Straight Lines-Quiz-5

Straight Lines Quiz-5

Dear Readers,

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. P(m ,n) (where m,n are natural numbers) is any point in the intertior of the quadrilateral formed by the pair of lines xy=0 and the lines 2x+y-2=0 and 4x+5y=20. The possible number of positions of the point P is

•  7
•  5
•  4
•  6

Solution

Q2. Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120^° with the x-axis is

•  x√3+y+8=0
•  x√3-y=8
•  x√3-y=8
•  x-√3 y+8=0

Solution

Q3. If the quadrilateral formed by the lines ax+by+c=0,a^' x+b^' y+c=0,ax+by+c^'=0,a^' x+b^' y+c^'=0 have perpendicular diagonals, then

•  
•  
•  
•  None of these

Solution

Q4. Let a and b be non-zero and real numbers. Then, the equation (〖ax〗²+〖by〗²+c)(x²-5xy+6y² )=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 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

Solution

Q5. If P(1+t/√2,2+t/√2) be any point on a line, then the range of the values of t for which the point P lies between the parallel lines x+2y=1 and 2x+4y=15 is

•  
•  
•  
•  None of these

Solution

Q6. If an triangle ABC,A≡(1,10), circumcentre ≡(-1/3,2/3) and orthocentre ≡(11/4,4/3), then the coordinates of mid-point of side opposite to A is

•  (1,-11/3)
•  (1, 5)
•  (1,-3)
•  (1, 6)

Solution

Q7. The area enclosed by 2|x|+3|y|≤6 is

•  3 sq. units
•  4 sq. units
•  12 sq. units
•  24 sq. units

Solution

Q8. Through a point A on the x-axis a straight line is drawn parallel to y-axis so as to meet the pair of straight lines ax²+2hxy+by²=0 in B and C. If AB=Bc, then

•  h²=4ab
•  8h²=9ab
•  9h²=8ab
•  4h²=ab

Solution

Q9. A variable line x/a+y/b=1 moves in such a way that harmonic mean of a and b is 8. then the least area of triangle made by the line with the coordinate axes is

•  8 sq. unit
•  16 sq. unit
•  32 sq. unit
•  64 sq. unit

Solution

Q10. The straight line ax+bx+c=0 where abc≠0 will pass through the first quadrant if

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•  
•  
•  

Solution