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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.
| 10601. |
4/(1!) +16/(3!)+(64)/(5!) + ......= |
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Answer» `E +1/e` |
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| 10602. |
For which of the following graphs the quadratic expression y=ax^(2)+bx+c the product abc is negative ? |
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| 10603. |
A hollow cone with base radius a cm and height b cm is placed on a table . Show that the volume of the largest cylinder that can be hidden underneath is (4)/(9) times volume of the cone . |
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| 10604. |
Find local minimum value of the function f given by f(x)=3+|x|, x in R. |
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| 10605. |
Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))|= 0. Then the number of elements in S is |
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Answer» INFINITELY many |
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| 10606. |
The solution set of inequation |x^(2)-2x|+|x-4|gt|x^(2)-3x+4| is a subset of |
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Answer» `(0, OO)` `|x^(2)-2x|+|4-x|gt|x^(2)-3x+4|` `IMPLIES (x^(2)-2x)(4-x|gt|x^(2)-3x+4|` `implies (x^(2)-2x)(4-x)cancelge 0` `implies (x^(2)-2x)(4-x)lt 0 implies x EPSILON (0, 2)uu(4, oo)` |
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| 10607. |
Evalute the following integrals int (x+ sqrt(x^(2) + 1))^(n)dx |
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| 10608. |
Write the following function in the simplest form : tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2))),agt0,(-1)/(sqrt(3))ltxlta/(sqrt(3)) |
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| 10609. |
If costheta=(-1)/(2)and0^(@)ltthetalt360^(@), then the values of theta are |
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Answer» `120^(@)and300^(@)` |
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| 10610. |
If y = sec^(-1) (sqrt(x+1)/(sqrt(x-1)))+ sin^(-1)(sqrt(x-1)/(sqrt(x+1))) then (dy)/(dx)= |
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Answer» a) `0` |
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| 10611. |
If |overset(to)(a) + overset(to)(b)| =| overset(to)(a) - overset(to)(b) |, prove that overset(to)(a) and overset(to)(b) are perpendicular |
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| 10612. |
Determine the differentials in each of the following cases. z = cos 2t - 2 cot t |
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Answer» Solution :`Z= cos 2T - 2 cot t` `dz = (- 2 sin 2t + 2 cosec^2 t) dt` |
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| 10613. |
If (x)=sqrt(x^2-2x+1),x in [0,2]then at x=1f'(x)=__________ |
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Answer» F'(x)=1 for all x |
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| 10614. |
Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each of the folowing BA |
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Answer» SOLUTION :`BA= [[1,3],[-2,5]], [[2,4],[3,2]]= [[1xx2+3xx3, 1xx4+3xx2],[-2xx2+5xx3, -2xx4+5xx2]]` = [[2+9, 4+6],[-4+15, -8+10]]=[[11,10],[11,2]]` |
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| 10615. |
If x+y le 2, x ge 0, y le 0 the point at which maximum value of 3x+2y attained will be |
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Answer» (0, 2) |
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| 10617. |
Find the vector and the Cartesian equations of the line through thepoint (5, 2,4)and which is parallel to the vector 3 hat i+2 hat j-8 hat k. |
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Answer» `barr=3hati+2hatj-8hatk+lambda(5hati+2hatj+4hatk),` |
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| 10619. |
A fair die is rolled. If 1 or 2 turns up bag A is picked, if 3 turns up bag B is picked, if 4 or5 or 6 turns up bag C is picked. A die is rolled, a bag is picked and a ball is drawn. What is the probability that the ball drawn is red given bag A contains 4 red and 5 white balls, bag B contains 3 red and 2 white balls and bag C contains 3 red and 4 white balls? If the ball drawn found to be red then find the probability that 3 turned up on the die? |
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| 10620. |
If Lim_(xto oo) (pcosx+xe^((1)/(x)))/(1+sinx+qcosx*e^((1)/(x)))=0, then which of the following is are incorrect about p,q ? |
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Answer» `p=0,qinR` `rArrp=0,q in R-{0}` |
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| 10621. |
Two events A and B will be independent if |
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Answer» <P>A and B are MUTUALLY exclusive |
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| 10622. |
(dy)/(dx) + 2 y tan x = sin x, y = 0 when x = (pi)/(3). |
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| 10623. |
Evalute the following integrals int (" cos x")/(sqrt(3 sin^(2) x - 4 sin x + 5))dx |
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| 10624. |
Approximately what was the ratio of trucks to passenger cars? |
| Answer» Answer :D | |
| 10625. |
If (dx)/(sin^(4)x+cos^(4)x)=(1)/(sqrt(2))tan^(-1)f(x)+C |
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Answer» F(X) = tan x - cot x |
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| 10626. |
Find approximate values of the following : 2^(3.02) |
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Answer» SOLUTION :LET `y = 2^x` Then `dy = 2^x IOG 2 dx` `rArr deltay = 2^x Iog 2 deltax` `2^(x+deltax) - 2^x = 2^x` Iog `2 deltax` `rArr 2^(x+deltax) = 2^x + 2^x` Iog `2 deltax` Then `2^(3.02) = 2^3 + 2^3` Iog 2 x 0.02 = 8 + 8 x0.3010 x 0.02 = 8+0.04816=8.04816` |
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| 10627. |
sech^(-1)(sintheta) is equal to |
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Answer» `LOG TAN . THETA/2 ` |
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| 10628. |
If 2 lt x lt 3then int(| x - 1 | + |x - 2| + |x -3| ) dx = |
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Answer» `- (X^(2))/(2) + C ` |
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| 10629. |
Find the Coefficient of x^(10) in (1+2x)/((1-2x)^(2)) |
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| 10630. |
Sum of four digit numbers formed with 2,3,4,5 using each digit any number of times is |
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Answer» `4xx1111xx64` |
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| 10631. |
A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan^(-1)(0.5). Water is poured into it at a constant rate of 5 cubic meter per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4 m. |
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| 10632. |
Solve x(dy)/(dx) + y+ xy cot x = 0 (x ne 0) |
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| 10633. |
Find the sum of C_1 + 2C_2 + 3C_3 + .... + nC_n |
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Answer» SOLUTION :`C_1 + 2C_2 + 3C_3 + .... + nC_n` = `sum_(k=1)^N kC_k` = `sum_(k=1)^n k.^nC_k` = `sum_(k=1)^n n("^(n-1)C_(k-1))` `nsum_(k=1)^n "^(n-1)C_(k-1) = `n("^(n-1)C_0 + ^(n-1)C_1 + .... + ^(n-1)C_(n-1))` `n.2^(n-1)` |
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| 10634. |
A: The transformed equation of x^(2) - y^(2) + 2x + 4y=0 when the origin is shifted to the point (-1,2) is X^(2) - Y^(2) +3=0. R: If x,y terms are elimianted form ax^(2) + 2hxy +by^(2) + 2gx + 2fy +c=0 by shifting the origin to (alpha, beta) then the transformed equation is ax^(2)+ 2hxy + by^(2) + galpha + f beta + c=0 |
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Answer» Both A and R are TRUE and R is the CORRECT explanation of A. |
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| 10635. |
Point A(3,2,4) B((33)/(5),(28)/(5),(38)/(5)), and (9,8,10) are given. The ratio in which B divided overline(AC) is |
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Answer» `5:3` |
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| 10636. |
(i) An urn contains 7 red and 3 black balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is red if it is know that the first ball drawn is red. (ii) A box contains 8 red and 10 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is green if it is know that the first ball drawn is red. |
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| 10637. |
On using row operation R_(1)rArrR_(1)-3R_(2) in the following matrix equation [{:(4,2),(3,3):}]=[{:(1,2),(0,3):}][{:(2,0),(1,1):}] we have |
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Answer» `[{:(-5,-7),(3,3):}]=[{:(1,-7),(0,3):}][{:(2,0),(1,1):}]` USING elementary row operation `R_(1)rArr-3R_(2)`. `[{:(-5,-7),(3,3):}]=[{:(1,-7),(0,3):}][{:(2,0),(1,1):}]` Since on using elementary row operation on `x=AB, we apply these operation SIMULTANEOUSLY on x and on the first matrix A of the PRODUCT AB on RHS. |
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| 10638. |
If a = costheta + i sin theta, b = cos 2theta - i sin 2theta, c = cos 3theta + i sin3thetaandif |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}| = 0then |
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Answer» `theta=2 k pi, k in Z` `=-(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)` `=(1)/(2) (a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]=0` `rArr a+b+c=0"or" a=b=c ` `" if" a+b+c =0 , ` we have `costheta + cos 2theta + cos 3theta =0` and `sintheta-sin 2theta + sin 3theta = 0` or`cos 2 theta (2 cos theta + 1)=0` and`sin 2 theta (1 -2 cos theta ) =0 .............(1)` which is notpossibleas `cos 2 theta = 0`given`sin 2 theta ne 0, cos theta ne 1/2` and`cos theta = 1/2` gives `sin 2 theta ne 0, cos thetane 1/2` . Therefore , Eq. `(1)` does nothold SIMULTANEOUSLY .Therefore , `a+b+c ne 0` `rArr a=b=c` `:. e^(itheta)=e^(-2itheta) =e^(3itheta)` whichis satisfied only byby `e^(i theta) =1`, i.e., `cos theta =1, sin theta =0` so `theta = 2k pi , k in Z` |
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| 10639. |
Which of the following is not always true? |
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Answer» `|VEC(a) + vec(b)|^(2) = |vec(a)|^(2) + |vec(b)|^(2) " if " vec(a) and vec(b)` are perpendicular to each other |
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| 10640. |
If the tangent drawn to the parabola y^(2) = 4x at (t^(2) , 2t)is the normal to the ellipse 4 x^(2) + 5y^(2) = 20 at ( sqrt (5) cos theta , 2 sin theta ), then |
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Answer» `5t^(4) + 4t^(2) = 1` |
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| 10641. |
Find the equation of plane with intercept 2,3 and 4 on x,y and z axis respectively. |
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| 10642. |
Find the area of the region bounded by y= cos x and the x-axis in the interval [0, 2pi] |
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| 10643. |
Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation (dV(t))/(dt) = - k (T - t), where hat(k) gt 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(t) of the equipment is |
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Answer» `L - (k (T -t)^(2))/(2)` |
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| 10644. |
Find the points of local extrema for the function f(x) = cos4x defined on [0,pi/2] |
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| 10645. |
The unit vector normal to the plane x + 2y + 3z - 6 = 0 is (1)/(sqrt(14))bari+(2)/(sqrt(14))barj+(3)/(sqrt(14))bark. |
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| 10646. |
Find the area of the triangle with vertices A(1,1,2), B(2,3,5) and C(1,5,5). |
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| 10648. |
Find the probability of getting. (i) two tails and one head when 3 coins are tossed. (ii) 2 heads when 4coins are tossed (iii) atleast one head when 5 coins are tossed (iv) a head an odd number of times a fair coin is tossed 200 times. |
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| 10649. |
Find the value of sin^(-1)sin((2pi)/3) |
| Answer» SOLUTION :`SIN^(-1) sin ((2PI)/3) = sin^(-1) sin(pi-pi/3) = sin^(-1) sin(pi/3) = pi/3` | |
| 10650. |
An unbiased die with faces 1, 2, 3, 4, 5, 6 is thrown n times and the list of 'n' numbers showing up is noted. What is the probability that among the numbers 1, 2, 3, 4, 5, 6 exactly two numbers appear in this list. |
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