsint(Z +a) +i (Gn -a)} is equal to.
ajo
3 @1
©) none of these (0) sin4a + cosa
MCO-Mutticorrect (1986, 2)
1 Leta and be nonzey
0 real numbers
wea) rete co hal 2(C08 - cosa) + cosa cosg= 1. Then which of
in| > | +3 tan!
: 2 (8) Btan(=),tan(B
erm §) eo “(5)-1m(f) 0
2 121 sBtan(S)
FW ERX cost e
La
A) tan? 2
3
(© tan?
3 Mathorution.167
be snc
(tan ®
wnoaer 10) {tng} 860) 156625) +5004 (1+s0c2"0) "
hen
3 roe
welis @n(Z a1
oa! ola) ' (1999, 3
Match the Matrix
4. Choose correct answer from C; to match wih Cy, If function i, Asinsa)
(1992, 2)
positive a
® vegalive
4
Subjective
1. WAsB4C=% prove nat ci() ot } (2000, 3)
2 Prove thet eotA—tanA = 2cot2A; using He same Hie that
Tana +2tan2A + 4tan4A +8cotBA = cola (1998, 8)
3. Prove na whenever defined, never les between 3 and 1/8, (1992, 4)
A+B
4. WeosA=meosB. then prove that oo 22) -(2f}n( 2° oA). (1990)
5, Provethat tan a+2 tan 2a-+4tan da ¢ 8.01 8a = CO (1988, 2)
Tn)_4
6 Showthat (sseong) toot remiss) i (1984)
J weeny = ches and ass soos en prove at
: iS ws
= ae and tan a tar
tana stan P= Leary (1984)
