Saved Bookmarks
This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Let `f(x)=f_(1)(x)-2f_(2)(x),` where `f_(1)(x)={{:(min{x^(2),|x|}",",|x|le1),(max{x^(2),|x|}",",|x|gt1):}` `"and "f_(2)(x)={{:(min {x^(2),|x|}",",|x|gt1),(max{x^(2),|x|}",",|x|le1):}` `"and let "g(x)={{:(min{f(t),-3letlex,-3lexlt0}),(max{f(t),0letltx,0lexle3}):}` The graph of `y=g(x)` in its domain is broken atA. 1 pointB. 2 pointsC. 3 pointsD. None of these |
| Answer» Correct Answer - A | |
| 2. |
Consider the function `f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):}` and`" "g(x)=sinx.` If `h_(1)(x)=f(|g(x)|)` `" and "h_(2)(x)=|f(g(x))|.` Which of the following is not true about `h_(1)(x)`?A. It is a periodic function with period `pi`B. The range is [0, 1]C. Domain RD. None of these |
| Answer» Correct Answer - D | |
| 3. |
Consider the function `f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):}` and`" "g(x)=sinx.` If `h_(1)(x)=f(|g(x)|)` `" and "h_(2)(x)=|f(g(x))|.` Which of the following is not true about `h_(2)(x)`?A. The domain is RB. It is periodic with period `2pi`C.D. The range is [0, 1] |
| Answer» Correct Answer - B | |
| 4. |
Let `f(x)=f_(1)(x)-2f_(2)(x),` where `f_(1)(x)={{:(min{x^(2),|x|}",",|x|le1),(max{x^(2),|x|}",",|x|gt1):}` `"and "f_(2)(x)={{:(min {x^(2),|x|}",",|x|gt1),(max{x^(2),|x|}",",|x|le1):}` `"and let "g(x)={{:(min{f(t),-3letlex,-3lexlt0}),(max{f(t),0letltx,0lexle3}):}` For `x in(-1,00),f(x)+g(x) `isA. `x^(2)-2x+1`B. `x^(2)+2x-1`C. `x^(2)+2x+1`D. `x^(2)-2x-1` |
| Answer» Correct Answer - b | |
| 5. |
Statement I The graph of `y=sec^(2)x` is symmetrical about the Y-axis. Statement II The graph of `y=tax` is symmetrical about the origin.A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement IB. Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement IC. Statement I is correct but Statement II is incorrectD. Statement II is correct but Statement I is incorrect |
| Answer» Correct Answer - A | |
| 6. |
Statement I The equation `|(x-2)+a|=4` can have four distinct real solutions for x if a belongs to the interval `(-oo, 4)`. Statemment II The number of point of intersection of the curve represent the solution of the equation.A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement IB. Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement IC. Statement I is correct but Statement II is incorrectD. Statement II is correct but Statement I is incorrect |
| Answer» Correct Answer - D | |
| 7. |
The number of real solutions of the equation `3^(-|x|)-2^(|x|)=0`, is |
| Answer» Correct Answer - c | |
| 8. |
The number of real solutions of the equation `1-x = [cosx]` isA. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 9. |
The number of solutions of `3^(|x|)=|2-|x||`, is |
| Answer» Correct Answer - B | |
| 10. |
The equation `e^x = m(m +1), m |
| Answer» Correct Answer - B | |
| 11. |
The total number of roots of the equation `| x-x^2-1|=|2x - 3-x^2|` is |
| Answer» Correct Answer - C | |
| 12. |
The number of roots of the equation `1+3^(x/2)=2^x` is |
| Answer» Correct Answer - B | |
| 13. |
The equation `x^2 - 2 = [sin x], where [.]` denotes the greatest integer function, hasA. infinity many rootsB. exactly one integer rootC. exactly one irrational rootD. exactly two roots |
| Answer» Correct Answer - B::C::D | |
| 14. |
Let f(x) be defined on [-2,2] and is given by `f(x)={{:(,-1,-2 le x le 0),(,x-1,0 lt x le 2):}` and g(x)`=f(|x|)+|f(x)|`. Then g(x) is equal toA. `-x, -2lex le0`B. `x, -2lexle0`C. `0,0 ltxle1`D. `2(x-1),1ltxle2` |
| Answer» Correct Answer - A::C::D | |
| 15. |
Consider the function `f(x)={{:(x-[x]-(1)/(2),x !in),(0, "x inI):}` where [.] denotes the fractional integral function and I is the set of integers. Then find `g(x)max.[x^(2),f(x),|x|},-2lexle2.`A. `x^(2),-2le x le-1`B. `1-x, -1 lt x le-(1)/(4)`C. `(1)/(2)+x, -(1)/(4)lt x lt0`D. `1+x, 0 le x lt1` |
| Answer» Correct Answer - A::B::C::D | |
| 16. |
Choice for the correct combination of elements from Column I and Column II are given as option (a), (b), (c), (d) out of which are correct. A. `{:(A,B,C,D),(p,q,r,s):}`B. `{:(A,B,C,D),(q,s,p,s):}`C. `{:(A,B,C,D),(q,p,s,r):}`D. `{:(A,B,C,D),(s,p,q,r):}` |
| Answer» Correct Answer - B | |