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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.
| 8001. |
The sum of all the four numbers is |
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Answer» 3 `a+2d=(a-d)^(2)+a^(2)+(a+d)^(2)` or `2d^(2)-2d+3a^(2)-a=0`(1) `therefored=1/2[1pmsqrt(1+2a-6a^(2))]`(2) Since d is a positive INTEGER, so `1+2a-6a^(2)gt0` or `6a^(2)-2a-1lt0` or `(1-sqrt7)/6ltalt(1+sqrt7)/6` or a=0 (`because` a is an integer) Hence, from (2), d=1 or 0 But since `dgt0`, `therefore` d=1 Hence, the four NUMBERS are -1,0,1,2. |
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| 8002. |
Consider the folowing statements I:The number of non trivial even divisors of the number 2^(a_(1)),3^(a_(2)),4^(a_(3)),5^(a_(4)),6^(a_(3)) is a_(2)+a_(4)+a_(5)+a_(2)a_(4)+a_(4)a_(5) Then |
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Answer» I is FALSEAND IIis FALSE |
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| 8003. |
If veca=hati-2hatj+hatk, vecb=hati+2hatj+3hatk, vec c=3hati+2hatj+hatk then the value of [veca xx vecb, vecbxx vec c, vec c xx veca] is : |
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Answer» 765 |
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| 8004. |
If the plane lambda x-mu y + vz =phi contains line (x-lambda)/(lambda) = (y - 2phi)/(mu) = (z-v)/(v) then the value of (mu)/(phi) is................ |
| Answer» ANSWER :A | |
| 8005. |
Find the number of ways in which 3 numbers in A.P. can be selected from 1, 2, 3,…….. 21. |
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Answer» |
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| 8006. |
If a, b, c are the number of functions, injections, constant functions from a set containing 3 elements into a set containing 6 elements respectively then the ascending order of a, b, c is |
| Answer» Answer :C | |
| 8008. |
Find the number of ways of arranging the letters of the word 'FATHER'so that the relative positions of vowels and consonants are not disturbed. |
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| 8009. |
An are of the catenary y= (a)/(2) (e^((x)/(a)) + e^(-(x)/(a)))=a cos h(x)/(a), whose end-points have abscissas 0 and x, respectively, revolves about the x-axis. Show that the surface area P and the volume V of the solid thus generated are related by the formula P=(2V)/(a) |
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Answer» <P> |
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| 8010. |
A chess match between two players A and B is won by whoever first wins a total of two games. Probability of A's winning, drawng and losing any particular game are 1/6, 1/3 and 1/2 respectively. (The game are independent). If the probability that B wins the match in the 4^(th)gams is p, then 6p is equal to |
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Answer» `=1/2xx1/6xx1/3xx1/2xx6+.^(3)C_(1)xx1/2xx1/3xx1/2xx1/2=6/72+3/36=(6+6)/72=1/6` |
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| 8011. |
If A[{:(3,-4),(1,1),(2,0):}] and B=[{:(2,1,2),(1,2,4):}] , then verifyAB = BA or not? |
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Answer» Solution :We have, `A=[{:(2,1,2),(1,2,4):}]_(2xx3) "and" B=[{:(4,1),(2,3),(1,2):}]_(3xx2)` So, AB and BA both are POSSIBLE [since, in both A-B and B-A, the number of COLUMNS of first is equal to the number of rows of SECOND] `therefore AB=[{:(2,1,2),(1,2,4):}]_(2xx3)[{:(4,1),(2,3),(1,2):}]_(3xx2)` `=[{:(8+2+2,2+3+4),(4+4+4,1+ 6+8):}]=[{:(12,9),(12,15):}]` and `BA=[{:(4,1),(2,3),(1,2):}]_(3xx2)[{:(2,1,2),(1,2,4):}]_(2xx3)` `= [{:(4xx2+1,4+2,8+4),(4+3,2+ 6,4+12),(2+2,1+4,2+8):}]=[{:(9,6,12),(7,8,16),(4,5,10):}]` |
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| 8012. |
A=[{:(2,1,2),(1,2,4):}] and B=[{:(4,1),(2,3),(1,2):}]Verify AB=BA or not. |
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Answer» SOLUTION :We have, `A=[{:(2,1,2),(1,2,4):}]_(2xx3) "and"B=[{:(4,1),(2,3),(1,2):}]_(3xx2)` So, AB and BA both are POSSIBLE [since, in both A-B and B-A, the number of columns of FIRST is EQUAL to the number of rows of second] `THEREFORE AB=[{:(2,1,2),(1,2,4):}]_(2xx3)[{:(4,1),(2,3),(1,2):}]_(3xx2)` `=[{:(8+2+2,2+3+4),(4+4+4,1+ 6+8):}]=[{:(12,9),(12,15):}]` and `BA=[{:(4,1),(2,3),(1,2):}]_(3xx2)[{:(2,1,2),(1,2,4):}]_(2xx3)` `= [{:(4xx2+1,4+2,8+4),(4+3,2+ 6,4+12),(2+2,1+4,2+8):}]=[{:(9,6,12),(7,8,16),(4,5,10):}]` |
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| 8013. |
Probability that A speaks truth is (4)/(5) A coin is tossed. A reports that a head appears. The probability that there was head is |
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Answer» `(4)/(5)` |
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| 8014. |
If the distance between the points (-1, -1, z) and (1, -1, 1) is 2 then z =_____. |
| Answer» Answer :A | |
| 8015. |
The solution of (x+y +1) (dy)/(dx) =1 is |
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Answer» `x+y+2 = C E^(y)` |
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| 8016. |
The parametric equations x=(2a(1-t^(2)))/(1+t^(2)) andy=(4at)/(1+t^(2)) represents a circle whose radius is |
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Answer» a |
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| 8017. |
Construct truth tables for the following and indicate which of these are tautologies (p vv ~~q)^^(q vv ~~ p) |
Answer» SOLUTION :
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| 8018. |
If |a| lt 1, b = sum_(k=1)^(oo) (a^(k))/(k) rArr a= |
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Answer» `sum_(K=1)^(OO)((-1)^(k)B^(k))/(k)` |
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| 8019. |
One ticket is selected at random from 100 tickets numbered 00, 01, 02, 03,…………..99. Suppose x is the sum of the digits and y is the product of the digits, then the probability that x = 9 and y = 0 is |
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Answer» `1/99` |
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| 8020. |
Assume an auto loan in the amount of $12,000 is made. The loan carries and interest change of 14%. What is the amount of interest owed in the first three years of the loan, assuming there are no payments on the loan, and there is ul("no") compounding? |
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| 8021. |
Find the area of the figure out only by the circle rho= sqrt3 sin varphi from the cardioid rho=1 + cos varphi |
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| 8022. |
If a_n = (1+2+3+......+n)/(n!) then a_1 +a_2+a_3 + ....oo = |
| Answer» ANSWER :B | |
| 8023. |
(i) int_(0)^(pi//2) x sin x cos x dx (ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx |
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| 8024. |
Find the value of x,y and z from the equation:[[4,3],[x,5]]=[[y,z],[1,5]] |
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Answer» SOLUTION :EQUATING the corresponding ELEMENTS on both SIDES we GET y=4, z=3, x=1 |
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| 8025. |
If ninN,"then "3^(2n+2)-8n-9 is divisible by |
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Answer» 574 |
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| 8026. |
int (dx)/((x^2-1)sqrt(x-1)) |
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| 8027. |
If |{:(x,4,10),(5,2,5),(7,3,x):}|=0 then x in ………… |
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Answer» `{10}` |
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| 8028. |
Prove the following : tan6^@.tan42^@.tan66^@.tan78^@ = 1 |
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Answer» SOLUTION :We have TAN3A = tanAtan(60^@-A)tan(60^@+A) Now putting `A=6^@` and `18^@`. in (1) we have `tan18^@=tan6^@tan54^@tan66^@......(2) and `tan54^@` =`tan18^@tan42^@tan78^@` ......(3) Multiplying (2) and (3) we have `tan18^@tan54^@` =`tan6^@tan54^@tan66^@tan18^@tan42^@tan78^@` or, 1=`tan6^@tan42^@tan66^@tan78^@`. |
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| 8029. |
Two finite sets A and B have m and n elements respectively. If the number of sub-sets of A is 224 more than the number of sub-sets of B, then m - n is equal to |
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Answer» 2 |
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| 8030. |
Find the areaof the regionboundedby thecurvey= sinx, x = (pi)/(2)and x =(3 pi)/(2). |
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| 8031. |
int_(0)^(pi/2) cos^(2) x dx |
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Answer» Solution :`int_(0)^(pi//2)COS^(2)x DX =int_(0)^(pi//2)((cos2x +1)/(2))dx` `=(1)/(2) int_(0)^(pi//2)cos 2x dx +(1)/(2)int_(0)^(pi//2)1DX` `=(1)/(2)[(sin 2x)/(2)]_(0)^(pi//2)+(1)/(2)[x]_(0)^(pi//2)` `=(1)/(2)[((sinpi)/(2)-(sin 0)/(2))+((pi)/(2)-0)]=(pi)/(4)` |
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| 8032. |
Fill in the gaps with correct answer .tanalpha = (1)/2, tanbeta = (1)/3, then alpha + beta = _____ |
| Answer» SOLUTION :`(PI)/4` | |
| 8033. |
Evaluate the following integrals. int(3x-1)/(2x^(2)-4x+3)dx |
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| 8034. |
Evaluate the following integrals. int(3x+1)/(2x^(2)-2x+3)dx |
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| 8035. |
Find (dy)/(dx) of the functions (cos x)^(y)= (cos y)^(x) |
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| 8036. |
Thee number of persons joining a cinema ticket counter is a minute has Poisson distribution with parameter 6. Find the probability that i) no one joins the queue in a particular minute ii) two or more persons join the queue is a minute. |
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| 8037. |
On N, define a relation ~ as follows: a,b in N, a~ b if gcd (a,b)=2 Then ~ is |
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Answer» REFLEXIVE but not symmetric |
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| 8038. |
A pairof lines S =0 together with the linesgiven by the equation 8x^(2)-14xy+3y^(2)+10x+10y-25=0 form a parallelogram if itsdiagonals intersect at point(3,2) then the equationS=0 is |
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Answer» `6x^(2) - 9xy+ y^(2)- 25 x + 30Y + 25 =0` |
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| 8039. |
The tangent to curve y_1=ax^2 + bx + 7/2 at (1,2) is parallel to normal at point (-2,2) on curve y_2=x^2 + 6x+10, then value of (a-2b) is |
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Answer» SOLUTION :(1,2) LIES on `y_1` `2=a+b+7/2 rArr a+b =-3/2`…(1) `((dy_1)/(dx))_(1,2)=-1/((dy_2)/(dx))_(2,2)` `2a+b=-1/2` From (1) & (2) a=1 & b=`-5/2` a-2b=6 |
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| 8040. |
A particle is projected vertically upward and is at a height h after t_(1) seconds and again after t_(2) seconds |
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Answer» `h="GT"_(1)t_(2)` |
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| 8041. |
Prove that sin18^@.cos36^@ = 1/4 |
| Answer» SOLUTION :`SIN18^@ COS36^@=(sqrt5-1)/4)((sqrt5+1)/4)=(5-1)/16=1/4` | |
| 8042. |
Bag-I contains 3 black and 2 white balls, Bag-II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball. |
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| 8043. |
Find the sum of n terms of the series (a+b)+(a^(2)+ab+b^(2))+(a^(3)+a^(2)b+ab^(2)+b^(3))+"......." where a ne 1,bne 1 and a ne b. |
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Answer» Solution : ` a ne1 B ne 0 and ane b ` Let S = ( a+ b) + `(a^(2) + ab + b^(2)+ ( a^(3) + a^(2) b+ ab^(2) +b^(3) + ….+ n ` terms `=(1) /( (a-b) ) [(a^(2)-b^(2)) + ( a^(3) -b ^(3)) + (a^(4) -b^(4) ) + ....+_n terms ]` `= (1) /((a-b) ) [a^(2) (1+ a+ ......+ nterms )- b ^(2)(1+ b+ b^(2) + .....+nterms ) ` ` =(1)/( (a- b) ) [ a^(2)* (1* (a^(n) -1) )/( (a-1) ) -b^(2) ( 1* (b^(n) -1))/( (b-1) ) ]` ` "" = (1)/( (a-b ) ) [a^(2) ((1- n^(2)))/( (1- a) ) - b^(2) ( ( 1- b^(n)))/( (1-b) ) ]` |
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| 8044. |
Let A = ((a,b),(c,d)) where a,b,c,d in R . If |a|,|b|,|c|,|d| lt= where k gt 0 then |
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Answer» det (A)` GT= 2hatk` |
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| 8045. |
int(1+tan^(2)x)/(1-tan^(2)x)dx=.... |
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Answer» `LOG((1-tanx)/(1+tanx))+C` |
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| 8046. |
If x/y=(cos A)/(cos B) then (xtannA+ytanB)/(x+y) is equal to |
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Answer» `COT((A+B)/2)` |
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| 8047. |
Let f: RrarrR be defined by f(x)={(2x , xgt3),(x^(2), 1ltxle3),(2x,xle1):} Then f(-1)+f(2)+f(4) is |
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Answer» 1)9 |
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| 8048. |
Solve the following : [[x,a,a],[m,m,m],[b,x,b]]=0 |
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Answer» SOLUTION :`[[X,a,a],[m,m,m],[B,x,b]]`=0 `rArr m[[x,a,a],[1,1,1],[b,x,b]]`=0 `rArr m[[x-a,0,a],[0,0,1],[0,x-b,b]]`=0 (REPLACING `C_1` and`C_2` by `C_1-C_2` and `C_2-C_3` RESPECTIVELY) `rArr mabs((x-a)(-x+b))`=0 `rArr m(x-a)(b-x)=0 rArr x=a,b` |
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| 8049. |
Consider the functions defined implicitly by the equationy^(3)-3y+x=0 on various intervals in the real line. If x in (-oo, -2)uu(2, oo), the equation implicitly defines a unique real-valued differentiable function y=f(x). If x in (-2, 2), the equation implicitlydefines a unique real-valued differentiable function y=g(x) satisfying g(0)=0. The area of the region bounded by the curve y=f(x), the X-axis and the lines x = a and x = b, where - oo lt a lt b lt -2, is : |
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Answer» `int_(a)^(b)(x)/(3[{F(x)}^(2)-1])dx + BF(b)-AF(a)` |
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| 8050. |
Evaluate the definite integrals int_(0)^(pi/2)cos^(2)xdx |
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Answer» |
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