Jee 2014 Booklet2 Hwt Straight Line
Short Description
Jee 2014 Booklet2 Hwt Straight Line...
Description
Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : STL [1]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (1, 2) and (3, 2), then the centroid of the triangle is : (A) (1, 7/3) (C) (1, 7 / 3)
2.
4.
7.
(1/3, 7/3) (1/ 3, 7 / 3)
8. (B) (D)
0 None of these
1
(B)
0
(C)
1
(D)
a 2 b2
4 7
If every point on the line ( a1 a2 ) x (b1 b2 ) y c is
(A)
a12 b12 a22 b22 (B)
a12 b12 a22 b22
(C)
a12 b12 a22 b22 (D)
None of these
The line parallel to x-axis passing through the intersection of the lines ax 2by 3b 0 and bx 2ay 3a 0 where (A) (B) (C) (D)
9.
If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the line joining the points 2
(B) (D)
( a, b) (0, 0) is :
The line joining A(b cos , b sin ) & B(a cos , a sin ) is produced to the point M(x, y) so that AM : MB = b : a, y sin then x cos 2 2 (A)
7 0
equidistant from the points ( a1 , b1 ) & ( a2 , b2 ) then 2c =
If p is the length of the perpendicular from the origin on x y 1 and a 2 , p 2 , b 2 are in A.P., then the line a b a4 2 p2a2 2 p4 (A) 1 (C) 1
3.
(B) (D)
(A) (C)
A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is: 3 x 4 y 25 x y 7 (A) (B) (C)
2
(a 1, a 1) and (2a, 2a ) ; then the orthocenter lies
10.
on the line :
above x-axis at a distance 3/2 from it above x-axis at a distance 2/3 from it below x-axis at a distance 3/2 from it below x-axis at a distance 2/3 from it
3x 4 y 7 0
(D)
4 x 3 y 24
Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of
(A)
y (a 2 1) x
(C)
x y 0
(D)
(a 1) 2 x (a 1) 2 y 0
(B)
y = 2ax
5.
OPQR is a square and M, N are the middle points of the sides PQ and QR respectively then the ratio of the areas of the square and the triangle OMN is : (A) 4:1 (B) 2:1 (C) 8:3 (D) 4:3
6.
Two points (a, 3) and (5, b) are the opposite vertex of a rectangle. If the other two vertices lie on the line y 2 x c which passes through the point (a, b) then the
the triangle is 1, then the set of values which k can take is given by :
(A)
{1, 3}
(B)
{0, 2}
(C)
{1, 3}
(D)
{3, 2}
value of c is :
VMC/Straight Line
1
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [2]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked ‘*’ may have More than One correct option. 1.
Let A 2, 3 and B 2, 1 be vertices of a triangle
a
ABC. If the centroid of this triangle moves on the line 2 x 3 y 1 , then the locus of the vertex C is the line :
2.
(A)
3x 2 y 5
(B)
2x 3y 7
(C)
2x 3y 9
(D)
3x 2 y 3
(C)
x2 y 2 1 x
3.
equal to : (A) 1 (C) 1 6.
Locus of mid point of the portion between the axes of x cos y sin p , where p is constant is : (A)
2
1 y
2
4 p2 2 y
2
(B) (D)
x
2
1 y
2
7.
4
p
A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an
(B)
y cos sin x sin cos a
(C)
y cos sin x cos sin a
(D)
y cos sin x sin cos a
9.
(B) (D)
1 q2
is
(2, 4) (3/4, 1/2)
(A)
1, 1
(B)
(0, 0)
(C)
(1, 1)
(D)
(2, 2)
The equations to the sides of a triangle are and 3 x y 0 . The line x 3 y 0, 4 x 3 y 5
x1 , y1 , x2 , y2
incentre (B) circumcentre orthocenter of the triangle
centroid
The area of the triangle formed For : (A) (B) (C) (D)
and
lie on a circle
*10.
The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p and q are the intercepts of
VMC/Straight Line
b
2
0 None of these
by the point
k , 2 2k , k 1, 2k and 4 k , 6 2k
x3 , y3 .
5.
1
If algebraic sum of distances of a variable line from points
(A) (C) (D)
If x1 , x2 , x3 and y1 , y2 , y3 are both in G.P. with the same
lie on an ellipse (B) are vertices of a triangle lies on a straight line
p
2
3 x 4 y 0 passes through the :
y cos sin x sin cos a
(A) (C) (D)
1
through the fixed point:
8.
(A)
common ratio, then the points
(2, 0), (0, 2) and 2 , 2 is zero, then the line passes
2
angle 0 with the 4 positive direction of x-axis. The equation of its diagonal not passing through the origin is :
4.
(B) (D)
2
Lines ax by c 0 where 3a 2b c 0 , a, b, c R are concurrent at the point. (A) (3, 2) (C) (3, 4)
x2 y 2 4 p2
1
1
the line L on the new axes, then
2
is 70 units.
four real values of k no integral value of k two integral values of k only one integral value of k
The quadrilateral ABCD formed by the points A(0, 0), B(3, 4), C(7, 7) and D(4, 3) is a : (A) rectangle (B) square (C) rhombus (D) parallelogram
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [3]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked ‘*’ may have More than One correct option. 1.
The triangle with vertices A(2, 7), B(4, y) and C 2 , 6 is right angled at A if : (A)
2.
y=1
1:3
(B)
2:3
(C)
3:1
a, b, c are in A.P.
(B)
a, b, c are in G.P.
(C)
a, b, c are in H.P.
10
(B)
20
(C)
25
1 2 3, 3
(B)
0, 4
0, 2
(C)
None of these
(D)
3:2
(D)
None of these
(D)
30
(D)
1 1 3 , 2
If the vertices A and B of a triangle ABC are given by (2, 5) and 4 , 11 and C moves along the line L1 : 9x + 7y + 4 = 0, the locus of the centroid of the triangle ABC is a straight line parallel to : (A) AB (B) BC (C)
7.
(D)
If the vertices of a triangle ABC are A 4 , 1 , B 1, 2 and C 4 , 3 , then the coordinates of the circumcentre of the triangle are : (A)
6.
(C)
The mid points of the sides AB and AC of a triangle ABC are 2 , 1 and 4 , 7 respectively, then the length of BC is : (A)
5.
y=0
The points P a, b c , Q b, c a and R c, a b are such that PQ = QR if : (A)
4.
(B)
The join of the points 3, 4 and 1, 2 is divided by y-axis in the ratio. (A)
3.
y 1
CA
(D)
L1
The number of lines that can be drawn through the point 4 , 5 at a distance 12 from the point 2 , 3 is : (A)
0
(B)
1
(C)
2
(D)
infinite
x y 1 meets the axis of y and axis of x at A and B respectively. A square ABCD is constructed on the line segment AB away 3 4 from the origin, the coordinates of the vertices of the square farthest from the origin are : (A) (7, 3) (B) (4, 7) (C) (6, 4) (D) (3, 8)
8.
The line
*9.
If the vertices P, Q, R of a triangle are rational points, which of the following points of the triangle PQR is(are) always rational point(s) ? (A) centroid (B) incentre (C) circumcentre (D) orthocenter
10.
Let A0, A1 A2 A3 A4 A5 be a regular hexagon with vertex A0 and A3 at (1, 0) and 1, 0 respectively. The equations representing A1 A4 and A2 A5 are : (A)
y 3x
VMC/Straight Line
(B)
x 3y
y x
(C)
3
(D)
None of these
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [4]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A line which makes an acute angle with the positive direction of x-axis is drawn through the point P(3, 4) to meet the lines x = 6 and y = 8 at R and S respectively then
7.
2 a 3, a 4
RS 8 2 3 , if
2.
3.
(A)
3
(B)
4
(C)
6
(D)
12
4.
5.
(A)
8.
6.
(C)
5 13
(D)
9.
square rhombus
1 sq unit 4 sq units
VMC/Straight Line
(B) (D)
a 1 x a 1 y 0
a 2a If A at 2 , 2at , B , and S(a, 0) are three points, 2 t t
If the line
t None of these
5x y meets the lines x 1, x 2, . . . x n
at points A1, A2, . . . . . . . . , An respectively, then
(O A1 )2 (O A2 )2 . . . (O An )2 is equal to : (A)
3n 2 3n
(C)
3n3 3n 2 2
(B)
2n3 3n 2 n
3 4 3 3 2 ( n 2n n ) One diagonal of a square is the portion of the line 3x + 2y = 12 intercepted between the axes. The coordinates of the extremity of the other diagonals not lying in the first quadrant are : (A) (B) (1, 1) ( 1, 1) (D)
10.
5 13 None of these
(C)
The area enclosed by the lines x y 1 is : (A) (C)
(B)
1 1 is independent of : SA SB (A) a (B) (C) both a and t (D)
distance of L from the origin is : (B)
then the orthocenter
then
If area of the triangle formed by the line L perpendicular to 5 x y 1 and the coordinate axes is 5, then the
5 2
a 4 , 2 a 3 ;
a 1 x a 1 y 0 a 1 x a 1 y 2a
(D)
If a, b, c are in A.P., then ax + by + c = 0 represents : (A) a single line (B) a family of concurrent lines (C) a family of parallel lines (D) None of these
(A)
y=x
(C)
The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6 x 2 y 7 , the PQRS must be a : rectangle (B) cyclic quadrilateral (D)
and
of the triangle lies on the line :
ABCD is a rectangle in the clockwise direction. The coordinates of A are (1, 3) and C are (5, 1), vertices B and D lie on the line y = 2x + c, then the coordinates of D are : (A) (2, 0) (B) (4, 4) (C) (0, 2) (D) (2, 4)
(A) (C)
If the circumcentre of a triangle lies at the point (a, a) and the centroid is the mid-point of the line joining the points
( 1, 1)
(D)
None of these
2 sq units None of these
4
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [5]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked ‘*’ may have More than One correct option. 1.
If y mi x whose
1 (i 1, 2, 3) represents three straight lines mi
slopes
are
the
roots
of
the
5.
2.
(4, 7) (7, 2)
(B) (D)
6.
3 ,1 2
8.
4x 3y 1
3 2
(B)
1,
(D)
1 ,3 2
VMC/Straight Line
(D)
6 x 5 y 14 0
6 x 5 y 56 0
6 x 5 y 14 0
(D)
The equation of a line bisecting the join of (2010, 1600) and (1340, 1080) and having intercept on the axes in the ratio 1 : 2 is : 2 x y 1680 (A)
(B)
x 2 y 1680
2 x y 2010
(D)
None of these
Let the coordinates of P be (x, y) and of Q be ( , ) where is the geometric and is the arithmetic mean of the coordinates of P. If the mid point of PQ is (42, 31) the coordinates of P are : (A) (16, 21) (B) (49, 25) (C) (31, 31) (D) None of these
9.
A straight line passes through the point (1, 1) and the portion of the line intercepted between x and y axes is divided at the point in the ratio 3 : 4. An equation of the line is : 3x 4 y 7 4x 3y 7 (A) (B) (C)
of the diagonal nearer the origin is : 5 x 6 y 14 0 (A) (B)
(C)
A straight is a rhombus. Its diagonals AC and BD intersect at the point M and satisfy BD = 2 AC. If the coordinates of D and M are (1, 1) and (2, 1) respectively, the
(C) 4.
7.
a family of concurrent lines a family of parallel lines u = 0 or v = 0 None of these
coordinates of A are : 1 3, (A) 2
The equations of the pairs of opposite sides of a rectangle
(C)
a b c and 1 1 1 then u + kv = 0 represents : a2 b1 c2
*3.
represents
are x 2 7 x 6 0 and y 2 14 y 40 0 , the equation
(2, 7) (1, 7)
If u a1 x b1 y c1 , v a2 x b2 y c2 0
(A) (B) (C) (D)
equation x 3 6 x 2 y 11xy 2 6 y 3 0
three straight lines passing through the origin, the slops of which form : (A) an A.P. (B) a G.P. (C) an H.P. (D) None of these
equation.
2m3 3m 2 3m 2 0 , A and B are the algebraic sum of the intercepts made by the lines on x-axis and y-axis respectively, then A B 0 if ( , ) is : (A) (C)
The
Image of the point ( 1, 3) with respect to the line y = 2x is: (A) (C)
10.
7 14 5, 5 (3, 1)
(B)
(1, 2)
(D)
(5, 1)
The point (a2, a) lies between the straight lines x y 6 and x y 2 for :
3x 4 y 1 0
5
(A)
all values of a
(B)
no value of a
(C)
2a 3 1
(D)
2a 3 1
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [6]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Perimeter of the quadrilateral bounded by the coordinate axes and the lines x y 50 and 3 x y 90 is : (A)
2.
80 20 2
(B)
80 10 10
80 20 2 10 10 (D)
(C)
110
If the sum of the slopes of the lines given by 3x 2 2cxy 5 y 2 0 is twice their product, then the value of c is : (A)
2
(B)
3
(C)
6
(D)
None of these
For Q.3 - 6 (A) (B) (C) (D)
Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True.
3.
Statement 1 :
If x + ky = 1 and x = a are the equations of the hypotenuse and side of a right angled isosceles triangle then k = a.
Statement 2 :
Each side of a right angled isosceles triangle makes an angle
Statement 1 :
Locus of the centroid of the triangle whose vertices are ( a cos t , a sin t ), (b sin t , b cos t ) and (1, 0) where t is a
4.
with the hypotenuse. 4
parameter is (3 x 1) 2 (3 y ) 2 a 2 b 2 .
5.
Statement 2 :
The centroid of a triangle is equi-distance from the vertices of the triangle.
Statement 1 :
If non zero numbers a, b, c are in Harmonic progression, then the straight line
x y 1 0 always passes through a b c
the fixed point (1, 1).
6.
1 1 1 , , are in arithmetic progression. a b c
Statement 2 :
If a, b, c are in Harmonic progression, then
Statement 1 :
The straight line (sin 3 cos ) x ( 3 sin cos ) y (5sin 7 cos ) 0 for all values of except
n , n is an integer; passes through the point of intersection of the lines x 3 y 5 0 and 3 x y 7 0 . 2 L1 L2 0 represents a line through the point of intersection of the lines L1 0, L2 0 for all non-zero finite
q Statement 2 :
values of . 7.
8.
8 The points 0, , (1, 3) and (82, 30) are the vertices of : 3 (A) obtuse angled triangle (B) (C) right angled triangle (D)
acute angled triangle None of these
Area of the rhombus enclosed by the lines ax by c 0 is : (A)
2a 2 bc
VMC/Straight Line
(B)
2b2 ca
2c 2 ab
(C)
6
(D)
None of these
HWT/Mathematics
Vidyamandir Classes 9.
The coordinates of the points A and B are respectively (3, 2) and (2, 3). P and Q are points on the line joining A and B such that AP = PQ = QB. A square PQRS is constructed on PQ as one side, the coordinates of R are : (A)
10.
4 7 3 , 3
(B)
13 0, 3
1 8 3, 3
(C)
(D)
2 3 , 1
A ray of light coming from the point (1, 2) is reflected at a point A on the axis of x and then passes through the point (5, 3). The coordinates of the point A are : (A)
5 13 , 0
VMC/Straight Line
(B)
( 7, 0)
13 5 , 0
(C)
7
(D)
(15, 0)
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [7]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
The incentre of the triangle with vertices (1, 3), (0, 0)
6.
Triangle is formed by the co-ordinates (0, 0), (0, 21) and (21, 0). Find the number of integral co-ordinates strictly inside the triangle. (Integral co-ordinates mean both x and y are integers) (A) 190 (B) 105 (B) 231 (D) 205
7.
A straight line L through the point (3, –2) is inclined at an
and (2, 0) is :
2.
3.
(A)
3 1, 2
(B)
2 1 , 3 3
(C)
2 3 , 3 2
(D)
1 1, 3
angle 60 to the line
three sides of a square, the equation of the fourth side nearer the point (1, 1) is :
x-axis, then the equation of L is :
(A)
2x y 6 0
(B)
2x y 6 0
(C)
2 x y 14 0
(D)
2 x y 14 0
The distance between the orthocenter and the circumcentre of the triangle with vertices (0, 0), (0, a) and (b, 0) is : 2
a b (A)
(C) 4.
8.
2
(B)
2 a b
a+b
(C)
11 8 88
(D)
9.
10.
The locus represented by the equation 2
2
( x y c) ( x y c) 0 is :
(A) (B) (C) (D)
(C)
3y x 3 2 3 0
(D)
3y x 3 2 3 0
If p be the length of the perpendicular from the origin on x y 1 , then a b
p 2 a 2 b2 1
8
2
1 a
2
(B) 1
b
2
p2 1
(D)
p
2
1 a2
1 b2
a 2 b2
The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is : (A)
2 2
(B)
2
(C)
2
(D)
1
If a + b + c = 0, then the family of lines 3ax by 2c 0 pass through fixed point. (A) (C)
a line parallel to x-axis a point a pair of straight lines a line parallel to y-axis
VMC/Straight Line
y 3x 2 3 3 0
p
8 11 None of these
(B)
(B)
(C)
The centroid of a triangle lies at the origin and the coordinates of its two vertices are (8, 0) and (9, 11), the
(A)
y 3x 2 3 3 0
(A)
a 2 b2 4
(D)
(A)
the line
area of the triangle in sq. units is :
5.
3 x y 1 . If L also intersects the
If x 2 y 3 0, x 2 y 7 0 and 2 x y 4 0 form
(2, 2/3) ( 2, 2 / 3)
(B) (D)
(2/3, 2) None of these
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [8]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Area of the triangle formed by the point (( a 3) ( a 4) , a 3) , (( a 2) ( a 3), a 2) , (( a 1) ( a 2), a 1) is : (A)
2.
25a 2
(B)
5a 2
24a 2
(C)
(D)
None of these
If p1 and p2 are the length of the perpendiculars form the origin upon the lines x sec y cos ec a and x cos y sin a cos 2 respectively, then : (A)
3.
8.
9.
None of these
3:4
(B)
4:3
(C)
9:4
(D)
4:9
1
(B)
2
(C)
3
(D)
5
H.P.
(B)
G.P
(C)
A.P.
(D)
None of these
5 5 3 3
(B)
5 5 0 3
5 5 3, 3
(C)
(D)
5 5 3 3
(D)
2 x 5 y 20
Find the reflection of the line x 2 y 3 0 in the line 3x 2 y 5 0 . (A)
29 x 2 y 31 0
(B)
29 x 2 y 31 0
(C)
29 x 2 y 31 0
(D)
29 x 2 y 31 0
If the point (5, 2) bisects the intercept of a line between the axis, then its equation is : (A) (B) (C) 5 x 2 y 20 2 x 5 y 20 5 x 2 y 20
3 3 3 3 The distance between the orthocenter and incentre of the triangle with vertices (1, 2), (2, 1) and is : 2 2
(A) 10.
(D)
The family of lines represented by x (1 ) y (2 ) 5 0 , being arbitrary, pass through a fixed point whose co-ordinates are : (A)
7.
p12 p22 a 2
(C)
If the lines ax 12 y 1 0 , bx 13 y 1 0 and cx 14 y 1 0 are concurrent, then a , b, c are in : (A)
6.
p12 4 p22 a 2
If the lines x q 0 , y 2 0 and 3x 2 y 5 0 are concurrent, the value of q is : (A)
5.
(B)
The line segment joining the points (1, 2) and ( 2,1) is divided by the line 3x 4 y 7 in the ratio : (A)
4.
4 p12 p22 a 2
0
(B)
2
(C)
3 3
(D)
None of these
( 1, 4)
(D)
(1, 4)
The image of the point (3, 8) in the line x 3 y 7 0 is : (A)
(1, 4)
VMC/Straight Line
(B)
( 1, 4)
(C)
9
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [9]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked ‘*’ may have More than One correct option. 1.
If a , b, c are in G.P. the area of the triangle formed by the line ax by c 0 with the co-ordinate axes is : (A)
2.
(B)
1 sq. units 2
(C)
1 sq. unit
(D)
2 sq. units
If the centroid of a triangle formed by the points (0, 0), (cos , sin ) and (sin , cos ) lies on the line y 2 x , then tan = (A)
*3.
1 sq. units 4
2
(B)
3
2
(C)
(D)
3
(D)
2
If the points ( ( 1 1) , (2 1, 3) and (2 2, 2 ) are collinear then = (A)
4
(B)
1 2
(C)
4
4.
Consider the family of lines ( a y 1) (2 x 3 y 5) 0 and (3x 2 y 4) ( x 2 y 6) 0 , equation of a straight line that belongs to both of the families is : (A) (B) (C) (D) x 2y 8 0 x 2y 8 0 2x y 8 0 2x y 8 0
5.
The co-ordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1, 0) and (2, 0) respectively. The equation of the diagonal CE is : (A)
6.
(B)
9.
10.
x 3y 4
(D)
None of these
(B)
1
(D) 2 2 2 A family of lines is given by (1 2 ) x (1 ) y 0 , being the parameter. The line belonging to this family at the maximum 2
distance from the point (1, 4) is : (A) (B) 4x y 1 0 8.
x 3 y 4 0 (C)
The distance of the line 2 x 3 y 4 from the point (1, 1) in the direction of the line x y 1 is : (A)
7.
3x y 4
5 2
(C)
33x 12 y 7 0 (C)
12 x 33 y 7
If a 0 , b 0 then the incentre of the triangle formed by the axes and the line
(A)
ab ab a b a 2 b2 a b a 2 b2
(B)
ab a b
(C)
ab ab a b a 2 b2 a b a 2 b2
(D)
a b 3 3
(D)
None of these
x y 1 is : a b
ab a b ab
ab
1 If the points ( 2,0), 1, and (cos ,sin ) are collinear then the number of values of 0, 2 is : 3 (A) 0 (B) 1 (C) 2 (D) Infinite The equation of the straight line through the intersection of lines 2 x y 1 and 3x 2 y 5 and passing through the origin, is : (A)
7x 3y 0
VMC/Straight Line
(B)
7x y 0
3x 2 y 0
(C)
10
(D)
x y 0
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : STL [10]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If A(2, 3) and B ( 2 1) are two vertices of triangle and third vertex moves on the line 2 x 3 y 9 , then the locus of the centroid of the triangle is : (A) (B) (C) (D) 2x 3y 1 x y 1 2x 3y 1 2x 3y 3
2.
The line L given by
3.
The line p( p 2 1) x y q 0 and ( p 2 1)2 x ( p 2 1) y 2q 0 are perpendicular to a common line for :
x y x y 1 passes through the point (13, 32). The line K is parallel to L and has the equation 1 . Then the 5 b c 3 distance between L and K is : 23 17 3 17 (A) (B) (C) (D) 15 15 17
(A) (C) 4.
(B) (D)
1
(B)
2
4
{1,3}
(C)
(D)
[ 3 2}
3x 4 y 7 0
(B)
4 x 3 y 24
3x 4 y 25
(C)
(D)
x y7
Let P be the point (1, 0) and Q be a point on the curve y 2 8 x . The locus of mid-point of PQ is : (A)
8.
(D)
A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is ; (A)
7.
2
(C)
Let A( h, k ) , B (1,1) and C (2,1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which ‘k’ can take is given by : (A) {1, 3} (B) {0, 2}
6.
Exactly two values of p No values of p
The perpendicular bisector of the line segment joining P (1, 4) and Q ( k ,3) has y-intercept 4 . Then, a possible value of k is : (A)
5.
Exactly one value of p More than two values of p
x2 4 y 2 0
(B)
x2 4 y 2 0
y2 4x 2 0
(C)
(D)
y2 4x 2 0
If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are ( 1, 2) and (3, 2) , then the centroid of the triangle is : (A)
9.
(B)
7 1 3
1 7 3 3
(C)
(D)
7 1 3
If the sum of the slopes of the lines given by x 2cxy 7 y 2 0 is four times their product, then c has value : (A)
10.
1 7 3 3
1
(B)
1
(C)
(D)
2
2
If the equation of the locus of a point equidistant from the points ( a1 , b1 ) and ( a2 b2 ) is ( a1 a2 ) x (b1 b2 ) y c 0 , then c = (A) (C)
1 2 a2 b22 a12 b12 2 1 2 a1 a22 b12 b22 2
VMC/Straight Line
a12 a22 b12 b22
(B)
a12 b12 a22 b22
(D)
11
HWT/Mathematics
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