A die is thrown ten times if getting an even number is considered as a success ,then the probability of four success is
If the angle 
between the line 
and the plane 
is such that sin = 1/3 the value of 
is
between the line and the plane is such that sin = 1/3 the value of is
If the angle between the line and the plane is such that sin = 1/3 the value of is
The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius
The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius
The angle between the lines 2x = 3y = –z and 6x = –y = –4z is
The angle between the lines 2x = 3y = –z and 6x = –y = –4z is
The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other if
The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other if
The image of the point (–1, 3, 4) in the 3 plane x – 2y = 0 is
The image of the point (–1, 3, 4) in the 3 plane x – 2y = 0 is
If a line makes an angle of 
with the positive directions of each of xaxis and yaxis, then the angle that the line makes with the positive direction of the zaxis is
with the positive directions of each of xaxis and yaxis, then the angle that the line makes with the positive direction of the zaxis is
If a line makes an angle of with the positive directions of each of xaxis and yaxis, then the angle that the line makes with the positive direction of the zaxis is
If (2, 3, 5) is one end of a diameter of the sphere x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0, then the coordinates of the other end of the diameter are
If (2, 3, 5) is one end of a diameter of the sphere x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0, then the coordinates of the other end of the diameter are
Let 
and 
If the vectors 
lies in the plane of 
and 
, then x equals
and If the vectors lies in the plane of and , then x equals
Let and If the vectors lies in the plane of and , then x equals
Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle a with the positive x-axis, then cos a equals
Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle a with the positive x-axis, then cos a equals
The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzplane at the point 
Then
Then
The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzplane at the point Then
If the straight lines 
and 
intersect at a point, then the integer k is equal to
and intersect at a point, then the integer k is equal to
If the straight lines and intersect at a point, then the integer k is equal to
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 
then the equation of the circle is
then the equation of the circle is
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference then the equation of the circle is
The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is
The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is
The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is
The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is
If the straight lines x = 1 + s, y = –3 
z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then 
equals
z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then equals
If the straight lines x = 1 + s, y = –3 z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then equals
Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of midpoint of PQ is
Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of midpoint of PQ is
The line parallel to thexaxis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) 
(0, 0) is
(0, 0) is
The line parallel to thexaxis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) (0, 0) is
If non zero numbers a, b, c are in H.P., then the straight line 
always passes through a fixed point. That point is
always passes through a fixed point. That point is
If non zero numbers a, b, c are in H.P., then the straight line always passes through a fixed point. That point is
If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2), then what will be the centroid of the triangle.
If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2), then what will be the centroid of the triangle.
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x+by – a = 0 passes through P and Q for
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x+by – a = 0 passes through P and Q for
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. What will be the locus of the centre of the circle?
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. What will be the locus of the centre of the circle?
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
An ellipse has OB as semi-minor axis, F and F' its focii and the angle FBF' is a right angle. Then what will be the eccentricity of the ellipse?
An ellipse has OB as semi-minor axis, F and F' its focii and the angle FBF' is a right angle. Then what will be the eccentricity of the ellipse?
The locus of a point 
moving under the condition that the line 
is a tangent to the hyperbola 
is
moving under the condition that the line is a tangent to the hyperbola is
The locus of a point moving under the condition that the line is a tangent to the hyperbola is
If the pair of lines ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
If the pair of lines ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
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 straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is,
The locus of the vertices of the family of parabolas 
is
is
The locus of the vertices of the family of parabolas is
In an ellipse, the distance between its focii is 6 and the minor axis is 8. Then its eccentricity is,
In an ellipse, the distance between its focii is 6 and the minor axis is 8. Then its eccentricity is,
If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 
square units, then what will be the equation of the circle?
square units, then what will be the equation of the circle?
If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area square units, then what will be the equation of the circle?
Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of chord of the circle C that subtend an angle of 
at its centre is
at its centre is
Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of chord of the circle C that subtend an angle of at its centre is
If (a, a2) falls inside the angle made by the lines, y = x/2, x > 0 and y = 3x, x > 0, then a belongs to
If (a, a2) falls inside the angle made by the lines, y = x/2, x > 0 and y = 3x, x > 0, then a belongs to
For the Hyperbola 
which of the following remains constant when a varies?
which of the following remains constant when a varies?
For the Hyperbola which of the following remains constant when a varies?
The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is
The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is
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 square unit, then the set of values which ‘k’ can take is given by
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 square unit, then the set of values which ‘k’ can take is given by
Let P = (–1, 0), Q = (0, 0) and R = 
be three points. What is the equation of the bisector of the angle PQR?
be three points. What is the equation of the bisector of the angle PQR?
Let P = (–1, 0), Q = (0, 0) and R = be three points. What is the equation of the bisector of the angle PQR?
If one of the lines of my2 + (1 – m2)xy – mx2 = 0 is a bisector of the angle between the lines xy = 0, then m is
If one of the lines of my2 + (1 – m2)xy – mx2 = 0 is a bisector of the angle between the lines xy = 0, then m is
Consider a family of circles that are passing through the point (–1, 1) and are tangent to x-axis. If (h, k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval
Consider a family of circles that are passing through the point (–1, 1) and are tangent to x-axis. If (h, k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval
The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a
The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a
A parabola has the origin as its focus and the line x= 2 as the directrix. Then the vertex of the parabola is at
A parabola has the origin as its focus and the line x= 2 as the directrix. Then the vertex of the parabola is at
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2 Then the length of the semi-major axis is
A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2 Then the length of the semi-major axis is
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
If a - b = 3 and a*a + b*b = 29, find the value of ab
If a - b = 3 and a*a + b*b = 29, find the value of ab
If a - b = 3 and a*a + b*b = 29, find the value of ab
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle 
with plane x + y = 3 are
with plane x + y = 3 are
The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle with plane x + y = 3 are
Two systems of rectangular axes have the same origin. If a plane cuts them at distance a, b, c and a', b', c' from the origin, then
Two systems of rectangular axes have the same origin. If a plane cuts them at distance a, b, c and a', b', c' from the origin, then
What is the shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x – 2y – 6z = 155?
What is the shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x – 2y – 6z = 155?
The radius of the circle in which the sphere x2 + y2 + z2 + 2x – 2y – 4z – 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is
The radius of the circle in which the sphere x2 + y2 + z2 + 2x – 2y – 4z – 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is
A tetrahedron has vertices at O (0, 0, 0), A (1, 2, 1), B (2, 1, 3) and C (–1, 1, 2). Then the angle between the faces OAB and ABC will be
A tetrahedron has vertices at O (0, 0, 0), A (1, 2, 1), B (2, 1, 3) and C (–1, 1, 2). Then the angle between the faces OAB and ABC will be
If 
= 0 and vectors 
and 
are non-coplanar, then the product abc equals
= 0 and vectors and are non-coplanar, then the product abc equals
If = 0 and vectors and are non-coplanar, then the product abc equals
The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d will be perpendicular, if and only if
The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d will be perpendicular, if and only if
The lines 
are copolar only if
are copolar only if
The lines are copolar only if
A line makes the same angle 
with each of the x and z axis. If the angle 
which it makes with yaxis, is such that 
then 
equals:
with each of the x and z axis. If the angle which it makes with yaxis, is such that then equals:
A line makes the same angle with each of the x and z axis. If the angle which it makes with yaxis, is such that then equals:
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The coordinates of each of the points of intersection are given by
A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The coordinates of each of the points of intersection are given by
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 square unit, then the set of values which ‘k’ can take is given by
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 square unit, then the set of values which ‘k’ can take is given by
Let P = (–1, 0), Q = (0, 0) and R = be three points. What is the equation of the bisector of the angle PQR?
be three points. What is the equation of the bisector of the angle PQR?
Let P = (–1, 0), Q = (0, 0) and R = be three points. What is the equation of the bisector of the angle PQR?
If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area square units, then what will be the equation of the circle?
square units, then what will be the equation of the circle?
If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area square units, then what will be the equation of the circle?
Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of chord of the circle C that subtend an angle of at its centre is
at its centre is
Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of chord of the circle C that subtend an angle of at its centre is
If (a, a2) falls inside the angle made by the lines, y = x/2, x > 0 and y = 3x, x > 0, then a belongs to
If (a, a2) falls inside the angle made by the lines, y = x/2, x > 0 and y = 3x, x > 0, then a belongs to
For the Hyperbola which of the following remains constant when a varies?
which of the following remains constant when a varies?
For the Hyperbola which of the following remains constant when a varies?
The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is
The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. What will be the locus of the centre of the circle?
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. What will be the locus of the centre of the circle?
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
An ellipse has OB as semi-minor axis, F and F' its focii and the angle FBF' is a right angle. Then what will be the eccentricity of the ellipse?
An ellipse has OB as semi-minor axis, F and F' its focii and the angle FBF' is a right angle. Then what will be the eccentricity of the ellipse?
The locus of a point moving under the condition that the line is a tangent to the hyperbola is
moving under the condition that the line is a tangent to the hyperbola is
The locus of a point moving under the condition that the line is a tangent to the hyperbola is
If the pair of lines ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
If the pair of lines ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
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 straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is,
The locus of the vertices of the family of parabolas is
is
The locus of the vertices of the family of parabolas is
In an ellipse, the distance between its focii is 6 and the minor axis is 8. Then its eccentricity is,
In an ellipse, the distance between its focii is 6 and the minor axis is 8. Then its eccentricity is,
If the straight lines x = 1 + s, y = –3 z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then equals
z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then equals
If the straight lines x = 1 + s, y = –3 z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then equals
Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of midpoint of PQ is
Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of midpoint of PQ is
The line parallel to thexaxis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) (0, 0) is
(0, 0) is
The line parallel to thexaxis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) (0, 0) is
If non zero numbers a, b, c are in H.P., then the straight line always passes through a fixed point. That point is
always passes through a fixed point. That point is
If non zero numbers a, b, c are in H.P., then the straight line always passes through a fixed point. That point is
If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2), then what will be the centroid of the triangle.
If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2), then what will be the centroid of the triangle.
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x+by – a = 0 passes through P and Q for
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x+by – a = 0 passes through P and Q for
if x1,x2,x3 are the roots of x^4-1 = 0 and w is the complex cube root of unity, the value of?
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is
A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is
A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is
If a 
0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then
0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then
If a 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference then the equation of the circle is
then the equation of the circle is
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference then the equation of the circle is
The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is
The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is
The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is
The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is
A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is
A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is
The normal to the curve x = a(1 + cos
), y = asin at always passes through the fixed point
), y = asin at always passes through the fixed point
The normal to the curve x = a(1 + cos), y = asin at always passes through the fixed point
Let A(2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
Let A(2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
The equation of the straight line passing through the point (4, 3) and making intercepts on the co ordinate axes whose sum is –1 is
The equation of the straight line passing through the point (4, 3) and making intercepts on the co ordinate axes whose sum is –1 is
If the sum of the slopes of the lines given by x2 – 2cxy – 7y2 = 0 is four times their product, then c has the value
If the sum of the slopes of the lines given by x2 – 2cxy – 7y2 = 0 is four times their product, then c has the value
The centres of a set of circles, each of radius 3, lie on the circle x2 + y2 = 25. The locus of any point in the set is
The centres of a set of circles, each of radius 3, lie on the circle x2 + y2 = 25. The locus of any point in the set is
The point of lines represented by 3ax2 + 5xy + (a – 2)y2 = 0 and ^ to each other for
The point of lines represented by 3ax2 + 5xy + (a – 2)y2 = 0 and ^ to each other for
Locus of mid point of the portion between the axes of 
where p is constant is
where p is constant is
Locus of mid point of the portion between the axes of where p is constant is
The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x2 + y2 = 9 is
The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x2 + y2 = 9 is
The equation of a circle with origin as a center and passing through equilateral triangle whose median is of length 3a is
The equation of a circle with origin as a center and passing through equilateral triangle whose median is of length 3a is
A triangle with vertices (4, 0), (–1, –1), (3, 5) is
A triangle with vertices (4, 0), (–1, –1), (3, 5) is
The foci of the ellipse 
and the hyperbola 
coincide. Then the value of b2 is
and the hyperbola coincide. Then the value of b2 is
The foci of the ellipse and the hyperbola coincide. Then the value of b2 is
The normal at the point (bt12, 2bt1) on a parabola meets the parabola again in the point (bt22, 2bt2), then
The normal at the point (bt12, 2bt1) on a parabola meets the parabola again in the point (bt22, 2bt2), then
If the two circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then
If the two circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then
The lines 2x – 3y= 5 and 3x – 4y= 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is
The lines 2x – 3y= 5 and 3x – 4y= 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is
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 angle 
with the positive direction of the x-axis. The equation of its diagonal not passing through the origin is
with the positive direction of the x-axis. The equation of its diagonal not passing through the origin is
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 angle with the positive direction of the x-axis. The equation of its diagonal not passing through the origin is
If the pairs of straight lines x2 – 2pxy – y2 = 0 and x2 – 2qxy – y2 = 0 be such that each pair bisects the angle between the other pair, then
If the pairs of straight lines x2 – 2pxy – y2 = 0 and x2 – 2qxy – y2 = 0 be such that each pair bisects the angle between the other pair, then
Locus of the centroid of the triangle whose vertices are (a cost, a sint), (b sint, –b cost) and (1, 0), where t is a parameter, is
Locus of the centroid of the triangle whose vertices are (a cost, a sint), (b sint, –b cost) and (1, 0), where t is a parameter, is
If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 45° at the major segment of the circle then value of m is
If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 45° at the major segment of the circle then value of m is
If C is the mid point of AB and P is any point outside AB, then
If C is the mid point of AB and P is any point outside AB, then
For any vector, 
the value of 
is equal to
the value of is equal to
For any vector, the value of is equal to
Let 
and 
Then 
depends on
and depends on
Let and
Then depends on
Let a, b and c be distinct nonnegative numbers. If the vectors 
and 
lie in a plane, then c is
and lie in a plane, then c is
Let a, b and c be distinct nonnegative numbers. If the vectors and lie in a plane, then c is
If 
are noncoplanar vector and 
is a real number then 
for
are noncoplanar vector and is a real number then for
If are noncoplanar vector and is a real number then for
If 
, where 
and 
any three vectors such that 
then and 
and are
, where and any three vectors such that then and and are
If , where and any three vectors such that then and and are
The values of a, for which the points A, B, C with position vectors 
and 
respectively are the vertices of a right angled triangle at c are
and respectively are the vertices of a right angled triangle at c are
The values of a, for which the points A, B, C with position vectors and respectively are the vertices of a right angled triangle at c are
If 
and 
are unit vectors and 
is the acute angle between them, then 
is a unit vector for
and are unit vectors and is the acute angle between them, then is a unit vector for
If and are unit vectors and is the acute angle between them, then is a unit vector for
The vector 
lies in the plane of the vectors 
and 
and bisects the angle between and 
. Then which one of the following gives possible values of 
and 
?
lies in the plane of the vectors and and bisects the angle between and . Then which one of the following gives possible values of and ?
The vector lies in the plane of the vectors and and bisects the angle between and . Then which one of the following gives possible values of and ?
The non-zero vectors 
are related 
Then the angle between and 
is
are related Then the angle between and is
The non-zero vectors are related Then the angle between and is
Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax are
Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax are
If 
and 
are three non-coplanar vectors, then 
equals
and are three non-coplanar vectors, then equals
If and are three non-coplanar vectors, then equals
Let 
and 
If 
is a unit vector such that 
and 
then 
is equal to
and If is a unit vector such that and then is equal to
Let and If is a unit vector such that and then is equal to
The vectors 
and 
are the sides of a triangle ABC. The length of the median through A is
and are the sides of a triangle ABC. The length of the median through A is
The vectors and are the sides of a triangle ABC. The length of the median through A is
are three vectors, such that 
then 
is equal to
are three vectors, such that then is equal to
are three vectors, such that then is equal to
Let 
and 
be three non-zero vectors such that no two of these are collinear. If the vector 
is collinear with 
and 
is collinear with 
(
being some nonzero scalar) then 
equals
and be three non-zero vectors such that no two of these are collinear. If the vector is collinear with and is collinear with ( being some nonzero scalar) then equals
Let and be three non-zero vectors such that no two of these are collinear. If the vector is collinear with and is collinear with ( being some nonzero scalar) then equals
A particle is acted upon by constant forces 
and 
which displace it from a point 
to the point 
The work done in standard units by the forces is given by
and which displace it from a point to the point The work done in standard units by the forces is given by
A particle is acted upon by constant forces and which displace it from a point to the point The work done in standard units by the forces is given by
If 
are non-coplanar vectors and 
is a real number, then the vectors 
and 
are non-coplanar fo
are non-coplanar vectors and is a real number, then the vectors and are non-coplanar fo
If are non-coplanar vectors and is a real number, then the vectors and are non-coplanar fo
Let 
be such that 
If the projection 
along 
is equal to that of 
along and , are perpendicular to each other then 
equals
be such that If the projection along is equal to that of along and , are perpendicular to each other then equals
Let be such that If the projection along is equal to that of along and , are perpendicular to each other then equals
Let 
and 
be non-zero vectors such that 
If 
is the acute angle between the vectors 
and 
then 
equals
and be non-zero vectors such that If is the acute angle between the vectors and then equals
Let and be non-zero vectors such that If is the acute angle between the vectors and then equals
If 
are vectors such that 
then what will be 
?
are vectors such that then what will be ?
If are vectors such that then what will be ?
If 
are vectors show that 
and 
then angle between vector 
and 
is
are vectors show that and then angle between vector and is
If are vectors show that and then angle between vector and is
If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a . b + b . c + c . a|, given that 
If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a . b + b . c + c . a|, given that
then
then
then
and 
are two vectors and 
is a vector such that 
then what is 
?
and are two vectors and is a vector such that then what is ?
and are two vectors and is a vector such that then what is ?