jee advanced paper

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PART-A [SINGLE CORRECT CHOICE TYPE] Q.3 Line L, perpendicular to the line with equation y = 3x – 5, contains the point (1, 4). The x-intercept of L, is (A) 12 (B) 13 (C) 14 (D) 15 ANS : B Q.6 The line x + 3y 2 = 0 bisects the angle between a pair of straight lines of which one has equation x 7y + 5 = 0 . The equation of the other line is : (A) 3x + 3y 1=0 (B) x 3y + 2 = 0 (C) 5x + 5y 3=0 (D) none ANS : C Q.5 If variable line 9ax + 4by = 5 (a, b > 0) always passing through (1, 1), then the maximum value of b 2 a 3 is equal to (A) 5 (B) 10 (C) 13 (D) 15 ANS : B 17. If (a, a 2 ) falls inside the angle made by the lines y = 2 x , x > 0 and y = 3x, x > 0, then a belong to (A) 2 1 , 0 (B) (3, ) (C) 3 , 2 1 (D) - - 2 1 , 3 ANS : C 12. If the sum of the slopes of the lines given by x 2 – 2cxy – 7y 2 = 0 is four times their product c has the value (A) –2 (B) –1 (C) 2 (D) 1 ANS : C [MULTIPLE CORRECT CHOICE TYPE] Q.13 The equation of the line L is 3x + 4y = 12. If a line M whose equation is 3x + 4y + k = 0 is 2 units from L, then the possible value of k is (A) 2 (B) – 22 (C) – 2 (D) 22 ANS : BC Q.9 If (1, 2) is the centroid of an equilateral triangle and (– 2, – 2) is one of the vertices, then (A) inradius of triangle is 2 5 . (B) area of triangle is 4 225 . (C) equation of side opposite to vertex (– 2, – 2) is 6x + 8y = 47. (D) area of triangle is 3 4 225 . ANS : ACD

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Page 1: jee advanced paper

PART-A[SINGLE CORRECT CHOICE TYPE]

Q.3 Line L, perpendicular to the line with equation y = 3x – 5, contains the point (1, 4). The x-interceptof L, is(A) 12 (B) 13 (C) 14 (D) 15 ANS : B

Q.6 The line x + 3y 2 = 0 bisects the angle between a pair of straight lines of which one has equationx 7y + 5 = 0 . The equation of the other line is :(A) 3x + 3y 1 = 0 (B) x 3y + 2 = 0 (C) 5x + 5y 3 = 0 (D) none ANS : C

Q.5 If variable line 9ax + 4by = 5 (a, b > 0) always passing through (1, 1), then the maximum value

of b2a3 is equal to

(A) 5 (B) 10 (C) 13 (D) 15 ANS : B

17. If (a, a2) falls inside the angle made by the lines y =

2

x, x > 0 and y = 3x, x > 0,

then a belong to

(A)

2

1,0 (B) (3, ∞) (C)

3,

2

1 (D)

−−

2

1,3

ANS : C

12. If the sum of the slopes of the lines given by x2 – 2cxy – 7y

2 = 0 is four times their

product c has the value

(A) –2 (B) –1 (C) 2 (D) 1 ANS : C

[MULTIPLE CORRECT CHOICE TYPE]

Q.13 The equation of the line L is 3x + 4y = 12. If a line M whose equation is 3x + 4y + k = 0 is 2 units fromL, then the possible value of k is(A) 2 (B) – 22 (C) – 2 (D) 22

ANS : BC

Q.9 If (1, 2) is the centroid of an equilateral triangle and (– 2, – 2) is one of the vertices, then

(A) inradius of triangle is2

5.

(B) area of triangle is4

225.

(C) equation of side opposite to vertex (– 2, – 2) is 6x + 8y = 47.

(D) area of triangle is34

225.

ANS : ACD

Page 2: jee advanced paper

Q.10 Among the lines passing through C (3, 1), BA is farthest from the origin and cuts x-axis and y-axisat A and B respectively, then(A) equation of AB is 4x + y =13 (B) equation of AB is 3x + y = 10

(C) |AB| =3

1010(D) area of AOB equals

3

50, where O is origin

ANS : BCD

Q.7 The slope of the line that bisects the angle formed by the lines l1 and l2 if l1 has a slope of 2 andl2 is a vertical line, can be

(A) 2 + 5 (B) 2 – 5 (C) 1 + 5 (D) 1 – 5 ANS AB

Q.11 Equation of straight line passing through (1, 2) and cuts off equal intercept on coordinate axes can be(A) x + y = 3 (B) 3x – y = 1 (C) x – y +1 = 0 (D) 2x – y = 0

ANS : AD

ANS : A->R, B->Q, C->S, D->P

[MATRIX TYPE]Q.51 Column-I Column-II

(A) In a plane a set of 8 parallel lines intersect a set of n parallel lines, (P) 6that goes in another direction, forming a total of 1260 parallelograms.The value of n is equal to (Q) 7

(B) Out of 12 points, p point are collinear (0 < p < 12).If the number of triangles formed with vertices at these points is 185,then the value of p, is equal to (R) 10

(C) Number of ways in which 5 personsA, B, C, D and Ecan be seated on round table ifAand D do not sit next (S) 12to each other

(D) Number of cyphers at the end of the number 50P25

Q.1 Column-I Column-II(A) Number of integral values of k for which the lines x + ky = 4 and (P) 0

2x – 3y = 6 intersect in the third quadrant, is

(B) A line with slope 4 and x-intercept – 8 contains the point P which (Q) 2is 40 units above the x-axis. The x-coordinate of point P, is

(C) A line with slope of4

1goes through the point (4, 3). If (– 4, k) is (R) 3

another point on the line, then the value of k is (S) 5

ANS : A->P, B->Q, C->S, D->R

If 2a2 – 7ab – ac + 3b2 – 2bc – c2 = 0 then the family of lines ax + by + c = 0 are either concurrentat the point P(x1, y1) or at the point Q(x2, y2). Find the sum (x1 + y1 + x2 + y2).

(D)

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PART-D[INTEGER TYPE]

Q.1 If distance between the two lines represented by the line pair,

x2 4xy + 4y2 + x 2y 6 = 0 is k , find k.ANS : 5

Q.1 If denotes the area of the triangle formed by the straight lines 7x – 2y+ 10 = 0, 7x + 2y – 10 = 0 andy + 2 = 0, find the sum of the digits in .

ANS : 5

Q.3 If (0, p) lies inside the triangle formed by the lines y + 3x + 2 = 0, 3y – 2x – 5 = 0 and4y + x – 14 = 0 then find the number of integral values of p.

ANS : 2

Q.5 Let ABCD in order be a square. The coordinates of A and C are (1, 3) and (5, 1) respectively.Find the product of the abscissae of B and D.

ANS : 8

Q.1 If exactly one root of the equation x2 + (k + 1) x + 5 k = 0 lies in (0, 5) then find the number ofintegral values of k.

ANS : 2