Geometric Applications of PNC

Q.

If vertices of parallelogram are respectively $(0,0),(1,0),(2,2)\mathrm{and}\left(1,2\right)$ then angle between diagonals is.

1. $\frac{\pi }{3}$

2. $\frac{\pi }{2}$

3. $\frac{3\pi }{2}$

4. $\frac{\pi }{4}$

Q.

Three straight lines $L1$, $L2$ and $L3$ are parallel and lie in the same plane. A total of $m$ points are taken on $L1$, $n$ points on. $L2$, $k$ points on $L3$. The maximum number of triangles formed with vertices at these points are.

1. ${}^{m+n+k}C_3$

2. ${}^{m+n+k}C_3-{}^{m}C_3-{}^{n}C_3$

3. ${}^{m+n+k}C_3+{}^{m}C_3+{}^{n}C_3$

4. None of these

Q. A and B are running around a circular track in opposite directions. They meet at a point 550 m from the starting point and continue running. Now, they meet at a point 350 m from the starting point, but in opposite directions as before. What is the length of the circular track?

Q. What is the maximum number of times x circles of the same size can intersect each other?

1. x(x-1)
2. x(x+1)/2
3. 2x
4. (x - 1)

Q. How many different straight lines can be formed by joining 14 different points of which 6 are collinear and rest are non-collinear?

1. 76
2. 62
3. 63
4. 64
5. 77

Q.

How many lines are determined by three distinct points?

Q.

Find the number of parallelograms formed if $10$ parallel lines in a plane are intersected by a family of $12$ parallel lines.

Q. What is the central angle corresponding to the total number of cellular phones (both Nokia and Samsung) sold by store S?

1. ${99.2}^{\circ }$
2. ${93.6}^{\circ }$
3. ${100.8}^{\circ }$
4. ${97.4}^{\circ }$
5. ${101.2}^{\circ }$

Q. A square is inscribed in a triangle with the two shorter sides p and q such that the square has a common right angle with the triangle. What is the perimeter of the square?

1. 
2. (pq)³
3. 
4. 

Q.

There are $p,q,r$ points on three parallel lines $L_1,L_{2}and{L}_3$all of which lie in one plane. The number of triangles which can be formed with vertices at these points is

1. ${}^{p+q+r}{C}_3$

2. ${}^{p+q+r}{C}_3{–}^p{C}_3{–}^q{C}_3{-}^r{C}_3$

3. ${}^p{C}_3{+}^q{C}_3{+}^r{C}_3$

4. none of these

Q.

P can paint a wall in 32 days and Q can do the same job in 24 days. With the help of R, they did the same job in 8 days only. Then, R alone can do the job in:

1. 92/5 days

2. 94/5 days

3. 96/5 days

4. None of these

5. 20 days

Q. If m parallel lines in a plane are intersected by a family of n parallel lines, calculate the number of parallelograms formed.

1. mn
2. 
3. [mn (m-1)(n-1)]
4. 
5. [mn (m+1)(n+1)]

Q.

In an equilateral triangle if $a,bandc$ denote the lengths of the perpendicular from $A,BandC$ respectively on the opposite sides, then

1. $a>b>c$

2. $a>b<c$

3. $a<b<c$

4. $a=b=c$

Q.

If the lines l${}_1$ and l${}_2$ are parallel then find the value of `x'.

1. 20

2. 25

3. 35

4. 65