IIT-JEE 2008 Paper 1 Offline | Straight Lines and Pair of Straight Lines Question 10 | Mathematics | JEE Advanced - ExamSIDE.Com

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1

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-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 :

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

2

IIT-JEE 2007

MCQ (Single Correct Answer)

+3

-0.75

Let $$O\left( {0,0} \right),P\left( {3,4} \right),Q\left( {6,0} \right)$$ be the vertices of the triangles $$OPQ$$. The point $$R$$ inside the triangle $$OPQ$$ is such that the triangles $$OPR$$, $$PQR$$, $$OQR$$ are of equal area. The coordinates of $$R$$ are

A

$$\left( {{4 \over 3},3} \right)$$

B

$$\left( {3,{2 \over 3}} \right)$$

C

$$\left( {3,{4 \over 3}} \right)$$

D

$$\left( {{4 \over 3},{2 \over 3}} \right)$$

3

IIT-JEE 2007

MCQ (Single Correct Answer)

+3

-0.75

The lines $${L_1}:y - x = 0$$ and $${L_2}:2x + y = 0$$ intersect the line $${L_3}:y + 2 = 0$$ at $$P$$ and $$Q$$ respectively. The bisector of the acute angle between $${L_1}$$ and $${L_2}$$ intersects $${L_3}$$ at $$R$$.

Statement-1: The ratio $$PR$$ : $$RQ$$ equals $$2\sqrt 2 :\sqrt 5 $$. 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 not 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.

4

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

+3

-0.75

Area of the triangle formed by the line $$x + y = 3$$ and angle bisectors of the pair of straight line $${x^2} - {y^2} + 2y = 1$$ is

A

2 sq. units

B

4 sq. units

C

6 sq. units

D

8 sq. units

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