PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the image  of: 

 (–5, 0, 3) in the xz-plane. 

Find the image  of: 

 (–4, 0, 0) in the xy-plane. 

Which term in the expansion of \[\left\{ \left( \frac{x}{\sqrt{y}} \right)^{1/3} + \left( \frac{y}{x^{1/3}} \right)^{1/2} \right\}^{21}\]  contains x and y to one and the same power?

Does the expansion of \[\left( 2 x^2 - \frac{1}{x} \right)\] contain any term involving x⁹?

A cube of side 5 has one vertex at the point (1, 0, –1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.

Planes are drawn parallel to the coordinate planes through the points (3, 0, –1) and (–2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.

Planes are drawn through the points (5, 0, 2) and (3, –2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed. 

Find the distances of the point P(–4, 3, 5) from the coordinate axes. 

The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.

Determine the points in zx-plane are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1). 

Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, –4).

Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).

Find the points on z-axis which are at a distance \[\sqrt{21}\]from the point (1, 2, 3). 

Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.

Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.

Prove that the point A(1, 3, 0), B(–5, 5, 2), C(–9, –1, 2) and D(–3, –3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.

Find the coordinates of the point which is equidistant  from the four points O(0, 0, 0), A(2, 0, 0), B(0, 3, 0) and C(0, 0, 8).

If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.

Find the locus of P if PA² + PB² = 2k², where A and B are the points (3, 4, 5) and (–1, 3, –7).

Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle.