## A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after?

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from

the start of service will be Rs. 11040 after?

## The radii r1, r2, r3 of escribed circles of a triangle ABC are in harmonic progression. If its area is 24 sq. cm and its perimeter is 24 cm, find the lengths of its sides?

The radii r1, r2, r3 of escribed circles of a triangle ABC are in harmonic progression. If its area is 24 sq. cm and its perimeter is 24 cm, find the lengths of its sides?

## A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even number of trials is?

A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even number of trials is?

## Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace?

Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace?

## For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is p. If he fails in one of the exams, then the probability of his passing in the next exam is p/2, otherwise it remains the same. Find the probability that he will qualify?

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is p. If he fails in one of the exams, then the probability of his passing in the next exam is p/2, otherwise it remains the same. Find the probability that he will qualify?

## A bag contains 5 white, 7 black and 8 red balls. A ball is drawn at random. Find the probability of getting: (i) red ball (ii) non-white ball

A bag contains 5 white, 7 black and 8 red balls. A ball is drawn at random. Find the probability of getting: (i) red ball (ii) non-white ball

## Find the probability of the event A if (i) odds in favour of event A are 5 : 7 (ii) odds against A are 3 : 4?

Find the probability of the event A if (i) odds in favour of event A are 5 : 7 (ii) odds against A are 3 : 4?

## How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

## The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point (0, 17/2 , -13/2) then a =? and b = ?

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point (0, 17/2 , -13/2) then a =? and b = ?

## 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

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

## 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 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

## 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

## A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is

## It is given that the events A and B are such that P(A)= 1/4,P(A/B)=1/2 andP(B/A)=2/3.ThenP(B)is

It is given that the events A and B are such that P(A)= 1/4,P(A/B)=1/2 andP(B/A)=2/3.ThenP(B)is

## AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is?

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is?

##
The x−coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is :

The x−coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is :

##
The area (in square units) bounded by the curves

x -axis, laying in the first quadrant

The area (in square units) bounded by the curves

x -axis, laying in the first quadrant

##
Let Tn be the number of all possible triangles formed by joining vertices of a n−sided regular polygon.IfTn+1 −Tn =1then the value of n is:

Let Tn be the number of all possible triangles formed by joining vertices of a n−sided regular polygon.IfTn+1 −Tn =1then the value of n is:

##
If

If

##
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

##
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is :

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is :

##
The real number k for which the equation, 2x^3 + 3x + k = 0 has two distinct real roots in [0, 1]

The real number k for which the equation, 2x^3 + 3x + k = 0 has two distinct real roots in [0, 1]

##
The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point :

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point :

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point :

##
If x, y, z are in A.P. and tan^−1x, tan^−1y and tan^−1z are also in A.P., then :

If x, y, z are in A.P. and tan^−1x, tan^−1y and tan^−1z are also in A.P., then :

##
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

##
The x−coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is :

## 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

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 *x*^{2} + y^{2} + z^{2} – x + z – 2 = 0 in a circle of radius

*x + 2y – z = 4*cuts the sphere

*x*in a circle of radius

^{2}+ y^{2}+ z^{2}– x + z – 2 = 0

The plane *x + 2y – z = 4* cuts the sphere *x ^{2} + y^{2} + z^{2} – x + z – 2 = 0* in a circle of radius

##
The angle between the lines *2x = 3y = –z* and *6x = –y = –4z* is

*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

*x = ay + b, z = cy + d*and

*x = a*are perpendicular to each other if

**'**y + b**'**, z = c**'**y + d**'**

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

*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

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 *x*^{2} + y^{2} + z^{2} – 6x – 12y – 2z + 20 = 0, then the coordinates of the other end of the diameter are

*x*, then the coordinates of the other end of the diameter are

^{2}+ y^{2}+ z^{2}– 6x – 12y – 2z + 20 = 0

If (2, 3, 5) is one end of a diameter of the sphere *x ^{2} + y^{2} + z^{2} – 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

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

*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

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

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

*2x + 3y + 1 = 0*and

*3x – y – 4 = 0*lie along diameters of a circle of circumference 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 *x*^{2} + y^{2}* – 2x = 0* is *A*B. Equation of the circle on *AB* as diameter is

*y = x*by the circle

*x*

^{2}+ y^{2}*– 2x = 0*is

*A*B. Equation of the circle on

*AB*as diameter is

The intercept on the line *y = x* by the circle *x ^{2} + y^{2}*

*– 2x = 0*is

*A*B. 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

*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

*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

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

*ax + 2by + 3b = 0*and

*bx – 2ay – 3a = 0,*where (a, b) (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

*a, b, c*are in H.P., then the straight line 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 *x*^{2} + y^{2} + 2ax + cy + a = 0 and *x*^{2} + y^{2} – 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

*x*and

^{2}+ y^{2}+ 2ax + cy + a = 0*x*intersect in two distinct points

^{2}+ y^{2}– 3ax + dy – 1 = 0*P*and

*Q*then the line

*5x+by – a = 0*passes through

*P*and

*Q*for

If the circles *x ^{2} + y^{2} + 2ax + cy + a = 0* and

*x*intersect in two distinct points

^{2}+ y^{2}– 3ax + dy – 1 = 0*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?

*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 *x*^{2} + y^{2} = p^{2} orthogonally, then the equation of the locus of its centre is

*(a, b)*and cuts the circle

*x*orthogonally, then the equation of the locus of its centre is

^{2}+ y^{2}= p^{2}

If a circle passes through the point *(a, b)* and cuts the circle *x ^{2} + y^{2} = p^{2}* 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?

*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

The locus of a point moving under the condition that the line is a tangent to the hyperbola is

##
If the pair of lines *ax*^{2} + 2(a + b)xy + by^{2} = 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

*ax*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

^{2}+ 2(a + b)xy + by^{2}= 0

If the pair of lines *ax ^{2} + 2(a + b)xy + by^{2} = 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(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

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?

*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?

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

*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

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, a*^{2}) falls inside the angle made by the lines, *y = x/2, x > 0 and y = 3x, x > 0,* then *a* belongs to

*(a, a*falls inside the angle made by the lines,

^{2})*y = x/2, x > 0 and y = 3x, x > 0,*then

*a*belongs to

If *(a, a ^{2})* 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?

*a*varies?

For the Hyperbola which of the following remains constant when *a* varies?

##
The equation of a tangent to the parabola *y*^{2} = 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

*y*is

^{2}= 8x*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 *y ^{2} = 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

*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?*

*P = (–1, 0), Q = (0, 0)*and R = 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 *my*^{2} + (1 – m^{2})xy – mx^{2} = 0 is a bisector of the angle between the lines *xy* = 0, then *m* is

*my*= 0 is a bisector of the angle between the lines

^{2}+ (1 – m^{2})xy – mx^{2}*xy*= 0, then

*m*is

If one of the lines of *my ^{2} + (1 – m^{2})xy – mx^{2} *= 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

*(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

*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 *x*^{2} + y^{2} + 2x + 4y – 3 = 0 is

*x*is

^{2}+ y^{2}+ 2x + 4y – 3 = 0

The point diametrically opposite to the point P(1, 0) on the circle *x ^{2} + y^{2} + 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

*(1, 0, 0), (0, 1, 0)*which makes an angle 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

**'**, 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 *x*^{2} + y^{2} + z^{2} + 4x – 2y – 6z = 155?

*12x + 4y + 3z = 327*to the sphere

*x*?

^{2}+ y^{2}+ z^{2}+ 4x – 2y – 6z = 155

What is the shortest distance from the plane *12x + 4y + 3z = 327* to the sphere *x ^{2} + y^{2} + z^{2} + 4x – 2y – 6z = 155*?

##
The radius of the circle in which the sphere *x*^{2} + y^{2} + z^{2} + 2x – 2y – 4z – 19 = 0 is cut by the plane *x + 2y + 2z + 7 = 0* is

*x*is cut by the plane

^{2}+ y^{2}+ z^{2}+ 2x – 2y – 4z – 19 = 0*x + 2y + 2z + 7 = 0*is

The radius of the circle in which the sphere *x ^{2} + y^{2} + z^{2} + 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

*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

*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

*x = ay + b, z = cy + d*and

*x = a*will be perpendicular, if and only if

**'**y + b**'**, z = c**'**y + d

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

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:

*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

*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

*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

*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

*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?*

*P = (–1, 0), Q = (0, 0)*and R = be three points. What is the equation of the bisector of the angle

*PQR?*

*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?

*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?

*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

*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

*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, a*^{2}) falls inside the angle made by the lines, *y = x/2, x > 0 and y = 3x, x > 0,* then *a* belongs to

*(a, a*falls inside the angle made by the lines,

^{2})*y = x/2, x > 0 and y = 3x, x > 0,*then

*a*belongs to

*(a, a ^{2})* 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?

*a*varies?

For the Hyperbola which of the following remains constant when *a* varies?

##
The equation of a tangent to the parabola *y*^{2} = 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

*y*is

^{2}= 8x*y = x + 2*. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

*y ^{2} = 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?

*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?

*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 *x*^{2} + y^{2} = p^{2} orthogonally, then the equation of the locus of its centre is

*(a, b)*and cuts the circle

*x*orthogonally, then the equation of the locus of its centre is

^{2}+ y^{2}= p^{2}

*(a, b)* and cuts the circle *x ^{2} + y^{2} = p^{2}* 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?

*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?

*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

The locus of a point moving under the condition that the line is a tangent to the hyperbola is

##
If the pair of lines *ax*^{2} + 2(a + b)xy + by^{2} = 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

*ax*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

^{2}+ 2(a + b)xy + by^{2}= 0

*ax ^{2} + 2(a + b)xy + by^{2} = 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(3, 4)*is such that its intercept between the axes is bisected at

*A*. Its equation is,

*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

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,

##
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

*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

*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

*ax + 2by + 3b = 0*and

*bx – 2ay – 3a = 0,*where (a, b) (0, 0) is

*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

*a, b, c*are in H.P., then the straight line always passes through a fixed point. That point is

*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 the circles *x*^{2} + y^{2} + 2ax + cy + a = 0 and *x*^{2} + y^{2} – 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

*x*and

^{2}+ y^{2}+ 2ax + cy + a = 0*x*intersect in two distinct points

^{2}+ y^{2}– 3ax + dy – 1 = 0*P*and

*Q*then the line

*5x+by – a = 0*passes through

*P*and

*Q*for

*x ^{2} + y^{2} + 2ax + cy + a = 0* and

*x*intersect in two distinct points

^{2}+ y^{2}– 3ax + dy – 1 = 0*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 *x*^{2} + y^{2} = 4 orthogonally, then the locus of its centre is

*x*orthogonally, then the locus of its centre is

^{2}+ y^{2}= 4

If a circle passes through the point (a, b) and cuts the circle *x ^{2} + y^{2} = 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(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

*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 *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

*2x + 3y + 1 = 0*and

*3x – y – 4 = 0*lie along diameters of a circle of circumference then the equation of the circle is

*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 *x*^{2} + y^{2}* – 2x = 0* is *A*B. Equation of the circle on *AB* as diameter is

*y = x*by the circle

*x*

^{2}+ y^{2}*– 2x = 0*is

*A*B. Equation of the circle on

*AB*as diameter is

*y = x* by the circle *x ^{2} + y^{2}*

*– 2x = 0*is

*A*B. 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

*x = 4*, then the equation of the ellipse is

*x = 4*, then the equation of the ellipse is

##
A point on the parabola *y*^{2} = 18x at which the ordinate increases at twice the rate of the abscissa is

*y*at which the ordinate increases at twice the rate of the abscissa is

^{2}= 18x

A point on the parabola *y ^{2} = 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

*x = a(1 + cos), 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

*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 *x*^{2} – 2cxy – 7y^{2} = 0 is four times their product, then *c* has the value

*x*is four times their product, then

^{2}– 2cxy – 7y^{2}= 0*c*has the value

If 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

##
The centres of a set of circles, each of radius 3, lie on the circle *x*^{2} + y^{2} = 25. The locus of any point in the set is

*x*= 25. The locus of any point in the set is

^{2}+ y^{2}

The centres of a set of circles, each of radius 3, lie on the circle *x ^{2} + y^{2}* = 25. The locus of any point in the set is

##
The point of lines represented by 3ax^{2} + 5xy + (a – 2)y^{2} = 0 and ^ to each other for

^{2}+ 5xy + (a – 2)y

^{2}= 0 and ^ to each other for

The point of lines represented by 3ax^{2} + 5xy + (a – 2)y^{2} = 0 and ^ to each other for

##
Locus of mid point of the portion between the axes of where *p* is constant is

*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 *x*^{2} + y^{2} = 9 is

*x*is

^{2}+ y^{2}= 9

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle *x ^{2} + y^{2} = 9* is

##
The equation of a circle with origin as a center and passing through equilateral triangle whose median is of length *3a* is

*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 *b*^{2} is

*b*is

^{2}

The foci of the ellipse and the hyperbola coincide. Then the value of *b ^{2}* is

##
The normal at the point *(bt*_{1}^{2}, 2bt_{1}) on a parabola meets the parabola again in the point *(bt*_{2}^{2}, 2bt_{2}), then

*(bt*on a parabola meets the parabola again in the point

_{1}^{2}, 2bt_{1})*(bt*, then

_{2}^{2}, 2bt_{2})

The normal at the point *(bt _{1}^{2}, 2bt_{1})* on a parabola meets the parabola again in the point

*(bt*, then

_{2}^{2}, 2bt_{2})##
If the two circles *(x – 1)*^{2} + (y – 3)^{2} = r^{2} and *x*^{2} + y^{2} – 8x + 2y + 8 = 0 intersect in two distinct points, then

*(x – 1)*and

^{2}+ (y – 3)^{2}= r^{2}*x*intersect in two distinct points, then

^{2}+ y^{2}– 8x + 2y + 8 = 0

If the two circles *(x – 1) ^{2} + (y – 3)^{2} = r^{2}* and

*x*intersect in two distinct points, then

^{2}+ y^{2}– 8x + 2y + 8 = 0##
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

*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

*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 *x*^{2} – 2pxy – y^{2} = 0 and *x*^{2} – 2qxy – y^{2} = 0 be such that each pair bisects the angle between the other pair, then

*x*and

^{2}– 2pxy – y^{2}= 0*x*be such that each pair bisects the angle between the other pair, then

^{2}– 2qxy – y^{2}= 0

If the pairs of straight lines *x ^{2} – 2pxy – y^{2} = 0* and

*x*be such that each pair bisects the angle between the other pair, then

^{2}– 2qxy – y^{2}= 0##
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

*(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 *x*^{2} + y^{2} = 1 subtends an angle of measure 45° at the major segment of the circle then value of *m* is

*y = mx*+ 1 of the circle

*x*= 1 subtends an angle of measure 45° at the major segment of the circle then value of

^{2}+ y^{2}*m*is

If the chord *y = mx* + 1 of the circle *x ^{2} + y^{2}* = 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

For any vector, the value of is equal to

##
Let and

Then 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

*a, b*and

*c*be distinct nonnegative numbers. If the vectors 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

If are noncoplanar vector and is a real number then for

##
If , 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

*a*, for which the points A, B, C with position vectors 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

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 ?

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

The non-zero vectors are related Then the angle between and is

##
Two common tangents to the circle *x*^{2} + y^{2} = 2a^{2} and parabola *y*^{2} = 8ax are

*x*and parabola

^{2}+ y^{2}= 2a^{2}*y*are

^{2}= 8ax

Two common tangents to the circle *x ^{2} + y^{2} = 2a^{2}* and parabola

*y*are

^{2}= 8ax##
If 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

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

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

##
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

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