IIT-JEE 1983
JEE Advanced / 56 questions
2026Mon, Apr 11, 1983 9:00 AM56 PYQs
1Straight Lines And Pair Of Straight Lines
The end \(A, B\) of a straight line segment of constant length \(c\) slide upon the fixed rectangular axes \(OX, OY\) respectively. If the rectangle \(OAPB\) be completed, then show that the locus of the foot of the perpendicular drawn from...
SUBJECTIVE+2 / -01983
2Straight Lines And Pair Of Straight Lines
The straight line \(5x + 4y = 0\) passes through the point of intersection of the straight lines \(x + 2y - 10 = 0\) and \(2x + y + 5 = 0.\)
T/F+1 / -01983
3Trigonometric Functions And Equations
Show that \($16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi } \over {15}}} \right)\cos \left( {{{16\pi } \over {15}}} \right) = 1\)$
SUBJECTIVE+2 / -01983
4Trigonometric Functions And Equations
Find all solutions of \(4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x\)
SUBJECTIVE+2 / -01983
5Trigonometric Functions And Equations
If \(\tan \,A = \left( {1 - \cos B} \right)/\sin B,\) then \(tan2A = tan\,B\).
T/F+1 / -01983
6Vector Algebra
If \(X.A=0, X.B=0, X.C=0\) for some non-zero vector \(X,\) then \(\left[ {A\,B\,C} \right] = 0\)
T/F+1 / -01983