If the letters in the English alphabets A to M represent the number from 1 to 13 respectively and N represents 0 and the letters O to Z correspond from -1 to -12, find the sum of integers for the names given below. For example, Math `rarr` Sum `rarr` 13 + 1 - 6 + 8 = 16: YOUR NAME

If the letters in the English alphabets A to M represent the number from 1 to 13 respectively and N represents 0 and the letters O to Z correspond from -1 to -12, find the sum of integers for the names given below. For example, Math rarr Sum rarr 13 + 1 - 6 + 8 = 16: SUCCESS

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and the sum of the numbers on them is noted. Find the probability of gettting each sum from 2 to 9 separately.

The plane denoted by P_(1) : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane P_(2) : 5x+3y+ 10 z = 25 . If the plane in its new position is denoted by P , and the distance of this plane from the origin is d, then find the value of [k//2] (where [*] represents greatest integer less than or equal to k).

A pair of numbers is picked up randomly (without replacement) from the set {1,2,3,5,7,11,12,13,17,19}. The probability that the number 11 was picked given that the sum of the numbers was even is nearly a. 0. 1 b. 0. 125 c. 0. 24 d. 0. 18

If the points (1,1,p) and (-3,0,1) are equidistant from the plane vecr.(3hati+4hatj-12hatk)+13=0 , then find the value o p.

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin. a.2x+3y+4z-12=0 b.3y+4z-6=0 c. x+y+z=1 d. 5y+8=0

Two different numbers are taken from the set {0,1,2,3,4,5,6,7,8,9,10}dot The probability that their sum and positive difference are both multiple of 4 is x//55 , then x equals ____.

Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,x-u=1,y-v=0,z-w=0),(,x+u=0,y+v=1,z+w=0),(,2x+3u=0,2y+3v=0,2z+3w=1):} As this system of equations is inconsistent, we say there is no right inverse for matrix A. The number of right inverses for the matrix [(1,-1,2),(2,-1,1)] is

Column I, Column II Four dice (six faced) are rolled. The number of possible out comes in which at least one dice shows 2 is, p. 210 Let A be the set of 4-digit number a_1a_2a_3a_4w h e r ea_1> a_2> a_3> a_4dot then n(A) is equal to, q. 750 The total number of three-digit numbers, the sum of whose digits is even, is equal to, r. 671 The number of four-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contains digit 1 is, s. 450