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. |
find the percentage error in calculating the volume of the cubical box if an error of `1%` is made in measuring the length of the edges of the cube. |
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Answer» let the edge of cube is `x` volume `v= x^3` `(dv)/(dx) = 3x^2` `del x = dx` `(dx)/x xx 100 = 1` `=> dx = x/100` `dv = del v` `= (dv)/(dx) xx dx= 3x^2 xx x/100 = (3x^3)/100` `(dv)/v xx 100 = (3x^3)/(100 xx v) xx 100 ` `= (3x^3)/(100 xx x^3) xx 100` percentage change in v error=`3%` Answer |
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| 2. |
Let `f`be differentiable for all `x ,`If `f(1)=-2a n df^(prime)(x)geq2`for all `x in [1,6],`then find the range of values of `f(6)dot`A. `f(6)=5`B. `f(6)lt5`C. `f(6)lt5`D. `f(6)gt8` |
| Answer» Correct Answer - D | |
| 3. |
Let`(a_0)/(n+1)+(a_1)/n+(a_2)/(n-1)++(a_(n-1))/2+a_n=0.`Show that there exists at least real `x`between 0 and 1 such that `a_0x^n+a_1x^(n-1)+a_2x^(n-2)++a_n=0`A. at least one zeroB. at most one zeroC. only 3 zerosD. only 2 zeros |
| Answer» Correct Answer - A | |
| 4. |
The distance travelled by a particle upto tiem x is given by `f(x)=x^(3)-2x+1.` The time c at which at velocity of the particle is equal to its average velocity between times x=-1 and x=2 sec. isA. 15 secB. `sqrt((3)/(2))` secC. `sqrt(3)` secD. `sqrt((7)/(3))` sec |
| Answer» Correct Answer - C | |
| 5. |
If `2a+3b+6c=0,`then prove that at least one root of the equation `a x^2+b x+c=0`lies in the interval (0,1).A. (0,1)B. (1,2)C. (2,3)D. none of these |
| Answer» Correct Answer - A | |