Tiêu đề PAIR OF STRAIGHT LINES.pdf ✅

PAIR OF STRAIGHT LINES WORKSHEET 1 CUQ 1. The separate equations of the lines 6x 2 + 5xy − 6y 2 = 0 are a) 2x − 3y = 0; 3x + 2y = 0 b) 2x + 3y = 0; 3x − 2y = 0 c) 2x − 3y = 0; 3x − 2y = 0 d) 2x + 3y = 0; 3x + 2y = 0 2. The equation 3x 2 − 5xy + 2y 2 = 0 represents a) Real and distinct lines b) Real and distinct lines c) Imaginary lines d) Coincident only 3. The angle between the pair of lines x 2 − 4xy + y 2 = 0 is a) 30∘ b) 45∘ c) 60∘ d) 90∘ 4. The sum of the slopes of the lines represented by 6x 2 − 5xy +y 2 = 0 is a) 5 b) 6 c) 7 d) 8 5. The equation of the pair of lines represented by the equations 2x + y = 0, x +2y = 0 is a) 2x 2 + 5xy + 2y 2 = 0 b) 2x 2 + 5xy − 2y 2 = 0 c) 2x 2 − 5xy + 2y 2 = 0 d) 2x 2 − 5xy − 2y 2 = 0 JEE MAIN LEVEL - 1 SINGLE CORRECT CHOICE TYPE: 1. The angle between the pair of lines y 2 cos2 θ − xycos2 θ + x 2 (sin2 θ − 1) = 0 is a) π 3 b) π 4 c) π 6 d) π 2 2. If the product of the perpendicular distances from (1, k) to the pair of lines x 2 − 4xy + y 2 = 0 is 3 2 units, then k = a) 4 b) 5 c) 6 d) 8 3. If θ is the acute angle between the pair of lines x 2 + 3xy − 4y 2 = 0, then sin θ = a) π 6 b) π 3 c) 5 √34 d) 3 √34 4. The equation to the pair of lines passing through the origin and perpendicular to 2x 2 + 5xy + 4y 2 = 0 is a) 4x 2 − 5xy + 2y 2 = 0 b) 4x 2 − 5xy − 2y 2 = 0 c) 4x 2 + 5xy + 2y 2 = 0 d) 4x 2 − 5xy − 2y 2 = 0 5. The product of perpendiculars from (l, m) to the pair of lines x 2 − y 2 = 0 is a) | l 2−m2 2 | b) l 2+m2 2 c) | l 2−2m2 √2 | d) | l 2+m2 √2 | 6. The area of the triangle formed by the lines x 2 + 4xy + y 2 = 0, x + y = 1 is a) √3 b) 2 c) 1 d) √3 2 7. The angle bisectors of the coordinate axes are a) x + 1 = 0, y = 0 b) x +y = 0, x −y = 0 c) x+ 1 = 0, y+ 1 = 0 d) x +y = 0, x −y − 5 = 0 JEE MAIN LEVEL -2 8. The sum of the slopes of the lines given by x 2 − 2cxy − 7y 2 = 0 is four times their product, then ' c ' has the value a) -5 b) -1 c) 2 d) 1 9. If one of the lines given by 6x 2 −xy − 4cy 2 = 0 is 3x +4y = 0, then the value of 'c' the value of is a) -3 b) -1 c) 3 d) 1 10. If one of the lines of 3x 2 −2xy − 8y 2 = 0 is per- pendicular to lx + y + 4 = 0 then the value of ' l ' is a) -1 b) 2 c) -3 d) 0 11. The equation of the bisectors of the angle between to the pair of lines 2x 2 + 3xy + y 2 = 0 is a) 3x 2 − 2xy + 3y 2 = 0 b) x 2 + xy −y 2 = 0


c) (−2,1) d) (2,−1) 2. The distance between the parallel lines 9x 2 − 6xy + y 2 + 18x − 6y + 8 = 0 is a) 1 √10 b) 2 √10 c) 4 √10 d) √10 3. The value of λ such that λx 2 − 10xy + 12y 2 + 5x − 16y − 3 = 0 represent a pair of straight lines is a) 1 b) -1 c) 2 d) -2 4. If the pair of straight lines xy −x −y + 1 = 0 and the line ax + 2y − 3 = 0 are concurrent, then a = a) -1 b) 3 c) 1 d) 0 5. If ax 2 + 2hxy +by 2 + 2gx + 2fy + c = 0 repre- sents a pair of parallel lines, then √ g2−ac f 2−bc = a) a b b) √ a b c) √ b a d) b a 6. The equation of the pair of lines joining the origin to the points of intersection of the curve S = ax 2 + 2hxy + by 2 + 2gx +2fy + c = 0 and the line lx + my + n = 0 is a) ax 2 +2hxy + by 2 +2(gx +fy) (lx+my) −n + c ( lx+my −n ) 2 = 0 b) ax 2 + 2hxy + by 2 + 2(gx + fy) (lx+my) −n + c ( lx+my −n ) 2 > 0 c) ax2 +2hxy + by2 +2(gx + fy) (lx+my) −n + c ( lx+my −n ) 2 < 0 d) ax 2 + 2hxy + by2 + 2(gx + fy) (lx−my) −n + c ( lx−my −n ) 2 < 0 7. The equation of the pair of lines through the point (a, b) and parallel to the coordinate axes is a) (x −b)(y − a) = 0 b) (x − a)(y + b) = 0 c) (x −a)(y −b) = 0 d) (x + a)(y − b) = 0 8. The angle between the pair of lines joining the origin to the points of intersection of the line and the curve is a) cos θ = a+b √(a+b) 2+2h2 b) cos θ = a+b √(a−b) 2+2 h2 c) cos θ = a+b √(a−b) 2+4h2 d) cos θ = a+b √(a−b) 2+h2 9. If the angle between the pair of lines joining the origin to the points of intersection of the curve and the line in ax 2 + 2hx +by 2 = 0 is 90∘ , then a) a +b > 0 b) a + b < 0 c) a +b = 0 d) None of these 10. If the angle between the pair of lines joining the origin to the points of intersection of the line and the curve is 60∘ then cos θ = a) 1 √2 b) √3 2 c) 1 2 d) 0 JEE MAIN LEVEL - 1 SINGLE CORRECT CHOICE TYPE: 1. The figure formed by the two pairs of lines x 2 − 6x +8 = 0, y 2 −5y + 6 = 0 is a a) Parallelogram b) Rhombus c) Rectangle d) Square 2. If (1, k) is the point of intersection of the lines given by 2x 2 + 5xy + 3y 2 + 6x + 7y + 4 = 0, then k = a) 2 b) -2 c) 1 d) -1 3. If 4xy + 2x +2ky + 3 = 0 represents a pair of straight lines, then k = a) 0 b) 1 c) 2 d) 3 4. The angle between the lines joining the origin to the points of intersection of the lines √3x + y = 2 and the curve x 2 + y 2 = 4 is a) π 6 b) π 4 c) π 3 d) π 2 5. The equation to the pair of lines passing through the point (−2,3) and parallel to the pair of lines x 2 + 4xy + y 2 = 0 is