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The total number of infections (one-one ...

The total number of infections (one-one into mappings) from `{a_1,a_2,a_3,a_4}` to`{b_1,b_2,b_3,b_4,b_5,b_6,b_7}` is

A

400

B

420

C

800

D

840

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The total number of injections (one -one into mappings ) from { a_(1),a_(2),a_(3) ,a_(4)}"to"{b_(1),b_(2),b_(3),b_(4),b_(5),b_(6),b_(7)} is -

If x_i=a_i b_i c_i,i=1,2,3 are three-digit positive integer such that each x_1 is a multiple of 19, then for some integers n , prove that |[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]| is divisible by 19.

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

Let vec a=a_1 hat i+a_2 hat j+a_3 hat k , vec b=b_1 hat i+b_2 hat j+b_3 hat k and vec c=c_1 hat i+c_2 hat j+c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a and vec b . If the angle between a and b is pi/6, then prove that |[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]|^2=1/4(a_1 ^2+a_2 ^2+a_3 ^2)(b_1 ^2+b_2 ^2+b_3 ^2)

Suppose a_1, a_2, are real numbers, with a_1!=0. If a_1, a_2,a_3, are in A.P., then (a) A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)] is singular (where i=sqrt(-1) ) (b)The system of equations a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9z=0 has infinite number of solutions. (c) B=[(a_1,i a_2),(ia_2,a_1)] is non-singular (d)none of these

A function is defined as f:{a_1,a_2,a_3,a_4,a_5,a_6}rarr{b_1,b_2,b_3} then number of functions in which f(a_i)neb_i is divisible by

If A={1,2,3,4}, B={2,3,4,5},C={1,3,4,5,6,7}. Find A-B

Which of the following is a mapping from A to B where A={1,2,3} and B={2,3,4}?

Consider the determinant Delta = |[a_1+b_1x^2,a_1x^2+b_1,c_1],[a_2+b_2x^2,a_2x^2+b_2,c_2],[a_3+b_3x^2,a_3x^2+b_3,c_3]| = 0 , \ w h e r e \ a_i ,b_i , c_i in R \ (i = 1,2,3) \ a n d \ x in R . Statement 1: The value of x satisfying Delta=0 are x=1,-1. Statement 2: If |[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|=0,t h e n \ Delta=0.

Let A={1,2,3,4,5}, B={4,5,6,7}. Find A-B.

PATHFINDER-FUNCTION-QUESTION BANK
  1. Let f:NrarrR be such that f(1)=1and f(1)+2f(2)+3f(3)+......+nf(n)=n(n+...

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  2. For the functionf(x)=[1/[[x]]] , where [x] denotes the greatest intege...

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  3. Letf :(-pi/2,pi/2)rarrR be given by f(x)=(log)(secx+tan x))^3 Then

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  4. If a in R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] deno...

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  5. Let R be the set of all real numbers f:RrarrR be given by f(x)=3x^2+1....

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  6. The function f(x)=x^2+bx+c, where b and c real constants , describes

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  7. The range of the function y=(pi^2/16+x^2) is ?

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  8. Letf(x)=2^100x+1,g(x)=3^100x+1 Then the set of real numbers x such tha...

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  9. Which of the following real valued functions is/are not even functions...

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  10. Letf:RrarrR be such that f is injective and f(x) f(y)=f(x+y) for all x...

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  11. The function f[0,3]rarr[1,29], defined by f(x)=2x^3-15x^2+36x+1,is

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  12. Let f(x)=ax^2+bx+c,g(x)=px^2+qx+r such that f(1)=g(1),f(2)=g(2)and f(3...

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  13. The total number of infections (one-one into mappings) from {a1,a2,a3,...

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  14. Let R be the set of real numbers and the functionsf:RrarrR and g:Rrarr...

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  15. Letf(x)=x^2 and g(x)=sinx for all xIR then the set of all x satisfying...

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  16. Letf:(0,1)rarrR be defined by f(x)=b-x/1-bx , where b is a constant su...

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  17. The domain of the function f(x)=sin^-1((8(3)^(x-2))/(1-3^(2(x-1)))) is

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  18. The domain of the function f(x)=1/sqrt(|x|-x) is

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  19. The even function of the following is

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  20. Iff(x+2y,x-2y)=xy, then f(x,y)is equal to

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