PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians.

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1 www. Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) ALP ADVANCED LEVEL PROBLEMS Straight Lines 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared b IITians. [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R is (A) a straight line (B) a circle (C) a parabola (D) pair of straight lines Q. A, B and C are points in the plane such that A(, ) ; B (5, 6) and AC = BC. Then (A) ABC is a unique triangle (B) There can be onl two such triangles. (C) No such triangle is possible (D) There can be infinite number of such triangles. Q. If A (, p ) ; B (0, ) and C (p, 0) are the coordinates of three points then the value of p for which the area of the triangle ABC is minimum, is (A) Straight Lines-ADVANCED LEVEL PROBLEMS (B) (C) or (D) none Q.4 Each member of the famil of parabolas = a + + has a maimum or a minimum point depending upon the value of a. The equation to the locus of the maima or minima for all possible values of 'a' is (A) a straight line with slope and intercept. (B) a straight line with slope and intercept. (C) a straight line with slope and intercept. (D) a circle Q.5 m, n are integer with 0 < n < m. A is the point (m, n) on the cartesian plane. B is the reflection of A in the line =. C is the reflection of B in the -ais, D is the reflection of C in the -ais and E is the reflection of D in the -ais. The area of the pentagon ABCDE is (A) m(m + n) (B) m(m + n) (C) m(m + n) (D) m(m + n) Q.6 The area enclosed b the graphs of + = and = is (A) (B) 4 (C) 6 (D) 8 Q.7 If P = (, 0) ; Q = (, 0) and R = (, 0) are three given points, then the locus of the points S satisfing the relation, SQ + SR = SP is : (A) a straight line parallel to ais (B) a circle passing through the origin (C) a circle with the centre at the origin (D) a straight line parallel to ais. Q.8 Two points A(, ) and B(, ) are chosen on the graph of f () = ln with 0 < <. The points C and D trisect line segment AB with AC < CB. Through C a horizontal line is drawn to cut the curve at E(, ). If = and = 000 then the value of equals (A) 0 (B) 0 (C) (0) / (D) (0) / Q.9 What is the -intercept of the line that is parallel to =, and which bisects the area of a rectangle with corners at (0, 0), (4, 0), (4, ) and (0, )? (A) (0, 7) (B) (0, 6) (C) (0, 5) (D) (0, 4) Q.0 Given A (, ) and AB is an line through it cutting the -ais in B. If AC is perpendicular to AB and meets the -ais in

2 Class (XI) C, then the equation of locus of mid- point P of BC is (A) + = (B) + = (C) + = (D) + = Q. AB is the diameter of a semicircle k, C is an arbitrar point on the semicircle (other than A or B) and S is the centre of the circle inscribed into triangle ABC, then measure of (A) angle ASB changes as C moves on k. (B) angle ASB is the same for all positions of C but it cannot be determined without knowing the radius. (C) angle ASB = 5 for all C. (D) angle ASB = 50 for all C. For more such free Assignments visit Q. Given = and a + b = are two variable lines, 'a' and 'b' being the parameters connected b the relation a a b + b = ab. The locus of the point of intersection has the equation (A) + + = 0 (B) + + = 0 (C) = 0 (D) + = 0 Q. If the lines + + = 0 ; = 0 and + + = 0, where + =, are concurrent then (A) =, = (B) =, = ± (C) =, = ± (D) = ±, = Q.4 Let (, ) ; (, ) and (, ) are the vertices of a triangle ABC respectivel. D is a point on BC such that BC = BD. The equation of the line through A and D, is (A) (C) + + = 0 (B) = 0 (D) + + = 0 = 0 Q.5 If the straight lines, a + am + = 0, b + (m + ) b + = 0 and c + (m + )c + = 0, m 0 are concurrent then a, b, c are in : (A) A.P. onl for m = (B) A.P. for all m (C) G.P. for all m (D) H.P. for all m., 4 then the co-ordinates of mid-point of side opposite to A is : (A) (, /) (B) (, 5) (C) (, ) (D) (, 6) Q.6 If in triangle ABC, A (, 0), circumcentre, and orthocentre Q.7 A is a point on either of two lines + = at a distance of 4 units from their point of intersection. The co-ordinates of the foot of perpendicular from A on the bisector of the angle between them are (A), (B) (0, 0) (C), (D) (0, 4) Q.8 Point 'P' lies on the line l { (, ) + 5 = 5}. If 'P' is also equidistant from the coordinate aes, then P can be located in which of the four quadrants. (A) I onl (B) II onl (C) I or II onl (D) IV onl Q.9 An equilateral triangle has each of its sides of length 6 cm. If (, ) ; (, ) and (, ) are its vertices then the value of the determinant, is equal to : Prepared B:

4 Jupiter (XI) 4 (A) (B) (C) 4 (D) 44 Q. Through a point A on the -ais a straight line is drawn parallel to -ais so as to meet the pair of straight lines a + h + b = 0 in B and C. If AB = BC then (A) h = 4ab (B) 8h = 9ab (C) 9h = 8ab (D) 4h = ab Q. The equation of the pair of bisectors of the angles between two straight lines is, 7 = 0. If the equation of one line is = 0 then the equation of the other line is : (A) 4 8 = 0 (B) + = 0 (C) = 0 (D) = 0 Q.4 Consider a quadratic equation in Z with parameters and as Z Z + ( ) = 0 The parameters and are the co-ordinates of a variable point P w.r.t. an orthonormal co-ordinate sstem in a plane. If the quadratic equation has equal roots then the locus of P is (A) a circle (B) a line pair through the origin of co-ordinates with slope / and / (C) a line pair through the origin of co-ordinates with slope / and (D) a line pair through the origin of co-ordinates with slope / and / Q.5 The image of the pair of lines represented b a + h + b = 0 b the line mirror = 0 is (A) a h b = 0 (B) b h + a = 0 (C) b + h + a = 0 (D) a h + b = 0 Q.6 Area of the triangle formed b the line + = and the angle bisectors of the line pair = 0 is (A) / (B) (C) / (D) Q.7 The distance of the point P(, ) from each of the two straight lines through the origin is d. The equation of the two straight lines is (A) ( ) = d ( + ) (B) d ( ) = + (C) d ( + ) = + (D) ( + ) = d ( + ) Q.8 Let PQR be a right angled isosceles triangle, right angled at P (, ). If the equation of the line QR is + =, then the equation representing the pair of lines PQ and PR is (A) = 0 (B) = 0 (C) = 0 (D) = 0 Q.9 The greatest slope along the graph represented b the equation 4 + = 0, is (A) (B) (C) (D) Q.40 If the straight lines joining the origin and the points of intersection of the curve = 0 and + k = 0 are equall inclined to the co-ordinate aes then the value of k : (A) is equal to (B) is equal to (C) is equal to (D) does not eist in the set of real numbers. Q.4 Vertices of a parallelogram ABCD are A(, ), B(,6), C(, ) and D(, 6). If a line passing through the origin divides the parallelogram into two congruent parts then the slope of the line is (A) (B) 8 (C) 5 8 [REASONING TYPE] (D) 8 (A) Statement- is true, statement- is true and statement- is correct eplanation for statement-. (B) Statement- is true, statement- is true and statement- is NOT the correct eplanation for statement-. (C) Statement- is true, statement- is false. (D) Statement- is false, statement- is true. Q.4 Consider the lines, L : ; L = ; L : and L 4 : Statement-: The quadrilateral formed b these four lines is a rhombus. Prepared B:

5 Jupiter (XI) 5 Statement-: If diagonals of a quadrilateral formed b an four lines are unequal and intersect at right angle then it is a rhombus. Q.4 Given a ABC whose vertices are A(, ) ; B(, ) ; C(, ). Let there eists a point P(a, b) such that 6a = + + ; 6b = + + Statement-: Area of triangle PBC must be less than the area of ABC Statement-: P lies inside the triangle ABC Q.44 Let points A, B, C are represented b (a cos i, a sin i ) i =,, and cos ( ) + cos ( ) + cos ( ) =. Statement- : Statement-: Orthocentre of ABC is at origin ABC is equilateral triangle. Q.45 Given the lines + = and + = 5 cut the aes at A, B and C, D respectivel. Statement- : ABDC forms quadrilateral and point (, ) lies inside the quadrilateral Statement- : Point lies on same side of the lines. Q.46 Consider a triangle whose vertices are A(, ), B(, ) and C(, ) where is a real number. Statement- : The area of the triangle ABC is independent of Statement- : The verte C of the triangle ABC alwas moves on a line parallel to the base AB. Q.47 Statement-: Centroid of the triangle whose vertices are A(, ); B( 9, 8) and C(5, ) lies on the internal angle bisector of the verte A. Statement-: Triangle ABC is isosceles with B and C as base angles. Q.48 Consider the line L: = = 0 and the points A( 5, 6) and B(, ) Statement-: There is eactl one point on the line L which is equidistant from the point A and B. Statement-: The point A and B are on the different sides of the line. Q.49 Consider the following statements Statement-: The equation = 0 represents two real lines on the cartesian plane. Statement-: A general equation of degree two a + h + b + g + f + c = 0 denotes a line pair if abc + fgh af bg ch = 0 For more such free Assignments visit [COMPREHENSION TYPE] Paragraph for Question Nos. 50 to 5 Consider a famil of lines (4a + ) (a + ) (a + ) = 0 where a R Q.50 The locus of the foot of the perpendicular from the origin on each member of this famil, is (A) ( ) + 4( + ) = 5 (B) ( ) + ( + ) = 5 (C) ( + ) + 4( ) = 5 (D) ( ) + 4( ) = 5 Q.5 A member of this famil with positive gradient making an angle of 4 with the line 4 =, is (A) 7 5 = 0 (B) 4 + = 0 (C) + 7 = 5 (D) 5 4 = 0 Q.5 Minimum area of the triangle which a member of this famil with negative gradient can make with the positive semi aes, is (A) 8 (B) 6 (C) 4 (D) Prepared B: Paragraph for Question Nos. 5 to 55

7 Jupiter (XI) 7 For more such free Assignments visit Maths Notes and Assignments for IIT-JEE: Phsics Notes and Assignments for IIT-JEE: Chemistr Notes and Assignments for IIT-JEE: New Chapters and Assignments are being regularl updated. Share it with our friends Sharing is Caring. Discuss among ourself or with our teachers in case of doubts. You can post our doubts on website comment section too and I will tr to answer as earl as possible. STRAIGHT LINE Q. A Q. D Q. D Q.4 A Q.5 B Q.6 D Q.7 D Q.8 A Q.9 C Q.0 A Q. C Q. A Q. D Q.4 D Q.5 D Q.6 A Q.7 B Q.8 C Q.9 D Q.0 A Q. D Q. A Q. B Q.4 A Q.5 A Q.6 A Q.7 C Q.8 B Q.9 D Q.0 C Q. D Q. B Q. A Q.4 D Q.5 D Q.6 A Q.7 A Q.8 B Q.9 C Q.40 B Q.4 B Q.4 C Q.4 A Q.44 A Q.45 D Q.46 A Q.47 A Q.48 B Q.49 D Q.50 D Q.5 A Q.5 C Q.5 B Q.54 C Q.55 D Q.56 A,C Q.57 A,B Q.58 A,B Q.59 A,C Q.60 (A) Q; (B) R; (C) S; (D) P Prepared B:

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R