InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If `x^((log_2 x)^(2)-6 log_2 x+11)=64` then x is equal toA. 2B. 4C. 6D. 8 |
| Answer» Correct Answer - A::B::D | |
| 2. |
The expression `log_2 5-sum_(k=1)^4 log_2(sin((kpi)/5))` reduces to `p/q,` where p and q are co-prime, the value of `p^2+q^2` isA. 13B. 17C. 26D. 29 |
| Answer» Correct Answer - B | |
| 3. |
Consider the quadratic equation `(log_10 8)x^2-(log_10 5)x=2(log_2 10)^-1 -x.` Which of the following quantities are irrational.A. sum of rootsB. product of rootsC. sum of coefficientsD. discriminant |
| Answer» Correct Answer - A::B | |
| 4. |
The value of `a^x-b^y` is (where`x=sqrt(log_ab)`and `y=sqrt(log_ba),agt0,bgt0` and `a,bne1`)A. 1B. 2C. 0D. -1 |
| Answer» Correct Answer - C | |
| 5. |
The value of x satisfying the inequation `x^(1/(log10^x)).log_10xlt1` , isA. `0ltxlt10`B. `0ltxlt10^10`C. `0ltxlt10^(1//10)`D. None of these |
| Answer» Correct Answer - C | |
| 6. |
The value of `a^((log_b(log_bx))/(log_b a)),` isA. `log_aN`B. `log_bN`C. `log_Na`D. `log_Nb` |
| Answer» Correct Answer - B | |
| 7. |
`log_2log_2(sqrt(sqrt(...sqrtsqrt2)))/(nTimes)` is equal to |
| Answer» Correct Answer - D | |
| 8. |
If x =`log_3(5)` and y =`log_17( 25)`, which one of the following is correct?A. `altb`B. a=bC. `agtb`D. None of these |
| Answer» Correct Answer - C | |
| 9. |
Suppose `U` denotes the number of digits in the number` (60)^(100)` and`M` denotes the number of cyphers after decimal, before a significant figure comes in `(8)^(-296)`. If the fraction U/M is expressed as rational number in the lowest term as `p//q` (given `log_(10)2=0.301` and `log_(10)3=0.477`) .The equation whose roots are p and q, isA. `x^2-3x+2=0`B. `x^2-5x+6=0`C. `x^2-7x+12=0`D. `x^2-9x+20=0` |
| Answer» Correct Answer - B | |
| 10. |
Suppose `U` denotes the number of digits in the number` (60)^(100)` and`M` denotes the number of cyphers after decimal, before a significant figure comes in `(8)^(-296)`. If the fraction U/M is expressed as rational number in the lowest term as `p//q` (given `log_(10)2=0.301` and `log_(10)3=0.477`) . The value of q isA. 5B. 2C. 3D. 4 |
| Answer» Correct Answer - C | |
| 11. |
Suppose `U` denotes the number of digits in the number` (60)^(100)` and`M` denotes the number of cyphers after decimal, before a significant figure comes in `(8)^(-296)`. If the fraction U/M is expressed as rational number in the lowest term as `p//q` (given `log_(10)2=0.301` and `log_(10)3=0.477`) . The value of p isA. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 12. |
Given ,log2=0.301 and log3=0.477, then the number of digits before decimal in `3^12times2^8`isA. 7B. 8C. 9D. 11 |
| Answer» Correct Answer - C | |
| 13. |
If `x=log_5(1000)` and `y=log_7(2058)`,thenA. `xgty`B. `xlty`C. `x=y`D. None of these |
| Answer» Correct Answer - A | |
| 14. |
The lengths of the sides of a traingle are `log_(10)12,log_(10)75andlog_(10)n`, where `n in N`. If a and b are the least ad greatest values of n respectively. The value of b-a is divisible byA. 221B. 222C. 223D. 224 |
| Answer» Correct Answer - C | |
| 15. |
If `log_(3)27.log_x7=log_(27)x.log_(7)3`, the least value of x isA. `7^-3`B. `3^-7`C. `7^3`D. `3^7` |
| Answer» Correct Answer - A | |
| 16. |
If `3^x=4^(x-1)`, then x equalsA. `(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)` |
| Answer» Correct Answer - A::B::C | |
| 17. |
The value of `log_(10)3` lies in the intervalA. `(2/5,1/2)`B. `(0,1/2)`C. `(0,2/5)`D. None of these |
| Answer» Correct Answer - A | |
| 18. |
If `|a| |
| Answer» Correct Answer - C::D | |
| 19. |
If `log_(10)5=a` and `log_(10)3=b`,thenA. `log_(10)8=3(1-a)`B. `log_(40)15=((a+b))/((3-2a))`C. `log_(243)32=((1-a)/b)`D. All of these |
| Answer» Correct Answer - A::B::C::D | |
| 20. |
The least value of n in order that the sum of first n terms of the infinite series `1+3/4+(3/4)^2+(3/4)^3+...`, should differ from the sum of the series by less than `10^-6`, is `(given log2=0.30103,log3=0.47712)`A. 14B. 27C. 53D. 57 |
| Answer» Correct Answer - C | |
| 21. |
There exists a positive number k such that ` log_2x+ log_4x+ log_8x= log_kx`, for all positive real no x. If k=`a^(1/b)` where (a,b) `epsilon` N, the smallest possible value of (a+b)=(C) 12 A) 75 (B) 65 (D) 63_A. 12B. 63C. 65D. 75 |
| Answer» Correct Answer - D | |
| 22. |
If `log_(10)2=0.3010...,` the number of digits in the number `2000^(2000)` isA. 6601B. 6602C. 6603D. 6604 |
| Answer» Correct Answer - C | |
| 23. |
The value of `(0.16)^("log"_(2.5)((1)/(3) + (1)/(3^(2)) + (1)/(3^(3)) + …."to" oo))`, isA. 2B. 4C. 6D. 8 |
| Answer» Correct Answer - B | |
| 24. |
The value of `log_((8-3sqrt7))(8+3sqrt7)` isA. -2B. -1C. 0D. Not defined |
| Answer» Correct Answer - B | |
| 25. |
Find the value of `(log)_(2sqrt(3))1728.`A. 6B. 8C. 3D. 5 |
| Answer» Correct Answer - A | |
| 26. |
Statement-1(Assertion and Statement -2 (reason) Each of these examples also has four alternative choices, only one of which is the correct answer. You have select the correct choice as given below. Statement-1 If p,q`in`N satisfy the equation `x^sqrtx=(sqrtx)^x ` and `qgtp`, then q is a perfect number . ,ltbgt If a number is equal to the sum of its factor, then number is known as perfect number.A. Statement -1 if true, Statement-2 is true, Statement-2 is a correct explanation for Statement -2B. Statement -1 if true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -2C. Statement -1 if true, Statement-2 is falseD. Statement -1 if false , Statement-2 is true |
| Answer» Correct Answer - D | |
| 27. |
Statement-1(Assertion and Statement -2 (reason) Each of these examples also has four alternative choices, only one of which is the correct answer. You have select the correct choice as given below. Statement -1 If `N=(1/0.4)^20`, then N contains 7 digit before decimal. Statement -2 Characteristic of the logarithm of N to the base 10 is 7.A. Statement -1 if true, Statement-2 is true, Statement-2 is a correct explanation for Statement -1B. Statement -1 if true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -1C. Statement -1 if true, Statement-2 is falseD. Statement -1 if false , Statement-2 is true |
| Answer» Correct Answer - D | |
| 28. |
IF `10^(log_p{log_q(log_rx)})`=1 and `log _q{log_r(log_px)}=0`. The value of q isA. `r^(p//r)`B. `plog_pr`C. `rlog_rp`D. `r^(r//p)` |
| Answer» Correct Answer - C | |
| 29. |
IF `10^(logp{logq(logr^x)})`=1 and `log _q{log_r(log_px)}=0`. The value of x isA. `q^r`B. `r^q`C. `r^p`D. rq |
| Answer» Correct Answer - B | |