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.
| 2301. |
Evaluate the following: int(1+x)e^xdx |
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Answer» SOLUTION :`INT(1+x)e^xdx` [Choolse 1+x as FIRST and `e^x` as SECOND FUNCTION] =`(1+x).e^x-int1.e^xdx` =`(1+x)e^x-e^x+C=xe^x+C` |
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| 2302. |
If the shortest distance from (2,-14) to the circle x^(2)+y^(2)+6x+4y-12=0 is d and the length of the tangent drawn from the same point to the circle is l then sqrt(d+1) = |
| Answer» Answer :B | |
| 2303. |
If A,B and C are the angles of a triangle such that cosA+cosB+cosC=0=sinA+sinB+sinC, then sin3A+sin3B+sin3C = |
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Answer» 1 |
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| 2304. |
If A and Bare two events such that 2P(A) = 3P(B), where 0 lt P(A) lt P(B) lt 1, thenwhich one of thefollowingis correct? |
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Answer» `P(A |B) lt P(B |A) lt P(A NNB)` `E={(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}` `therefore n(E)=6` Total number of events, n(S)=36 `therefore "PROBABILITY"=(n(E))/(n(S))=(6)/(36)=(1)/(6)` |
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| 2305. |
the sum of the first n terms of a sequence is an^(2) + bn. Then the sum of the next n terms is |
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Answer» `3an^(2) + 2^(BN)` |
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| 2306. |
If y = a cos (log x) + b sin (log x), show that x^(2) y_(2) + xy_(1) + y = 0. |
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| 2307. |
Obtain following definite integrals : overset(1)underset(0)int (x)/(sqrt(1+x^(2)))dx |
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| 2308. |
Let f:[-2,3] to [0,oo) b e a continuous function such that f(1-x)=f(x) for all x in [-2, 3]. If R_(1) is the numerical value of thearea of the region bounded by y=f(x), x = -2, x=3 and the axis of x and R_(2)=int_(-2)^(3)x f(x) dx, then: |
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Answer» `3R_(1)=2R_(2)` |
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| 2309. |
The sum of three numbers is 9 . If we multiply third number by3and add to thesecond number , we get 16 . By addinig the first and the third numbers and then subtracting twice the second number from this sum , we get 6 . Use these informations and find the system of linear equations. Hence, find the three numbers using matrices. |
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| 2310. |
Construct the graph of the function f(x)=-|(x^(2)-9)/(x+3)-x+(2)/(x-1)|and comment upon the following (a) (-oo,0) (b) uarrin (1, 5/3) and darr in (-oo,1)uu(5/3,oo)-{-3} (c) x=5/3 (a) Range of the function, (b) Intervals of monotonocity, (c) Point(s) where f is continuous but not differentiable, (d) Point(s) where f fails to be continuous and nature of discontinuity. (e) Gradient of the curve where f crosses the axis of y. |
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Answer» (d) removable discont.at `x=-3`(missing POINT ) and non removable discont. at`x=1` (infinite TYPE) (e) `-2` |
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| 2311. |
Find the conditionthat the lines x=py +q, z=ry +s and x=p'y +q', z= r'y+s' may be perpendicular to each other. |
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| 2312. |
Let f:N to Y be a function defined as f (x) =4x +3, where, Y = {y in N : y = 4x +3 for some x in N}. Show that f is invertible. Find the inverse. |
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| 2313. |
Integrate the following functions : int(x-1)/(sqrt(x+4))dx |
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| 2314. |
If ""^(n)P_(4):""^(n)P_(3)=2:1 then is |
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Answer» 5 |
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| 2315. |
Using differentials, find the approximate values of the following: (i) root(4)15(ii)(82)^(1//4) |
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| 2316. |
Find the numerically greatest term in the expansion of(3x-5y)^(17) when x = 3/4 , y = 2/7. |
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| 2317. |
Show that x^(2) + y^(2) -6x -9y +13 =0, x^(2) +y^(2) -2x -16y =0 touch each other . Find the point of contact and the equation of common tangent at their point of contact. |
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| 2318. |
The value of 1+sum_(k=0)^14{(cos)((2k+1)pi)/(15)+(isin)((2k+1)pi)/(15)} is |
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Answer» 0 |
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| 2319. |
Examine the consistency of the following system of equation 5x-y+4z=5 2x+3y+5z=2 5x -2y+6z =-1 |
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Answer» Solution :Here A =[[5,-1,4],[2,3,5],[5,-2,6]] ` A| = 51 != 0` `THEREFORE`The given SYSTEM is CONSISTENT. |
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| 2320. |
A vertical lamp-post, 6m high, stands at a distance of 2 m from a wall, 4 m high . A 1.5 m tall man starts to walk away from the wall on the other side of the wall,in line with the lamp-post the maximumdistance to which the man can walk remaining in the shadow is |
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Answer» `5/2`m |
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| 2321. |
The tangent at any point P on the ellipse meets the tangents at the vertices A & A^(1)of theellipse(x^(2))/(a^(2))+( y^(2))/(b^(2))=1 at L and M respectively. a b Then AL. A^(1)M = |
| Answer» Answer :B | |
| 2322. |
A dice is tossed twice. Find variance if random variable X denotes the numbers of odd integers obtain on it. |
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| 2323. |
Let |vec(x)|=|vec(y)|=|vec(x)+vec(y)|=1 and if measure of the angle between vec(x) and vec(y) is alpha, then cos alpha = ………… |
| Answer» Answer :A | |
| 2324. |
Let f(x) = x^(3) + 2x^(2) -x be a real valued function. Then, the value of Langrange's constant C in (-1, 2)is |
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Answer» `(-4 + sqrt76)/(3)` |
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| 2325. |
If log _(tan 30^(@)) ( (2 |z|^(2) + 2 |z| - 3)/(|z| + 1)) lt -2 , then |
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Answer» `|Z| lt 3//2` |
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| 2326. |
If1,3,4,0are therootsofax^4 +bx^3 +cx^2 +dx +e =0then therootsofa(x +3)^4 +b (x+3)^3 + c(x+3)^2 +d(x+3) + e=0are |
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Answer» `3,9,0,12` |
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| 2327. |
If int(dx)/((1+x^(2))sqrt(1-x^(2)))=F(x)andF(1)=0, then for x gt 0, f (x) is equal to |
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Answer» `(1)/(2)TAN^(-1)((sqrt(2x))/(sqrt(1+x^(2))))+(PI)/(sqrt(2))` |
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| 2328. |
Let the f : R to R be defined by f(x)=2x+cos x, then f ……………. |
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Answer» has a MINIMUM at `X = PI` |
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| 2329. |
intdx/(sqrt(9-25x^2) |
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Answer» `sin^(-1)((5X)/3)+c` |
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| 2330. |
Show that the locus of the point of intersection of the lines x cos alpha+ Y sin alpha = a , x sin alpha - y cos alpha = b (alphaisa para- meter) is a circle. |
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| 2331. |
If f(x) = .^(40)C_(1).x(1-x)^(39) + 2..^(40)C_(2)x^(2)(1-x)^(38)+3..^(40)C_(3)x^(3)(1-x)^(37)+"….."+40..^(40)C_(40)x^(40), then the value of f(3) is |
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Answer» 120 `T_(r)=r..^(40)C_(r).x^(r)(1-x)^(40-r)` `= 40x..^(39)C_(r-1).x^(r-1)(1-x)^(40-r)` `:. f(x)=40x(x+1-x)^(39)` `= 40x` |
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| 2332. |
If the quadratic equation x^(2) + 2 (k + 1) x + 9k - 5 = 0has exactly one positive root, then k lies in the set |
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Answer» `[5//9, INFTY)` |
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| 2333. |
Find the locus of the point whpse polars with respect to the circles x^(2) + y^(2) - 4 x - 4y - 8 = 0and x^(2) +y^(2) - 2x + 6y - 2 = 0 |
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Answer» <P> |
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| 2334. |
The tangent at A(-1,2) on the circle x^(2) + y^(2) -4x -8y + 7=0 touches the circle x^(2) + y^(2) + 4x + 6y =0 at B. Then, a point of trisection of AB is |
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Answer» `(0,(1)/(3))` |
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| 2335. |
If a variable circle S=0 touches the line y=x and passes through the point (0,0) then the fixed point that lies on the common chord of the circles x^(2)+y^(2)+6x+8y-7=0andS=0 is |
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Answer» `((1)/(2),(1)/(2))` |
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| 2336. |
A and B are independent events. Also P(A cap B)= (1)/(8) and P(A' cap B')=(3)/(8) then find P(A) and P(B). |
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Answer» ` P(A)= (1)/(4), P(B)=(1)/(2)` |
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| 2337. |
Let f:R to R and g:R to R is define by f(x)=2x-1 and g(x)=5x+2, then find (g circ f)(x) |
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| 2338. |
The distance of the plane barr (12,-4,3) = 65 from the origin is .......... |
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Answer» 1 |
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| 2339. |
IF x gt -cthen theminimumvalueof(( a+x) (b +x))/(c+x)is |
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Answer» `SQRT(a-c)+sqrt(b-c)` |
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| 2340. |
On the following graph, what is the y - coordiante of the point on the line that has an x - coordinate of -3? |
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| 2341. |
Three players A, B and C toss a coin cyclically in that order (that is A, B, C, A, B, C, A, B,…) till a head shows. Let p be the probability that he coin shows a head. Let alpha, beta and gamma be respectively the probabilities that A, B and C gets the first head. Prove that beta = (1 - p) alpha. Determine, alpha, beta and gamma (in terms of p). |
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Answer» <P> |
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| 2342. |
For a non-zero real number x, u, v, w if the points with position vectors A((x-u)i+xj+xk),B(x i+(x-v)j+xk),C(x i+xj+(x-w)k)andD((x-1)i+(x-1)j+(x-1)k) are coplanar, then (1)/(u)+(1)/(v)+(1)/(w) is equal to_________ |
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| 2343. |
If the distance between the foci of an ellipse is 8 and length of latus rectum is18/5, then the eccentricity of ellipse is: |
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Answer» `2/5` `rArr b^2=a^2-(ae)^2 rArr a^2=b^2+16` Length of L.R. `(2b^2)/a = 18/5 rArr b^2=9/5A` `rArr a^2=99/5 + 16 rArr 5a^2-99-80=0` `5a^2-25a+16a-80=0` `5a(a-5)+16(a-5)=0` (a-5)(5a+16)=0 `a=5 rArr e=4/5` |
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| 2344. |
Let U be set with number of elements in U is 2009. Consider the following statements : I : If A, B are subsets of U with n(AuuB)=280, then n(A'nnB')=x_(1)^(3)+x_(2)^(3)=y_(1)^(3)+y_(2)^(3) for some positive integers x_(1), x_(2)y_(1), y_(2) II : If A is a subset of U, with n(A)=1681 and out of these 1681 elements, exactly 1075 elements belong to a subset B of U, then n(A-B)=m^(2)+p_(1)p_(2)p_(3) for some positive integer m and distinct primes p_(1), p_(2), p_(3) Which of the statements given above is/are correct ? |
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Answer» `I` only |
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| 2345. |
Let P (a, b) and Q(c, d) are the two points on the parabola y^2=8x such that the normals at them meet in (18, 12). Then the product (abcd) is: |
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Answer» 412 |
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| 2347. |
If the trace of the matrixA=[(x-2,e^(x), -sinx),("cos"x^(2),x^(2)-x+3,"In"|x|),(cot x,"tan"^(-1)x,x-7)] is zero, then x is equal to : |
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Answer» `-2 or 3` |
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| 2348. |
From the equations which representsthe following Pair of lines. , y = mx , y = nx |
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Answer» SOLUTION :y - mx = 0 , y = NX = 0 or , (y-mx)(y-nx)= 0 or, `y^2 - nxy - MXY + mnx^2 = 0` or, y^2 - XY(m+n) + mnx^2` = 0 |
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| 2349. |
If 33theta = pi, then cos theta cos2theta cos4theta cos8theta cos16theta is : |
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Answer» `1/16` |
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| 2350. |
Find the sum of series 1 ^(2) + (1 ^(2) + 2 ^(2)) + (1 ^(2) + 2 ^(2)) + (1 ^(2) + 2 ^(2) + 3 ^(2)) +…. upto n terms |
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