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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.
| 1751. |
If the lactus recturm of a hyperbola through one focus subtends 60^@ at the other focus then its eccentricity is |
| Answer» Answer :B | |
| 1752. |
Prove that the following sequences converage and find their limits: (a) x_(1)=sqrt2, x_(2)=sqrt(2+sqrt2), x_(3)=sqrt(2+sqrt(2+sqrt2)),....., x_(n)=sqrt((2+sqrt(2+.....2)))..... (b) x_(n)=(2^(n))/((n+2)!) (c) x_(n)=(E(ny)) the sequence of successive decimal appromations 1:1:4,, 1.41, 1.414, of the irratioanl number sqrt2 (e) x_n=(n!)/(n^(n)). |
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| 1753. |
Evaluate the following integral int (" cos x + x sin x")/(x (x + cos x)) dx |
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| 1754. |
X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. For variable X, approximately what percentile corresponds to a value of 2 ? |
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| 1755. |
At the point, x=1, the function : f(x)=x^(3)-1,1ltxltoo=x-1,-ooltxle1 is : |
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Answer» DISCONTINUOUS and not DIFFERENTIABLE |
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| 1756. |
For any vectors vec(a),vec(b) and vec( c ). Out of the following, which statement is true ? |
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Answer» `VEC(a)XX(vec(B)xx vec( C ))=(vec(a)xx vec(b))xx vec( c )` |
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| 1757. |
A random variable X has the following probability distribution: Determine (i) K (ii) P(X lt 3) (iii) P(X gt 6) (iv) P(0 lt X lt 3) |
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| 1759. |
Let a ne 0 and P(x) be a polynomial of degree greater then 2.If P(x) leaves remianders a and a- when divided, respectively, by x + a and x - a, then find the remainder when P(x) is divided by x^(2) - a^(2). |
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Answer» Solution :According to the question P(-a) = and P(a) = - a. Let the REMAINDER, when P(x) is divided by `x^(2)-a^(2)` be AX + B. Then `P(x) = Q (x) (x^(2)-a^(2))` + Ax + B, where Q (x) is the quotient PUTTING x = a, we get P(a) = 0 + Aa + B orAa + B = - a...(1) Putting x = - a, we get `-Aa + B = a`...(2) Solving (1) and (2) , we get B = 0and A = - 1 Hence, the requriedremainder = Ax + B = - x |
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| 1760. |
For a certain frequencytable which has been partly reproduced here , the arithmetic mean was found to be Rs. 28.07 Income (in Rs)""15 "" 20 "" 25"" 30 "" 35"" 40 No. of workers:"" 8"" 12 "" ? "" 16 ""? "" 10 If the total number of workers is 75, then the missing frequencies are |
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Answer» ` 14, 15` |
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| 1762. |
If A is a non-singular matrix of order 3, then |adj A| = |A|^(n) here the value of n is |
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Answer» 2 |
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| 1763. |
From the set {1, 2, 3, ...13}, two numbers x, y are drawn one-by-one with replacement. The probability x^(2)-y^(2) shall be divisible by 3 is |
| Answer» Answer :C | |
| 1765. |
If there is an error of 0.05 cm is made while measuring the side 10 cm of a cube, then the error in the volume is |
| Answer» Answer :C | |
| 1766. |
If alpha, beta and gamma are the roots of the equation x^(3)-3x^(2)+4x+4=0, then the value of |(a^(2)+1,1,1),(1,beta^(2)+1,1),(1,1,gamma^(2)+1)| is equal to |
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Answer» 32 |
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| 1767. |
int_(0)^(pi//4) sqrt(cot x dx) =? |
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Answer» `(Pi SQRT(2))/(4)+(1)/(sqrt(2)) LOG (sqrt(2)-1)` |
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| 1768. |
Normal at any pint on the ellipse 9x^(2)+16^(2)=144 meets the co-ordinate axes at A and B respectively then maximum of Delta OQB (O being origin) is |
| Answer» Answer :A | |
| 1769. |
Evaluate the integral underset(0)overset(1) int x^(5) (1-x)^(5//2)dx |
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| 1770. |
An automobile driver travels from plane to a hill station 120 Km distant at an average speed of 30 km per hour. He then makes the return trip at an average speed of 25 km per hour. He covers another 120 km distance on plane at an average speed of 50 km per hour. His average speed over the distance of 360 km will be |
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Answer» `(30+25+50)/(3)` km/hr |
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| 1771. |
The pairs of straight line x^(2) - 3xy + 2y^(2) = 0 and x^(2) - 3xy + 2y^(2) + x - 2 = 0 form a |
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Answer» square but not rhombus |
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| 1772. |
How many 5 digited numbers that can be formed using 0,1, 2, 3, 4, 5, 6 that are divisible by 7 when repetition is allowed. |
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| 1773. |
If A, B, C the angles of an acute angled Delta ABCand D=|{:((tan B+ tan C)^(2), ""tan ^(2)A, tan ^(2)A),(""tan ^(2)B, (tan A +tan C)^(2), tan ^(2)A), (""tan ^(2)C, tan ^(2)C, (tan + tan B)^(2)):}|,then the least integral values of (D)/(1000) is |
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| 1774. |
Locus of the centre of circle of radius 2 which rolls on out side the rim of the circle x^(2)+y^(2)-4x-6y-12=0 is |
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Answer» `X^(2)+y^(2)-4x-6y=0` |
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| 1775. |
If a rod AB of length 2 units slides on coordinate axes in the first quadrant. An equilateral triangle ABC is completed with C on the side away from O. Then, locus of C is |
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Answer» `X^(2)+y^(2)-XY+1=0` |
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| 1776. |
Integrate the functions 1/sqrt(1+x) |
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| 1777. |
The rootsof (x-a) (x-a -1) +(x-a-1) +(x-a-2) +(x-a)(x-a-2)=0 ain RR are always |
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Answer» EQUAL |
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| 1778. |
Let f(x)={{:(|x^(3)+x^(2)+3x+sinx(3+sin(1)/(x)), x ne 0), (0,x=0):} Then the number of points where f(X) attians its minimum value is _______. |
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Answer» Let `g(x)=x^(3)+x^(2)+3x+sinx` `therefore g(x)=3x^(2)+2x+3+cosx` `=3(x^(2)+(2x)/(3)+1)+cosx` `=3{(x+1/3)^(2)+8/9}+coxgt0` and `2lt3+sin(1/x)lt4` Hence minimum value of `f(x) is 0 at x=0` Hence number of POINTS =1 |
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| 1779. |
The rate of increase in the number of bacterai in a certain becteria culture is propotional to the number present at that time. If is found that the number doubles in4hours, then at the end of 12 hours, the number of bacteria are |
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Answer» 4 times the original |
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| 1780. |
The value of sqrt3cot20^(@)-4cos20^(@) is |
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Answer» `1` `=(sqrt(3)cos20^(@))/(sin20^(@))-4cos 20^(@)` `=(sqrt(3)COS 20^(@)-4sin20^(@)cos20^(@))/(sin20^(@))` `=(2[sqrt(3)/(2)cos 20^(@)-2sin20^(@)cos20^(@)])/(sin20^(@))` `=(2(SIN60^(@)cos20^(@)-sin40^(@)))/(sin20^(@))` `=([2sin60^(@)cos20^(@)-2sin40^(@)])/(sin20^(@))` ` =(sin80^(@)+sin40^(@)-2sin40^(@))/(sin20^(@))` `=(sin80^(@)-sin40^(@))/(sin20^(@))` `=(2cos60^(@).sin20^(@))/(sin20^(@))` `2xos60^(@)=1` |
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| 1781. |
Evaluate int [ " log" (log x) + (1)/((log x )^(2)) ] dx |
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| 1782. |
Solution of differential equation (x^(2) -2x+2y^(2))dx + 2xy dy=0 is |
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Answer» `y^(2) =2x - (1)/(4) x^(2) + (C )/(x^(2))` |
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| 1783. |
Find the values of 'a' for which the vector vec( r )=(a^(2)-4)hati+2hatj-(a^(2)-9)hatk makes acute angles with the co-ordinate axes. |
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| 1784. |
Solve the equation for x, y, z and t, if 2[(x, y),(z,t)]+3[(1,-1),(0,2)]=3[(3,5),(4,6)] |
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| 1785. |
Find 'C' of Lagrange's mean value theorem for the function f(x) =x^(3)-5x^(2)-3x in [1, 3] |
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| 1786. |
If (22)/(7) and pi appear as two distinct terms of an A.P., then common difference of the A.P. must be |
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Answer» an integer |
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| 1787. |
The radius of the circle circumscribing the triangle ABC, is equal to |
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Answer» ` (sqrt10)/(2)` |
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| 1788. |
One useful way of defining sequences is by a recursion relation. Many recurrence relations can be transformed to some know sequences, say GP or sometimes nth term can be found by algebraic jugglery Some chochlates are distributed between 25 children in such a way that first child gets 5 chocolates , second child gets 7 choloates and in (n -a)^(th) child . The total number of chocolates distributed is |
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Answer» 3250 |
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| 1789. |
One useful way of defining sequences is by a recursion relation. Many recurrence relations can be transformed to some know sequences, say GP or sometimes nth term can be found by algebraic jugglery Let {a_(n)} + 2a_(2) + 3a_(3) + …+ (n-1) a_(n-1) = n^(2) a_(n). n ge 2 The value of a_(786)is |
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Answer» `(1)/(789)` |
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| 1790. |
HgI_2 (yellow) will be turned into Hgl2 (med) variety on |
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Answer» Heating |
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| 1791. |
If Sbe the surface area of V be the volumeofa sphere of radius r. Then (dv)/(dt) = (r)/(k) (ds)/(dt). Value of k is |
| Answer» Answer :C | |
| 1792. |
A committee of 4 students is selected from a group of 8 boys and 4 girls. Given that there is at least one girl in the committee. Find probability of an event that there are exactly 2 girls in the committee. |
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| 1793. |
The plane passing through the point(-2,-2, 2) and containing the line joining the points (1, 1, 1) and (1, -1, 2) makes intercepts on the co-ordinate axes, then sum of the lengths of intercepts is |
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Answer» 3 |
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| 1794. |
Using propertiesof determinantsprove that: |(1+a,1,1),( 1,1+b,1),(1,1,1+c)| =abc +bc +ca +ab |
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| 1795. |
The value of E=81 log_(0.3) ((1)/(sqrt2+2sqrt3)-sqrt4(2sqrt3)) is simplified so: |
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Answer» 16 |
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| 1796. |
Jared has four pennies (1 cent), one nickel (5 cents) and one dime (10 cents). {:("Quantity A","Quantity B"),("The number of different cent",20),("values that Jared can achieve",),("using one or more of his coins",):} |
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| 1797. |
Find the remainder when x^(6)-4x^(5)+3x^(4)-2x^(2)+x-1 is divided with x+2 |
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| 1799. |
The vertices of a triangle OBC are O(0, 0), B(-3, -1) and C(-1, -3). If the line joining the point Don OC and E on OB is parallel to BC and the perpendicular distance of O from DE is 1/2, then the equation of DE is |
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Answer» `x+y+sqrt(2)=0` |
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| 1800. |
Examin the following functions for continuity. f(x)= (x^(2)-25)/(x+5), x ne -5. |
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