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Frequently Asked IIT-JEE Latest Exam Pattern - IIT-JEE Sample Question with Solutions Page 45

(#M40021800) IIT-JEE QUESTION function Keep an EYE

Consider the statements:
P : There exists some x such that f(x) + 2x = 2(1 + x2)
Q : There exists some x  such that 2f(x) + 1 = 2x(1 + x)

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(#M40021798) IIT-JEE QUESTION probability Keep an EYE

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is
option
a) 127/216
b) 125/216
c) 108/216
d) 91/216

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(#M40021795) IIT-JEE QUESTION probability Keep an EYE

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then find P(E)

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(#M40021794) IIT-JEE QUESTION parabola Keep an EYE

Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by

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(#M40021793) IIT-JEE QUESTION circle Keep an EYE

The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point

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(#M40021790) IIT-JEE QUESTION function Keep an EYE

Let f(x) = x^2 and g(x) = sinx for all x (R). Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x), where (f o g) (x) = f(g(x)), is

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(#M40021788) IIT-JEE QUESTION circle Keep an EYE

Two parallel chords of a circle of radius 2 are at a distance 3+1 apart. If the chords subtend at the centre, angles of ki and 2 ki, where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k].

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(#M40021787) IIT-JEE QUESTION function Keep an EYE

Let f be a function defined on R (the set of all real numbers) such that f(x) = 2010 (x - 2009)^1 (x - 2010)^2(x - 2011)^3 (x - 2012)^4, for all x (R). If g is a function defined on R with values in the interval (0,0) such that f (x) = ln (g (x)), for all x R, then the number of points in R at which g has a local maximum is

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(#M40021784) IIT-JEE QUESTION coordinate geometry Keep an EYE

If the distance of the point P (1, -2, 1) from the plane x+2y-2z=i, where i > 0, is 5, then the foot of the perpendicular from P to the plane is

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(#M40021783) IIT-JEE QUESTION straight line Keep an EYE

Consider the lines given by
L1 : x + 3y - 5 = 0
L2 : 3x - ky - 1 = 0
L3 : 5x + 2y - 12 = 0
Match the Statements/Expressions in Column I with the Statements/ Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 + 4 matrix given in the ORS. Column I Column II
(A) L1, L2, L3 are concurrent, if (p) k = -9
(B) One of L1, L2, L3 is parallel to at least one of the other two, if
(q) k = -65
(C) L1, L2, L3 form a triangle, if
(r) k = 56
(D) L1, L2, L3 do not form a triangle, if (s) k = 5

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