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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.
| 8951. |
Find dy/dx,x=4t,y=4/t |
| Answer» SOLUTION :`x=4t,y=4/tdx/dt=4dy/dt=-4/t^2dy/dx=(dy/dt)/(dx/dt)=(-4/t^2)/4=(-1)/t^2` | |
| 8952. |
Find the angles between the pair of lines whose slopes are , 1/sqrt3,1. |
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Answer» SOLUTION :LET `m_1=1/sqrt3,m_2=1` `TANTHETA=(m_2-m_1)/(1+m_1m_2)= (1-1/sqrt3)/(1+1 1/sqrt3)=(sqrt3-1)/(sqrt3+1)` `theta=15^@`. |
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| 8953. |
Let there be a bag containing 5 white, 4 red and 3 green balls. Three balls are drawn. If X denotes the number of green balls. Exhibit X. |
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Answer» Solution :X can TAKE values = 0, 1, 2, 3 `therefore`X is random variable with its range {0, 1, 2, 3} |
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| 8954. |
By using elementary operations, find the inverse of the matrix A=[(1,2),(2,-1)]. |
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| 8955. |
A particle moves along a straight line accordingto the law s=t^3-3t^2+5t. Find its velocity and acceleration at the end of 1 sec. |
| Answer» SOLUTION :`s=t^3-3t^2+5trArr(ds)/(dt)=3t^2-6t+5rArr(d^2s)/(dt^2)=6t-6` At the end of 1 SEC The velocity `=(ds)/(dt)]_(r=1)=2` The ACCELERATION `=(d^2s)/(dt^2)]_(t=1)=0` | |
| 8956. |
Find the number of pairs (x, y) so that y can be subtracted from a without borrowing where x, y are two digit numbers. |
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| 8957. |
Determine order and degree (if defined) of differential equations 2(d^(2)y)/(dx^(2)) = cos3x + sin 3x |
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| 8958. |
For |x| lt 1, the (r + 1)^(th) term in the expansion of sqrt(1 - x) is |
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Answer» `(1.3.5……..(2r-3))/(R!) (X/2)^r` |
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| 8959. |
The number of ways of selecting 10balls out of an unlimited number of white,red ,blue and green balls is |
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Answer» 270 |
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| 8960. |
sinh^(-1) (2^(3/2)) is equal to |
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Answer» `log(3+sqrt(8))` |
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| 8961. |
If a_(n+1)=sqrt((1)/(2)(1+a_(n))), then : cos((sqrt(1-a_(0)^(2)))/(a_(1)a_(2)a_(3)...."to "oo)) equals : |
| Answer» ANSWER :D | |
| 8962. |
Find the angle between the pair of lines vec(r)=3hat(i)+5hat(j)-hat(k)+lambda(hat(i)+hat(j)+hat(k))" and "vec(r)=7hat(i)+4hat(k)+mu(2hat(i)+2hat(j)+2hat(k)) |
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| 8963. |
Find dy/dx of the following y=sin^(-1)((2x)/(1+x^2)) |
| Answer» SOLUTION :`y=sin^-1((2X)/(1+x^2))=2tan^-1xtherefore(DY)/(dx)=2xx1/(1+x^2)=2/(1+x^2)sin^-1((2x)/(1+x^2))=2tan^-1x` | |
| 8964. |
If 2d is the shortest distance between the lines x=0,(y)/(b)+(z)/(c)=1,y=0,(x)/(a)-(z)/(c)=1, then |
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Answer» `(1)/(a)+(1)/(B)+(1)/(C)=(1)/(d)` |
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| 8965. |
Write the value of int(d(x^2+1))/(1+x^4)dx |
| Answer» SOLUTION :`INT(d(x^2+1))/(1+x^2)``int(d(x^2+1))/(1+x^4)=int(2xdx)/(1+(x^2)^2)`=`int(DT)/(1+t^2)=tna6-1x^2+c` | |
| 8966. |
int(x^2+3x+5)/((x+2)(x^2+2x+3))dx= |
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Answer» `log|x+2|-(1)/(sqrt(2))tan^(-1)((x+1)/(sqrt(2)))+C` |
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| 8968. |
A group of 2n students consisting of n boys and n girls are to be arrangedin a row suchthat adjacentmembers are of opposite sex. The number of ways in which this can be done is |
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Answer» `2(N!)` |
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| 8969. |
A={a, b, c},B={1,2} then the number of relations from A to B is |
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Answer» 32 |
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| 8970. |
If A and B are two events such that P(A) gt 0 and P(B) ne 1,then P(A | B') is ………. |
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Answer» <P>`1- P(A | B')` |
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| 8971. |
Method of integration by parts : int cos(logx)dx=....+c |
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Answer» `(x)/(2)[COS(LOGX)+SIN(logx)]` |
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| 8972. |
The vector area of the Delta ABC whose vertices are a,b,c is |
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Answer» `{(a xx B) + (b xx c) + (c xx a)}` |
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| 8973. |
If A = (1, 2, 3, 4), then the number of functions on the set A, which are not one-one, is: |
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Answer» 240 |
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| 8974. |
Intergrate the following: intsin((3x)/4)cos(x/2)dx |
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Answer» Solution :`intsin((3x)/4)COS(x/2)dx` =1/2 int2sin((3x)/4).cos(x/2)dx` =`1/2 int{SIN((5X)/4)+sin(x/4)}dx` =`1/2. 4/5(-cos((5x)/4))-1/2. 4COS(x/4)+C` =`-2/5cos((5x)/4)-2cos(x/4)+C` |
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| 8975. |
If x is real, then minimum value of (x^2-x+1)/(x^2+x+1) is |
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Answer» `1/3` |
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| 8976. |
If int[log(logx)+(1)/((logx)^(2))]dx =x[f(x) - g(x)] + C, then : |
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Answer» `f(X)=LOG(logx),G(x)=(1)/(logx)` |
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| 8977. |
According to the sliding - filament model of muscle contraction, the molecules that moves to shorten a muscle are :- |
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Answer» ACTIN |
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| 8978. |
If the length of the tangent from (5,4) to the circle x^(2) + y^(2) + 2ky = 0 is 1 the n find k. |
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| 8979. |
The radius of nien point circle of the triangle formed by (6, 2), (4, 6),(0, 4) is |
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Answer» `sqrt(7)//2` |
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| 8980. |
Let alpha, beta are two real roots of equation x ^(2) + px+ q =0, p ,q, in R, q ne 0. If the quadratic equation g (x)=0 has two roots alpha + (1)/(alpha) , beta + (1)/(beta) such that sum of its roots is equal to product of roots, then number of integral values g can attain is : |
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| 8981. |
Evaluate the following integrals. int_(theta)^(pi/2)(sqrt(tanx))/(sqrttanx+sqrtcotx)dx |
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| 8983. |
A straight line x-2y-4=0 is shifted parallelto it by 3 units away from the origin and then rotated by an angle of 30^(@) in the anti-clockwise direction.If the slope of the new line formed is m, then the integral part of 'm' is |
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Answer» `-(13pi)/(12)` |
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| 8984. |
Find the area of the region bounded by y= sin x and y= cos x between x=0 and x= (pi)/(2) |
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| 8986. |
A straight line x-2y-4=0 is shifted parallel to it by 3 units away from the origin and then rotated by an angle of 30^(@) in the anti-clockwise direction.If the slope of the new line formed is m, then the integral part of 'm' is |
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Answer» -1 |
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| 8987. |
Evaluate the integrals . underset(-1)overset(2)int (x^(2))/(x^(2)+2)dx |
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| 8988. |
Sometimes we are just concerned with finding integral solutions to equations. Consider the equation tan^(-1).(1)/m+tan^(-1).(1)/n=tan^(-1).(1)/lambda, where m,n, lambda in N If lambda is such that lambda^2=1 is a prime, then how many solutions (m,n) are there for the equation? |
| Answer» ANSWER :B | |
| 8989. |
Which of the following are / is true |
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Answer» `e^(pi) gt pi ^(e)` |
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| 8991. |
Prove that thefunctions do not have maxima or minima: g(x) = log x |
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| 8992. |
Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2 |
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| 8993. |
For the circles x^(2) +y^(2) +2lambda x+ c =0 , x^(2) +y^(2) +2my - c=0the number of common tangents whenc ne 0is |
| Answer» ANSWER :B | |
| 8994. |
Rewrite the given statement with "if then" in five different ways conveying the same meaning1) If p is prime number then sqrtpis an irrational number |
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Answer» Solution :r : If p is prime number then `SQRTP`is an irrational number Above statements r corresponds TOTWO statements p and q p : p is a prime number q : `sqrtp` is an irrational number Then , if p then qis same as the following (i) p `rArr`q , p is a prime number implies that `sqrtp` is an irrational number (ii) p is sufficent condition for q If we lnow that a number p is prime , then it is sufficent to conclude that `sqrtp` is a prime number p only if q A number p is prime only if `sqrtp` is an irrational number (IV) `sqrtp` is an irrational number is NECESSARY conndition for p to be prime (V) `~q rArr ~p` i.e., If `sqrtp` is not an irrational number then p is not a prime number |
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| 8995. |
If six coins are tossed then find the probability of getting atleast 4 heads, given that all the coins are not showing same result. |
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| 8997. |
Find the area of the triangle with vertices at(2,7),(1,1),(10,8) using determinants. |
| Answer» SOLUTION :47/2 SQ. UNITS | |
| 8998. |
Find number of plane havin maximum number of atoms in CD_(4)? |
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| 9000. |
Mean and standard deviation of the random variable X are (7)/(3) and (14)/(9) respectively. Then find value of n and p. |
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Answer» `(1)/(3)` |
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