### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

### Math Assignment Class X Ch-7 | Coordinate Geometry

Math Assignment, Class X,

Chapter 7 Coordinate Geometry

Extra questions of chapter 7 class 10 Coordinate Geometry with answer and  hints to the difficult questions. Important and useful math assignment for the students of class 10

For better results

• Students should learn all the basic points of  Coordinate Geometry
• Student should revise N C E R T book thoroughly with examples.
• Now revise this assignment. This assignment integrate the knowledge of the students.

# ASSIGNMENT FOR 10 STANDARDCOORDINATE GEOMETRY

Question 1
Find the distance between the following points:-
a) (-6,7) and (-1,-5) Ans [13]

b) (a,0) & (0,b) Ans [$\sqrt{a^{2}+b^{2}}$]

c) ($\sqrt{3}$+1,1) & (0,$\sqrt{3}$) Ans [$\sqrt{8}$]

d) (a + b, a - b) & (a - b, a + b) Ans [$2\sqrt{2}$b]

Question 2
Find the distance of the following points from the origin:-

a) (5, -12)     Ans [13]

b) (-5, 5)       Ans [5$\sqrt{2}$ ]

c) (-4, -6)     Ans [2$\sqrt{13}$]

Question 3
Find the value of k for which the following points are collinear:
(a) (3,2), (4, k), (5,3)           Ans [5/2]
b) (3,5), (m, 6), (1/2, 15/2)  Ans [2]
c) (2,5), (k,11/2), (4,6)        Ans [3]

Question 4
Find the ratio in which the point P(b, 1) divides the join of A(7, -2) and B(-5, 6). Also find b
Ans [3:5, b = 5/2,]

Question 5
Find the ratio in which the point P(a, -2) divides the join of A(-4, 3), & B(2, -4). Also find a.
Ans [5 : 2, a = 2/7]

Question 6
The coordinates of the mid- point of the line joining the points (2p + 2, 3) & (4, 2q + 1) is (2p, 3q). Find the value of p & q.
Ans [3, 1]

Question 7
If A (6,-1), B(1,3), C (k,8) are such that AB = BC. Then find the value of k
Ans [k = 5, -3]

Question 8
Find the coordinates of the point equidistant from the A(5, 8), B(5, -5),and C (1, -5) [3, 3/2]

Question 9

Find the type of quadrilateral formed by:-
a) A(2, -2), B(14, 10), C(11, 13), D(-1, 1)     Ans [Rectangle]
b) A(0,-2), B(3,1), C(0,4), D(-3,1)                Ans [Square]
c) A(-3,5), B(3,1), C(0,3), D(-1,-4)               Ans [No]
d) A(4,5), B(7,6), C(4,3), D(1,2)                  Ans [Parallelogram]
e) A(3,0), B(4,5), C(-1,4), D(-2,-1)              Ans [Rhombus]

Question 10
Find the area of the quadrilateral formed in question 9.

Question 11
Find p if A(6,1), B(8,2), C(9,4), D(p,3) are the vertices of a parallelogram
Ans [p = 7]

Question 12
The mid- point of the line segment joining (2a+4) & (-2,3b) is (1,2a+1). Find the value of a & b.
Ans [a = b = 2]

Question 13
In what ratio the line segment joining the points A(-2,-3) & (3,7) is divided by the y-axis. Also find the coordinates of the point of division.
Ans [2 : 3, point of division (0,1)]

Question 14
If A(5,-1), B(-3,-2), C(-1,8)are the vertices of triangle ABC. Find the length of the median through A and the centroid of the triangle .
Ans [$\sqrt{65}$] , (1/3, 5/3)

Question 15
In what ratio does the line x-y-2 = 0 divides the line segment joining (3,-1)& (8,9) If the points A(x, y), B(-5, 7) and C(-4, 5) are collinear then show that 2x + y + 3 = 0
Ans [2 : 3]

Question 16
Prove that the points A(0,0), B(5,5), C(-5,5)are the vertices of a right isosceles triangle.

Question 17
Find the value of p for which A(-5,1), B(1,p), C(4,-2) are collinear
Ans [p = -1]

Question 18

Find the centroid of the following points:-

a) A(4,7), B(2,1), C(3,6) Ans [3, 14/3]
b) A(2,3), B(4,5), C(3,4) Ans [3,4]

Question 19
Coordinates of the mid points of sides of a triangle are A(1,1), B(2,-3), C(3,4). Find the centroid of the triangle ABC.
Ans [2,2/3]

Question 20
If A(2,1), B(3,4), C(0,1) are three consecutive vertices of parallelogram. Find the 4th vertex.
Ans [-1,-2]

Question 21
If the coordinates of the mid –points of the sides of a triangle are (1,1), (2,-3), and (3,4).Find the coordinates of the centroid of the triangle.
Ans 2, 2/3

Question 22
Find the length of the median of a triangle whose vertices are A(-1, 3), B(1, -1), C(5, 1)
Ans [5, $\sqrt{10}$ , 5]

Question 23
Find the ratio in which the line segment joining the points (-10,2), & (3,-5) is divided by y-axis
Ans [10:3]

Question 24
If A(1,k), B(4,-3), C(-9,7)are the vertices of triangle and its area is 15 sq. Unit. Find k
Ans [-3,21/13]

Question 25
The opposite vertices of a square are (-1, 2), (3, 2). Find the coordinates of other two vertices.
Ans [(1,4),(1,0)]

Question 26
If the line joining the points (2, 1) & (5, -8) is trisected by the points P & Q. If point P lie on the line 2x - y + k = 0 Find k.
Ans [k = -8]

Question 27
Find the reflection (image) of the point (7,-5) in the point (-3,1)
Ans [-13,7] [Hint:- point (-3,1) is the mid -point of the point given point and the reflection]

Question 28
Find the ratio in which the point (-3,k)divides the line segment joining the points (-5,-4) & (-2,3). Hence find the value of k
Ans [2:1, k = 2/3]

Question 29
If (-2,2), (x,8) & (6,y) are three concyclic points whose centre is (2,5). Find x and y.
Ans [x = 6,-2, y = 8, 2]

Question 30
Find the value of k if P(2,4) is equidistant from the points A(5, k) & B(k,7)
Ans [k = 3]

Question 31
Show that the point p(-4, 2) lies on the line segment joining the points A(-4,6) & B(-4,-6)

Question 32
The points A(2, 9), B(a, 5), C(5, 5)are the vertices of a right angled triangle at B. Find a and the area of triangle ABC
Ans [a = 2, Area = 6cm2

Question 33
Find the centre of the circle passing through the points (6, -6), (3, -7) & (3, 3)

Question 34
Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.

Question 35
Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear.
Ans [4x - 5y = 3]

Question 36
Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2).
Ans [(0,-2)]

Question 37
The centre of the circle is (2a-1,7) and is passes through the points (-3,-1). If the diameter of the circle is 20cm. Find the value of a.
Ans [a = -4,2]

Question 38
The mid point of the sides of a triangle are (5,4),(4,6) and (5,7).Find the coordinates of the vertices of the triangle
Ans [(4, 3), (6, 5), (4, 9)]

Question 39
In what ratio the line segment joining the points (-2,-3) & (3,7) divided by the y-axis. Also find the coordinates of the point of division.
Ans [2:3, (0,1)]

Question 40
Find the coordinates of the point equidistant from the points A(-2,-3), B(-1,0), C(7,-6)
Ans [3,-3]

Question 41
Two vertices of a triangle ABC are given by A(6,4) & B(-2,2) and its centroid is (3,4). Find the coordinates of the third vertex C of triangle ABC.
Ans [56]