IIT JEE Previous Year Question paper

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Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
(A)2 5 20 0 − − = x y (B) 2 5 4 0 − + = x y
(C) 3x − 4y + 8 = 0 (D) 4x − 3y + 4 = 0

Equation of the circle with AB as its diameter is
(A) x2 + y2 − 12x + 24 = 0 (B) x2 + y2 + 12x + 24 = 0
(C) x2 + y2 + 24x − 12 = 0 (D) x2 + y2 − 24x − 12 = 0

The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is
[Note: The trace of a matrix is the sum of its diagonal entries.]
(A) (p − 1) (p2 − p + 1) (B) p3 − (p − 1)2
(C) (p − 1)2 (D) (p − 1) (p2 − 2)

The number of A in Tp such that det (A) is not divisible by p is
(A) 2p2 (B) p3 − 5p
(C) p3 − 3p (D) p3 − p2

An AC voltage source of variable angular frequency ω and fixed amplitude V0 is connected in series with a
capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased
A) the bulb glows dimmer B) the bulb glows brighter
C) total impedance of the circuit is unchanged D) total impedance of the circuit increases
IIT JEE Model paper




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