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Frequently Asked IIT-JEE Latest Exam Pattern - IIT-JEE Sample Question with Solutions Page 47

(#M40021766) IIT-JEE QUESTION coordinate geometry Keep an EYE

A line with positive direction cosines passes through the point P(2, - 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ
equals??

Asked In IIT-JEE MAN (12 years ago)

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(#M40021764) IIT-JEE QUESTION coordinate geometry Keep an EYE

The normal at a point P on the ellipse x^2 + 4y^2 = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points??

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(#M40021763) IIT-JEE QUESTION matrix matching Keep an EYE

(A) If -1 < x < 1, then f(x) satisfies (p) 0 < f(x) < 1
(B) If 1 < x < 2, then f(x) satisfies (q) f(x) < 0
(C) If 3 < x < 5, then f(x) satisfies (r) f(x) > 0
(D) If x > 5, then f(x) satisfies (s) f(x) < 1

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(#M40021762) IIT-JEE QUESTION geometry Keep an EYE

For k > 0, the set of all values of k for which k ex - x = 0 has two distinct roots is??

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(#M40021761) IIT-JEE QUESTION geometry Keep an EYE

The positive value of k for which kex -x = 0 has only one root is

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(#M40021760) IIT-JEE QUESTION geometry Keep an EYE

Lines L1 : y - x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R.
STATEMENT -1 : The ratio PR : RQ equals 2 2 : 5.
because
STATEMENT -2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
(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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(#M40021759) IIT-JEE QUESTION geometry Keep an EYE

Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5.
STATEMENT -1 : The parametric equations of the line of intersection of the given planes are
x = 3 + 14t,
y = 1 + 2t, z = 15t
because
STATEMENT -2 : The vectors 14i + 2j +15k is parallel to the line of intersection of the given planes.
(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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(#M40021758) IIT-JEE QUESTION geometry Keep an EYE

Let f(x) = 2 + cosx for all real x.
STATEMENT -1 : For each real t, there exists a point c in [t, t + i] such that f(c) = 0.
because
STATEMENT -2 : f(t) = f(t + 2i) for each real t.

(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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(#M40019755) IIT-JEE QUESTION Keep an EYE

Consider the two curves C1 : y^2 = 4x, C2 : x^2 + y^2 – 6x + 1 = 0. Then,
(A) C1 and C2 touch each other only at one point
(B) C1 and C2 touch each other exactly at two points
(C) C1 and C2 intersect (but do not touch) at exactly two points
(D) C1 and C2 neither intersect nor touch each other

Asked In IIT-JEE Chandni Maurya (12 years ago)

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(#M40019754) IIT-JEE QUESTION Keep an EYE

Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c) (x2 – 5xy + 6y2) = 0 represents
(A) four straight lines, when c = 0 and a, b are of the same sign
(B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a
(C) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
(D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a.

Asked In IIT-JEE Chandni Maurya (12 years ago)

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