Related InterviewSolutions

• If `3^(x)=4^(x-1)`, then `x=`A. `(2log_(3)2)/(2log_(3)2-1)`B. `(2)/(2-log_(2)3)`C. `(1)/(1-log_(4)3)`D. `(2log_(2)3)/(2log_(2)3-1)`
• The value of `6+log_(3/2)(1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2).....))))` is
• Solve the following equations : `(i) log_(x)(4x-3)=2` `(ii) log_2)(x-1)+log_(2)(x-3)=3` `(iii) log_(2)(log_(8)(x^(2)-1))=0` `(iv) 4^(log_(2)x)-2x-3=0`
• Solve for `x` `(i) 2^(|x+1|)+2^(|x|)=6` and `x in I` `(ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2|` `(iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0`
• Let `alphaa n dbeta`be nonzero real numbers such that `2(cosbeta-cosalpha)+cosalphacosbeta=1`. Then which of the following is/are true?`sqrt(3)tan(alpha/2)+tan(beta/2)=0``sqrt(3)tan(alpha/2)-tan(beta/2)=0``t a n""(alpha/2)+sqrt(3)tan(beta/2)=0``t a n""(alpha/2)-sqrt(3)tan(beta/2)=0`A. `sqrt(3)tan((alpha)/(2))-tan((beta)/(2))=0`B. `tan((alpha)/(2))-sqrt(3)tan((beta)/(2))=0`C. `tan((alpha)/(2))+sqrt(3)tan((beta)/(2))=0`D. `sqrt(3)tan((alpha)/(2))+tan((beta)/(2))=0`
• Let `alpha,beta`, are two real solution of equation `(log_(10)x)^2 + log_(10)x^2 = (log_(10))^2 -1,` then` sqrt1/(alpha beta)`equal to`(i) 20 (ii) 3 (iii) 10 (iv) 1`A. `20`B. `3`C. `10`D. `1`
• If `log_(1/2) ((x^2+6x+9)/(2(x+1)) )< - log_2(x+1)` then complete set of values of x isA. `(-1,1+2sqrt(2))`B. `(1-2sqrt(2),2)`C. `(-1,oo)`D. `(1-2sqrt(2),1+2sqrt(2))`
• If `A = sin^2x + cos^4 x`, then for all real x :A. `(3)/(4) le A le 1`B. `(13)/(16) le A le 1`C. `1 le A le 2`D. `(3)/(4) le A le (13)/(16)`
• The solution set of the inequality `|9^x-3^(x+1) + 15| < 2.9^x - 3^x` isA. `(-oo,1)`B. `(1,oo)`C. `(-oo,1]`D. `[2,oo)`
• Solve the following rational in equalities `(i) ((x-1)(x+2))/((x-3)(x+3)) lt 0` `(ii) ((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))ge0` `(iii) ((x^(2)-3x+1)^(3))/((x-1)(x+2))le0` `(iv) (x(2^(x)-3^(x)))/((x^(2)+x+1)(x-1))gt0` `(v) ((x-1)(x-2)(x-3))/((x+1)(x+2)(x+3)) le1` `(vi) 1 lt (3x^(2)-7x+8)/(x^(2)+1) le2`