JEE Advanced 2013 Paper 1 Offline | Straight Lines and Pair of Straight Lines Question 4 | Mathematics

1

JEE Advanced 2013 Paper 1 Offline

MCQ (Single Correct Answer)

+4

-1

For $$a > b > c > 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c = 0$$ and $$bx + ay + c = 0$$ is less than $$\left( {2\sqrt 2 } \right)$$. Then

A

$$a + b - c > 0$$

B

$$a - b + c < 0$$

C

$$a - b + c = > 0$$

D

$$a + b - c < 0$$

2

IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

+4

-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

A

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

B

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

C

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

D

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

3

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-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 :

A

P lies on the line segment RQ

B

Q lies on the line segment PR

C

R lies on the line segment QP

D

P, Q, R are non-collinear

4

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-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

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

B

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

C

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

D

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