Question & Answer

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

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

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

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:

The lines  are copolar 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

If  = 0 and vectors   and  are non­-coplanar, then the product abc equals

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

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

What is the shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x² + y² + z² + 4x – 2y – 6z = 155?

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

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

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 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

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

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

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

The time period of a charged particle undergoing in a circular motion in a uniform magnetic field is independent of its

If a current is passed through a spring then the spring will

Question 

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question 1

Two discs of the samematerial and thickness have radii 0.2 m and 0.6 m. Their moments of inertia about their axes will
be in the ratio of

A wheel rotates with a constant acceleration of 2.0 radian/sec2. It the wheel starts from rest, the number of revolutions it makes in the first ten seconds will be approximately

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

A torque of 30 N-m is applied on a 5 kg wheel whose moment of inertia is 2kg-m2 for 10 sec. The angle covered by the wheel in 10 sec will be

A constant torque of 1000 N -m, turns a wheel of moment of inertia 200 kg -m2 about an axis passing through the centre. Angular velocity of the wheel after 3 s will be

A particle performs uniform circular motion with an angular momentum L. If the frequency of a particle's motion is doubled and its kinetic energy is halved, the angular momentum becomes.

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

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver?

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

The angular momentum of a system of particles is conserved

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

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

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

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 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?

In an ellipse, the distance between its focii is 6 and the minor axis is 8. Then its eccentricity is,

The locus of the vertices of the family of parabolas  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,

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

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