Maths Question & Answer

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 :

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

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 

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 ?

What is the value of (1 + cot θ - cosec θ)(1 + tan θ + sec θ)?

Let k = 4 cosx cos2x cos3x - cosx cos2x cos3x then k is equals to

The value of the expression  is ?

If = 0 and if = then what is the value of k?

If , then k is equals to

Let and

If = (1+2^-x)^-1 and = (1+2^1+x)^-1 then the value of is equal to:

The value of is:

The value of the expression is

is eqal to?

Which of the followings is not equals to unity?

Find the probability of 4 turning up for at least once in two tosses of a fair die?

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?

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?

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?

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 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

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 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

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 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:

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 ?

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]

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 :

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 :

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 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 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 (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

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

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

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

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

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

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

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

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

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,

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 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

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?

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 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

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

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

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 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

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

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

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

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

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 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?

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

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

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

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

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,

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

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

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 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