## Straight Lines Quiz-17 Assertion - Reasoning Type

The unit Straight Line holds sheer significance in the JEE Advanced and other engineering exams. It has a weightage of 6% pairing with Circles. With focused practice good marks can be fetched from this section. These questions are important in achieving your success in JEE and Other Engineering Exams..

Q1. Statement 1: If point of intersection of the lines 4x+3y=Î» and 3x-4y=Î¼ ∀Î»,Î¼∈R is(x1,y1), then the locus of (Î»,Î¼) is x+7y=0,∀ x1=y1

Statement 2: If 4Î»+3Î¼>0 and 3Î»-4Î¼>0, then (x1,y1 ) is in first quadrant
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q2. Statement 1: If a,b,c are variable such that 3a+2b+4c=0, then the family of lines given by ax+by+c=0 pass through a fixed point (3, 2)

Statement 2: The equation ax+by+c=0 will represent a family of straight the passing through a fixed point iff there exists a relation between a,b and c
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q3. Statement 1: The ratio PR:PQ equals 2√2:√5.

Statement 2: In any triangle, bisector of an angle divides the triangle into two similar triangles.
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution

Q4. Statement 1: If the lines 2x+3y+19=0 and 9x+6y-17=0 cut the axis in A,B and y-axis at C,D, then points A,B,C,D are concyclic

Statement 2: Since OA×OB=OC×OD, where O is origin, therefore A,B,C,D are concyclic
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q5. Statement 1: If the point (2a,-5,a2) is on the same side of the line x+y-3=0 as that of the origin, then a∈(2,4)

Statement 2: The points (x1,y1 ) and (x2,y2 ) lie on the same or opposite sides of the line ax+by+c=0, as ax1+by1+c and ax2+by2+c have the same or opposite signs
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  t>Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q6. Statement 1: If sum of algebraic distance from points A(1,1),B(2,3),C(0,2) is zero on the line ax+by+c=0, then a+3b+c=0

Statement 2: The centroid of triangle is (1, 2)
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution

Q7. Statement 1: The incentre of a triangle formed by the lines x cos⁡〖(Ï€/9)〗+y sin⁡〖(Ï€/9)〗=Ï€,x cos⁡〖(8Ï€/9)〗+y sin⁡〖(8Ï€/9)=〗 Ï€;x cos⁡〖(13Ï€/9)〗+y sin⁡〖(13Ï€/9)〗=Ï€ is (0, 0)

Statement 2: Any point equidistant from the given three non-concurrent straight lines in the plane is incentre of the triangle
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q8.
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q9. Statement 1: Lines passing through the given point and is equally inclined to the given two lines are always perpendicular

Statement 2: Angle bisector of the given two lines are always perpendicular
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
Q10. Statement 1: The joint equation of lines y=x and y=-x is y2=-x2, i.e., x2+y2=0

Statement 2: The joint equation of lines ax+by=0 and cx+dy=0 is (ax+by)(cx+dy)=0, where a,b,c,d are constant
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution

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