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Frequently Asked IIT-JEE Latest Exam Pattern - IIT-JEE Sample Question with Solutions Page 46

(#M40021781) IIT-JEE QUESTION statement type Keep an EYE

Which of the following is true?
(A) f(x) is decreasing on (-1, 1) and has a local minimum at x = 1
(B) f(x) is increasing on (-1, 1) and has a local maximum at x = 1
(C) f(x) is increasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1
(D) f(x) is decreasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1

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(#M40021780) IIT-JEE QUESTION statement type Keep an EYE

Let a solution y = y(x) of the differential equation
x x^2 - 1 dy (-y) y^2 - 1 dx = 0 satisfy y(2) = 23.
STATEMENT -1 : y(x) = sec sec 1 x^6
and
STATEMENT -2 : y(x) is given by 2
1 2 3 1 1 y x x = -
(A) STATEMENT 1 is True, STATEMENT -2 is True; STATEMENT -2 is a correct explanation for STATEMENT -1
(B) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is NOT a correct explanation for STATEMENT -1.
(C) STATEMENT -1 is True, STATEMENT -2 is False
(D) STATEMENT -1 is False, STATEMENT -2 is True

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(#M40021779) IIT-JEE QUESTION statement type Keep an EYE

Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3 and b4 = b3 + a4.
STATEMENT -1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.
and
STATEMENT -2 : The numbers b1, b2, b3, b4 are in H.P.
(A) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is a correct explanation for STATEMENT -1
(B) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is NOT a correct explanation for STATEMENT -1.
(C) STATEMENT +1 is True, STATEMENT -2 is False
(D) STATEMENT +1 is False, STATEMENT -2 is True

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(#M40021776) IIT-JEE QUESTION circle Keep an EYE

A particle P starts from the point z0 = 1 + 2i, where i = -1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves 2 units in the direction of the vector i + j and then it moves through an angle 2i in anticlockwise direction on a circle with centre at origin, to reach a point z2. The point z2 is given by

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(#M40021775) IIT-JEE QUESTION hyperbola Keep an EYE

Consider a branch of the hyperbola x^2 - 2y^2 - 22 x - 42 y - 6 = 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is?

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(#M40021773) IIT-JEE QUESTION straight line Keep an EYE

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions ip = 2.0 eV, iq = 2.5 eV and ir = 3.0 eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is??

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(#M40021772) IIT-JEE QUESTION straight line Keep an EYE

Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations:
3x - y - z = 0
-3x + z = 0
-3x + 2y +z = 0.
Then the number of such points for which x^2 + y^2 + z^2 = 100 is

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(#M40021770) IIT-JEE QUESTION hyperbola Keep an EYE

The maximum value of the function f(x) = 2x^3 - 15 x^2 + 36x - 48 on the set A = {x|x^2 + 20 = 9x|} is?

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(#M40021769) IIT-JEE QUESTION hyperbola Keep an EYE

An ellipse intersects the hyperbola 2x^2 - 2y^2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates axes, then

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(#M40021767) IIT-JEE QUESTION progressions Keep an EYE

If the sum of first n terms of an A.P. is cn2, then the sum of squares of these n terms is?

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