JEE ADVANCED is an national level entrance exam conducted for admission to Prestigious institution like IITs and this exam is known for its very high toughness level and high critical thinking is required for this exam so it is very necessary to solve previous year JEE ADVANCED PAPER to develop cri...
SECTION 1 (Maximum marks: 24)
• This section contains EIGHT (08) questions.
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 TO 9, BOTH INCLUSIVE.
• For each question, enter the correct integer corresponding to the answer using the mouse and the on
screen virtual numeric keypad in the place designated to enter the answer.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct integer is entered;
Zero Marks : 0 If the question is unanswered;
Negative Marks : −1 In all other cases.
Q.1 𝜋 𝜋 1
Let 𝛼 and 𝛽 be real numbers such that − 4 < 𝛽 < 0 < 𝛼 < 4 . If sin(𝛼 + 𝛽) = 3 and
2
cos(𝛼 − 𝛽) = 3 , then the greatest integer less than or equal to
sin 𝛼 cos 𝛽 cos 𝛼 sin 𝛽 2
( + + + )
cos 𝛽 sin 𝛼 sin 𝛽 cos 𝛼
is _____________.
Q.2 If 𝑦(𝑥) is the solution of the differential equation
𝑥𝑑𝑦 − (𝑦 2 − 4𝑦)𝑑𝑥 = 0 for 𝑥 > 0, 𝑦(1) = 2,
and the slope of the curve 𝑦 = 𝑦(𝑥) is never zero, then the value of 10 𝑦(√2 ) is _____________.
If 𝐴7 − (𝛽 − 1)𝐴6 − 𝛽𝐴5 is a singular matrix, then the value of 9𝛽 is ___________.
Q.7 Consider the hyperbola
𝑥2 𝑦2
− =1
100 64
with foci at 𝑆 and 𝑆1 , where 𝑆 lies on the positive x-axis. Let 𝑃 be a point on the hyperbola, in the
𝜋
first quadrant. Let ∠𝑆𝑃𝑆1 = 𝛼, with 𝛼 < 2 . The straight line passing through the point 𝑆 and
having the same slope as that of the tangent at 𝑃 to the hyperbola, intersects the straight line 𝑆1 𝑃 at
𝑃1 . Let 𝛿 be the distance of 𝑃 from the straight line 𝑆𝑃1 , and 𝛽 = 𝑆1 𝑃. Then the greatest integer
βδ 𝛼
less than or equal to
9
sin 2 is _____________.
Q.8 Consider the functions 𝑓, 𝑔 ∶ ℝ → ℝ defined by
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