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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.
| 26801. |
If the coefficients of three consecutive terms in the expansion of (1+x)^n are 45, 120 and 210 then the value of n is |
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Answer» 8 |
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| 26802. |
S=25.33H+353.16 The linear regression model above is based on an analysis of the relationship between SAT math scores (S) and the number of hours spent studying for SAT math (H). Based on this model, which of the following statements must be true? I. The slope indicates that as H increases by 1, S decreases by 25.33. II. For a student that studies 15 hours for SAT math, the predicted SAT math score is greater than 700. III. There is a negative correlation between H and S. |
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Answer» I only |
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| 26803. |
Let S=overset(oo)underset(k=1)Sigma (k(10)^(k)+2^(k+1)5^(k))/(5^(k)2^(2k+1)(k+1)), thenS= |
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Answer» |
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| 26804. |
If f(x)=int_(0)^(x)t sintdt, then f'(x)= . . . . . . |
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Answer» COSX + X sin x |
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| 26805. |
Let x be a real number , [x] denotes the greatest integer function, {x} denotes the fractional part and (x) denotes the least integer function, then solve the following: "(i)" (x)^(2)=[x]^(2)+2x "" (ii) [2x]--2x=[x+1] "(iii)" [x^(2)]+2[x]=3x, 0 le x le 2 "(iv)" y=4-[x]^(2) and [y]+y=6 "(v)" [x]+abs(x-2) le 0 " and " -1 le x le 3 |
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Answer» (iv) {1,-1, `pm` 1+k, where k is any positive proper fraction} (v) no solution |
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| 26806. |
Equation of circle with centre (3,-1) and which cuts off a chord of length 6 on the line 2x-5y+18=0 is |
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Answer» `X^(2)+y^(2)+6x+2y+28=0` |
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| 26808. |
Find the range of the following functions (i) f(x) = log_(2)(sqrt(x-4) + sqrt(6-x)), 4 le x le 6 (ii) f(x) = 9^(x) - 3^(x) + 1 |
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Answer» Solution :(i) We have `f(x) = log_(2) (sqrt(x-4) + sqrt(6-x)), 4 le x le 6` In the domain INDICATED the function is well defined. To find the range, let `y = log_(2)(sqrt(x-4) + sqrt(6-x))` `rArr 2^(y) = sqrt(x-4) + ssqrt(6-x) = t`, say (let `2^(y) = t gt 0`) `rArr t^(2) = (x-4) + (6-x) + 2 sqrt((x-4)(6-x))` `rArr t^(2) = 2+2sqrt(-x^(2) + 10 x - 24) rArr t^(2) - 2 = sqrt(1-(x-5)^(2))` We observe that `0 le sqrt(1-(x-5)^(2)) le 1`, we have `0 le t^(2) - 2 le 2` `rArr 2 le t^(2) le 4` `rArr -2 le t le -sqrt(2)` or `sqrt(2) le t le 2` But `t = 2^(y) = +ve` always, HENCE `sqrt(2) le t le 2` `rArr 2^(1//2) le 2^(y) le 2^(1)` `rArr (1)/(2) le y le 1` (`because 2^(y)` is an increasing function) `rArr R_(f) = [(1)/(2), 1]` (ii) We have, `f(x) = 9^(x) - 3^(x) + 1 = (3^(x))^(2) - 2 xx 3^(x) xx (1)/(2) + (1)/(4) + (3)/(4) = (3)/(4) + (3^(x) - (1)/(2))^(2) ge (3)/(4), AA x in D_(f)` Let `y = t^(2) - t + 1, t = 3^(x) gt 0` `rArr t^(2) - t + (1-y) = 0` `rArr t = (1 +-sqrt(1-4(1-y)))/(2) = (1 +- sqrt(4y - 3))/(2)` For any `y in [(3)/(4), oo)` there always exists ONE value of t, viz, `t = (1+sqrt(4y-3))/(2)` (observe that t has to be positive) and consequently for eveery `y in [(3)/(4), oo)` there exists one value of `x in R`. Here the range of function is `[(3)/(4), oo)`. |
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| 26809. |
Write the equation of the line (x-5)/3=(y+4)/7=(z-6)/2 in vector form. |
| Answer» SOLUTION :GIVEN EQUATION is `x=ay+b,z=cy+drArr(x-b)/a=y=(z-d)/C` | |
| 26810. |
The pole of 2x+3y=0 with respect to x^(2)+y^(2)+6x-4y=0 is |
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Answer» `((-5)/6,5/4)` |
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| 26811. |
Express the following as trigonometric ratios of some acute angles.sin (-3333^@) |
| Answer» Solution :`SIN (-3333^@) = -sin 3333^@ = -SING(37 (pi)/2 + 3^@) = -(-1)^((37-1)/2) COS 3^@ = -cos 3^@` | |
| 26812. |
IF x=int_0^4 (dt)/sqrt(1+9t^2) and (d^2y)/(dx^2) =ay, then a is equal to: |
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Answer» 3 |
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| 26813. |
The locus of z satisfying |z| + |z-1| = 3 is |
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Answer» a CIRCLE |
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| 26814. |
Differentiate the functions (sin x)^(x) + sin^(-1) sqrtx |
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| 26816. |
Let g(x) = int_(0)^(x) f(t) dt and f(x) satisfies the equation f(x +y) = f(x) + f(y) + 2xy -1 for all x, y in R and f'(0) =2 then |
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Answer» g INCREASES on `(0, oo)` and DECREASES on `(-oo, 0)` |
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| 26817. |
Evaluate the definite integrals int_(0)^(1)xe^(x^(2))dx |
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| 26818. |
Find the probability of getting 5 exactly twice in 7 throws of a die. |
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| 26820. |
Evaluation of definite integrals by subsitiution and properties of its : int_(-1)^(1)log[x+sqrt(x^(2)+1)]dx=......... |
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Answer» 0 |
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| 26821. |
What is the order of the matrixA=[{:(1,1,9,-11),(2,3,8,-15),(3,-7,-12,-6):}]?Write the elements a_(12),a_(21),a_(24),a_(31),a_(34),of a matrix A. |
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| 26822. |
Let the function, f:[-7,0]toR be continuous on [-7,0] and differentiable on (-7,0). If f(-7)=-3 and f'(x)le2, for all x in(-7,0), then for all such functions f,f(-1)+f(0) lies in the interval : |
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Answer» `[-6,20]` |
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| 26823. |
A student answers a multiple choice question with 5 altenatives, of which exactly one is correct. The probability that he knows the correct answer is p, 0 < p < 1. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered tha question correctly, the probabilty that he did not tick the answer randomly, is- |
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Answer» `(3p)/(4P + 3)` |
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| 26825. |
int x^(4)(1+ log x) dx = |
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Answer» |
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| 26827. |
Let S(k)=1+3+5+...+(2k-1)=3+k^(2). Then which of the following is true? |
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Answer» `S(k)rArrS(k-1)` |
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| 26828. |
If A = (1, 2), B = (2,1) and P is a variable point satisfying the condition |PA - PB| = 3, then the locus of P is |
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Answer» `8x^2 + 2xy + 8y^2 + 27x + 27y + 45 =0` |
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| 26829. |
A deler wishes to purchase a number of fans and sewing machines.He has only Rs. 5760 to invest and has space for at most 20 times. A fan costs him Rs.360 and a sewing machine Rs.240. He expects to sell a fan at a profit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assumign that he can sell all the items that he buys, how should he invest his money to maximize the profit? Solve graphically and find the maximum prodit. |
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Answer» `x+yle20,360x+240yle5760an x GE0,yge0.` |
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| 26830. |
One of the diagonals of a square is the portion of the line x/2+y/3=2 intercepted between the axes. Then the extremitites of the other diagonal are |
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Answer» (5,5), (-1,1) `(x-2)/(3//SQRT(13)) = (y-3)/(2//sqrt(13)) =R` For the extremities of the diagonal, `r =+-sqrt(13).` Hence, `x-2 = +-3, y-3=+-2` x=5,-1 and y5,1 Therefore, the extremities of the diagonal are (5,5) and (-1,1). |
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| 26831. |
Using differentials, find the approximate value of each of the up to 3 places of decimal. (0.999)^((1)/(10)) |
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Answer» |
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| 26832. |
There are 10 parallel lines intersected by a family of 5 parallel lines. The number of parallelograms thus formed in the net work is |
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Answer» 225 |
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| 26833. |
If (20)^(19)+2(21)(20)^(18)+3(21)^(2)(20)^(17)+….+20(21)^(19)=k(20)^(19) then k is equal to |
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Answer» 400 |
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| 26834. |
Killogg is a new cereal formed of a mixture of bran and rice, that contains at leat 88 grams of protein and at least 36 milligrams of iron. Knowing that bran contains 80 grams of protein and 40 milligrams of iron per kilogem, and that rice contains 100 grmas of protein and 30 milligrams of iron per kilogrm, find the minimum cost of productin this new cereal if bran costs Rs.5 per kilogram and ric costs Rs.4 per kilogram. |
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Answer» `(x xx(80)/(1000))+(yxx(100)/(1000))ge(88)/(1000),` `(x xx(40)/(1000))+(y xx(30)/(1000))ge(36)/(1000),` x geand y GE0.` |
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| 26835. |
Let ABC be an acute- angled triangle and AD, BE, and CF be its medians, where E and F are at (3,4) and (1,2) respectively. The centroid of DeltaABC G(3,2). The height of the altitude drawn from point A is (in units) |
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Answer» `4sqrt(2)` |
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| 26836. |
If z=i^("ii") where i=sqrt(-1), then |z| is equal to : |
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Answer» 1 `rArr i^(i)=(e^((IX)/(2)))^(i)=e^(-(pi)/(2))` `rArr z=(i)^((i)^(i))=1^(.e^(-(pi)/(2)))` `rArr|z|=1` |
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| 26837. |
If A is 5xx4 matrix and B is 4xx5 matrx, then 2\AB-I_(5)|+|BA-I_(4)|)+1 is__ |
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| 26838. |
Let A be the set of n ( ge 3) distinct elements.The number of triplets (a,b,c) of the elements of A in which at least co-ordinates are equal is |
| Answer» Answer :D | |
| 26839. |
ABCD is a square field with each side equal to 100 m. Two poles of equal heights stand at E, the mid point of DC and at the corner B of the field, subtending respectively angles alpha and 30^(@) at the corner A of the field. The value of alpha satisfies |
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Answer» `cos 2 ALPHA = (11)/(19)` |
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| 26840. |
A balloon which always remains spherical is being inflated by pumping in 10 cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is 15cm. |
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Answer» 1)`(1)/(pi)cm//sec` |
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| 26841. |
If A =[{:( alpha , a ),( beta , b),( gamma, c):}] then(A)A^(T)is |
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Answer» a non-SINGULAR MATRIX |
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| 26842. |
The polar of (3,-1) w.r.t the circle x^(2)+y^(2)_2x-4y+1=0 is |
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Answer» `4x-3y+6=0` |
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| 26843. |
One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent ? (i) E : 'the card drawn is a spade F: 'the card drawn is an ace' (ii) E : 'the card drawn is black' F: 'the card drawn is a king' (iii) E: 'the card drawn is a king or queen' F: 'the card drawn is a queen or jack'. |
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Answer» |
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| 26845. |
Integration by partial fraction : int(adx)/(b+ce^(x))=....+c |
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Answer» `(a)/(B)LOG((E^(X))/(b+ce^(x)))` |
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| 26846. |
A particle starting from a point A and moving with a positive constant acceleration along a straight line reaches another point B in time T. Suppose that the initial velocity of the paticle is u gt 0 and P is the midpoint of the line AB. If the velocity of the particle at point P is nu_(1), and if the velocity at time T/2 is nu_(2), then |
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Answer» `nu_(1)=nu_(2)` |
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| 26847. |
Integrate the following functions x^2/(2+3x^3)^3 |
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Answer» Solution :Let t = `2+3x^3`, Then DT = `9x^2 DX gt x^2 dx = 1/9 dt` therefore `int x^2/(2+3x^3)^3 dx = int 1/t^3 1/9 dt` =`1/9 int r^(-3) dt = 1/9 xx t^(-3+1)/(-3+1) +c` `1/(-18) t^(-2) +c = -1/(18t^2) +c` =`-1/(18(2+3x^3)^2 +c`. |
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| 26848. |
The slope of the tangent at (1, 2) to the curve x=t^(2)-7t+7 and y=t^(2)-4t-10, is |
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Answer» `8/5` |
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| 26849. |
The value of lim_(xrarr1^(-))(sqrtpi-sqrt(4tan^(-1)x))/(sqrt(1-x)) is equal to |
| Answer» Answer :D | |
| 26850. |
If f : R to R and g : R to R are given by f(x)=|X| and g(x)=[x] for each x in R then {x in R : g(f(x))le f(g(x))} is equal to |
| Answer» ANSWER :D | |