Combination Based on Geometry

Q.

Out of $10$points in a plane $6$ are in a straight line. The number of triangles formed by joining these points are?

1. $100$

2. $150$

3. $120$

4. None of these

Q.

A (1, 2) and B(5, 5) are two points. Starting from A, line segments of unit length are drawn either rightwards or upwards only, in each step, until B is reached. Then, the number of ways of connecting A and B in this manner is

1. 45

2. 50

3. 40

4. 35

Q. Let there be 9 fixed points on the circumference of a circle . Each of these points is joined to every one of the remaining 8 points by a straight line and the points are so positioned on the circumference that atmost 2 straight lines meet in any interior point of the circle . The number of such interior intersection points is

1. 126
2. 351
3. 756
4. 526

Q. Question 8 (i)
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

Q. Prove that parallelograms are on the same base and between the same parallel lines are equal in area.

Q. Number of diagonals of a convex hexagon is

1. $6$
2. $3$
3. $12$
4. $9$

Q. Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1}-T_n=10$, then the value of N is

1. 10
2. 8
3. 7
4. 5

Q. Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided reqular polygon. If $T_{n+1}-T_n=10,$ then the value of $n$ is;

1. 10
2. 8
3. 7
4. 5

Q. A convex polygon has 44 diagonals, find the number of sides of his this polygon.

Q. If the area of the circle is $A_1$ and the area of the regular pentagon inscribed in the circle is $A_2$ then the ratio $A_1\mid A_2$ be $\frac{\pi }{k}\sec \left(\frac{\pi }{h}\right)$.Find $k\ast h$ ?

Q. A regular hexagon is inscribed in an equilateral triangle, as shown. If the hexagon has an area of $12$, find the area of this triangle.

Q. How many diagonals are there is a polygon having 12 sides ?

1. 12
2. 24
3. 36
4. 54

Q. Which of the following is true for Scalene right angled triangle?

1. Contains one right angle
2. Two other equal angles
3. No equal sides
4. None of these

Q.

Let $n\ge 2$ be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is ?___

Q. Let $a,b,c$ are the Arithmetic means between two numbers such that $a+b+c=15$ and $p,q,r$ be Harmonic mean between same numbers such that $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=\frac{5}{3}$ then the numbers are

1. $3,10$
2. $9,1$
3. $3,12$
4. $3,15$

Q. The angle of a sector in a given circle is $40$ degrees and the area of the sector is equal to $20c{m}^2$. Calculate the arc length of the sector.

1. $7.4$ cm
2. none of these
3. $5.3$ cm
4. $6.5$ cm

Q. Find the total Number of Parallelograms in the given figure ?

1. $2$
2. $3$
3. Can't be determined
4. $1$

Q. Points A, B, C, D are on a circle with centre P The names of any three radii and 'any three chords of the circle are

1. $3chordsarethesegments-AB,PAandPCand3radiiarethesegments-AB,PB\&AD.$
2. $3chordsarethesegments-AB,BCandADand3radiiarethesegments-PA,PB\&PC.$
3. $3chordsarethesegments-PB,BCandPCand3radiiarethesegments-PA,AB\&BC.$
4. $3chordsarethesegments-PA,PCandPDand3radiiarethesegments-AB,BC\&DC.$

Q. The straight line joining the mid-points of the opposite sides of a parallelogram divides it into two parallelograms of equal area.

1. True
2. False

Q. If in a tetrahedron, edges in each of the two pairs of opposite edges are perpendicular, then show that the edges in the third pair are also perpendicular.

Q. Find the maximum number of diagonals that can be drawn in n-sides polygon. Also, find number of diagonals if
i. n=12 sides
ii. n=15 sides
iii. decagon

Q. The number of diagonals that can be drawn in a polygon of 100 sides is:

1. 4850
2. 4950
3. 98
4. 9900

Q. The number of triangles are _____ less than the number of sides formed by the diagonals from one vertex.

1. 5
2. 2
3. 8
4. 3

Q. $\angle D<\angle B$
If the above statement is true then mention answer as 1, else mention 0 if false

Q. If $\frac{t}{4}=5$, then $t$ is equal to

1. $4$
2. $5$
3. $20$
4. None of these

Q.

A parallelogram is cut by two sets of m lines parallel to its sides. The number of parallelograms thus formed is

1. ${(}^m{C}_2{)}^2$

2. ${(}^{m+1}{C}_2{)}^2$

3. ${(}^{m+2}{C}_2{)}^2$

4. None of these