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Using RSA key crypto system with a = 1, b = 2 etc; value for encryption if prime value are p = 7 and q = 11, the legal value for secret key is .

a)69

b)49

c)49

d)119
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both c and b options are 49?
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i think 49 will be the answer

three condition should be follow to choose key

(1) n=p*q=7*11

n=77

(2) Euler  Totient  function $\phi(n)=(p-1)(q-1)${if p and q are prime numbers}

$\phi(n) =6*10=60$

(3) now choose e such that 1<e<$\phi(n)$ and e and $\phi(n)$ should be coprime

means GCD(e,$\phi(n)$)=1

by seeing option only 49 is satisfying the condition because 49 is less than 60 and also GCD(49,60)=1

then (e,n) will be used as public key which will be used to encrypt the message .

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Prateek but u calculated e?

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Yeah you are right ,I think question is about e otherwise i don't know what is mean by secret key
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question is about to find d,not secret key but five legal values.for d

i think ans will be 49