IIT-JEE 2011 Paper 1 Offline | Straight Lines and Pair of Straight Lines Question 6 | Mathematics

IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

-1

A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle $${60^ \circ }$$ to the line $$\sqrt {3x} + y = 1.$$ If $$L$$ also intersects the x-axis, then the equation of $$L$$ is

$$y + \sqrt {3x} + 2 - 3\sqrt 3 = 0$$

$$y - \sqrt {3x} + 2 + 3\sqrt 3 = 0$$

$$\sqrt {3y} - x + 3 + 2\sqrt 3 = 0$$

$$\sqrt {3y} + x - 3 + 2\sqrt 3 = 0$$

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Consider three points $$P = ( - \sin (\beta - \alpha ), - cos\beta ),Q = (cos(\beta - \alpha ),\sin \beta )$$ and $$R = (\cos (\beta - \alpha + \theta ),\sin (\beta - \theta ))$$ where $$0 < \alpha ,\beta ,\theta < {\pi \over 4}$$. Then :

P lies on the line segment RQ

Q lies on the line segment PR

R lies on the line segment QP

P, Q, R are non-collinear

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Consider the lines given by:

$${L_1}:x + 3y - 5 = 0$$

$${L_2}:3x - ky - 1 = 0$$

$${L_3}:5x + 2y - 12 = 0$$

Match the Statement/Expressions in Column I with the Statements/Expressions in Column II.

	Column I		Column II
(A)	L$$_1$$, L$$_2$$, L$$_3$$ are concurrent, if	(P)	$$K = - 9$$
(B)	One of L$$_1$$, L$$_2$$, L$$_3$$ is parallel to atleast one of the other two, if	(Q)	$$K = - {6 \over 5}$$
(C)	L$$_1$$, L$$_2$$, L$$_3$$ form a triangle, if	(R)	$$K = {5 \over 6}$$
(D)	L$$_1$$, L$$_2$$, L$$_3$$ do not form a triangle, if	(S)	$$K = 5$$

A - iv; B - ii; C - iii; D - i, ii

A - iv; B - i, ii; C - iii; D - i, ii, iv

A - iv; B - i; C - iii; D - i, ii

A - ii; B - i, iii; C - iii; D - i, ii, iv

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let a and b be non-zero real numbers. Then, the equation

$$(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0$$ represents :

four straight lines, when c = 0 and a, b are of the same sign

two straight lines and a circle, when a = b, and c is of sign opposite to that of a

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

a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

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