28278 + Interview Questions in Maths in Class 12

1.	Prove that : (1)/(2) cos^(-1) ((1+ 2 cos x)/( 2+cosx) ) = tan^(-1) ((1)/(sqrt(3)) "tan" (x)/(2))
Answer» SOLUTION :N/A

Discussion

2.	Solvetheequation 6x^4 -13 x^3 -35x^2-x+3=0 giventhat2 +sqrt(3)is a root
Answer» ANSWER :`(-1)/(3) ,(-3)/(2) ,2 +- SQRT(3)`

Discussion

3.	Let f(x) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):} If the number of points where f(x) is nonderivable in [–2, oo) is 3 then the value of \|a + b\| is (Note: [y] and sgn (y) denote greatest integer function and signum function of y respectively).
Answer» Solution :`F(X) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):}` `{(-1,",", -2 le x < -1),(0,",", -1 le x < 0),(1,",", 0 < x < 1),(2,",", 1 le x < 2),(ax^(2) - bx,",", x ge 2):}` For only 3 points of non-derivable in `[-2, OO)` Then it should be derivable at x = 2 So, `f(x) = 2, [ "At" x = 2]` `f'(2) = 0 [ "At" x = 2]` `4A - 2b = 2 ""......(1)` `4a - b = 0 ""......(2)` From (1) & (2) `a = -1/2 & b = -2` `\| a + b \|= 2.50`

Discussion

4.	If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p-q),
Answer» ANSWER :1

Discussion

5.	Which of the following is correctly matched.
Answer» `XeF_6 " " sp^3d^2` DISTORTED octahedral `XeF_5^+ " " sp^3d^2` square PYRAMIDAL `XeF_5^(-) sp^3d^3` PENTAGONAL planar `XeOF_4 " " sp^3d` sea saw Answer :B,C

Discussion

6.	f(x) is a continuous and differentiable function. f'(x) ne 0 and \|{:(f'(x),f(x)),(f''(x),f'(x)):}\|=0.If f(0)=1 and f'(0)=2 then f(x)=....
Answer» `X^(2)+x+1` `2e^(x)-1` `e^(2X)` `4E^((x)/(2))-3` ANSWER :C

Discussion

7.	Findproducts : [[1,0],[0,k]][[a,b],[c,d]]
Answer» SOLUTION :`[[1,0],[0,k]][[a,b],[c,d]]` `=[[1.a+0.c""1.b+0.d],[0.a+k.c" "0.b+KD]]=[[a,b],[KC,kd]]`

Discussion

8.	A sequence a_(1),a_(2), …..a_(n)of real numbers is such that a_(1) = 0 ,\|a_(2)\|=\|a_(1)-2\|,\|a_(3)\|=\|a_(2)-2\|,---\|a_(n)\| = \|a_(n-1)-2\| . Then the maximum value of the arithmetic mean of these numbers is _____.
Answer» ANSWER :`RARR (a_(1)+a_(2)+....+a_(N))/n LE 1 `

Discussion

9.	If the relation R on the set {1,2,3}be defined by R = {(1,2)}.Then , R is .........
Answer» REFLEXIVE TRANSITIVE SYMMETRIC NONE of these Solution :N/A

Discussion

10.	The vectices of a triangle are A(1,7), B(-5, -1) and C(-1, 2). Then, the equation of a bisector of the angleABC is
Answer» `x-y + 4=0` `x+y + 4 =0` `2x-3y + 6 = 0` `x-2y + 4 = 0` ANSWER :A

Discussion

11.	Find \|x\|, if for a unit vector a (vecx-veca)(vecx+veca)=12
Answer» ANSWER :`SQRT(13)`

Discussion

12.	A balanced dice is thrown twice and the sum of the numbers appearing on the top face is observed to be 7. What is the conditional probability that the number 2 has appeared at least once ?
Answer» ANSWER :`(1)/(3)`

Discussion

13.	A strictly increeasing sequence of positive integers a _(1), a _(2), a _(3)… has the property that for ever positive integer k, the subsequence a _(2k -1), 2 _(2k), a _(2k +1) is geometric and the subsequence a _(2k), 2 _(2k +1), a _( 2k +2) is arithmetic. Suppose that a _(13)= 2016. Find a _(1).
Answer» ANSWER :504

Discussion

14.	Differntiate the following functions by proper substitution.cos^(-1)(2t^2-1)
Answer» SOLUTION :`y=COS^(-1)2t^2-1)`[PUT`t=costheta` `=cos^(-1)(2cos^2theta-1)` `=cos^(-1)cos2theta=2theta=2 cos^(-1)` `thereforedy/dx=-2/sqrt(1-t^2)`

Discussion

15.	Integrate the following functions: sin^-1x/(sqrt(1-x^2)
Answer» SOLUTION :Let t= `sin^-1x`. Then `DT = 1/sqrt(1-x^2)dx` THEREFORE` INT (sin^-1x)/sqrt(1-x^2) dx = int t dt = t^2/2+c` `(sin^-1x)^2/2 +c`

Discussion

16.	If a,b,c are linearly independent, ((a + 2b). (2b + c) xx (5c + a))/(a. (b xx c)) = k then k is
Answer» 10 14 18 12 Answer :D

Discussion

17.	Value of int_(2)^(3)(dx)/(sqrt((a+x^(3)))) is
Answer» LESS than 1 greater than 2 lies between 3 and 4 none of these Answer :A

Discussion

18.	For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=vec(0)\|vec(a)\|=3,\|vec(b)\|=4,\|vec( c )\|=5, then evaluate 2(vec(a)vec(b)+vec(b)vec( c )+vec( c )*vec(a)).
Answer» 100 50 `-25` `-50` ANSWER :D

Discussion

19.	Freedom equation of a line is (whereare direction cosines) x = x_(1) + lr, y =y_(1) +mr, z=z_(1) + nr, where:
Answer» R is the DISTANCE of (X,y,Z) from `(x_(1), y_(1), z_(1))` `\|r\|` is the distance of (x,y,z) from `(x_(1),y_(1) ,z_(1))` r is the distance of `(x_(1), y_(1), z_(1))` from the origin NONE of these Answer :B

Discussion

20.	If G is the centroid of DeltaABC, then (AG^(2)+BG^(2)+CG^(2))/(AB^(2)+BC^(2)+CA^(2))=
Answer» 1 3 `1//3` -1 Answer :C

Discussion

21.	If (x+iy)^(1//3)=a+ib, " then " (x)/(a)+(y)/(b) equals
Answer» `4(a^(2)-b^(2))` `2(a^(2)-b^(2))` `2(a^(2)+b^(2))` None of these Solution :We KNOW that `(VEC(a)xxvec(b)).(vec(c )xxvec(d))=\|(vec(a).vec(c),vec(a).vec(d)),(vec(b).vec(c ),vec(b).vec(d))\|=\|(lambda,4),(9,lambda)\|=lambda^(2)-36` Since `vec(a)xxvec(b)` and `vec(c)xxvec(d)`are prependicular so `lambda = 6`.

Discussion

22.	Prove that the sequence x_(1)=sqrtx, x_(2)=sqrt(a+sqrta), x_(3)=sqrt(a+sqrt(+sqrt(a)), x_(n)=sqrt(a+sqrt(a+.....+sqrta)) has the limits b=(sqrt(4a+1)+1)//2
Answer» ANSWER :s

Discussion

23.	Two particles A and B move from rest along a straight line with constant accelerations f and h respectively. If A takes m seconds more than B and describes n units more than that of B acquiring the same speed, then
Answer» `(f+h)m^2=fhn` `(f-h)m^2=fhn` `(h-f)N=(1)/(2)fhm^2` `(1)/(2)(f+h)n=fhm^2` ANSWER :C

Discussion

24.	If (x)/(b)+ (b)/(x)=(a)/(b)+(b)/(a)then x=
Answer» `a^2orb^2 // a^3` ` a orb^2 //a` `a^2orb//a` `a orb^2 // a^2 ` ANSWER :B

Discussion

25.	Let 0 lt P(A) lt 1, 0 lt P(B) lt 1 and P(AcupB) = P(A) + P(B) - P(A) P(B). Then
Answer» P(B\|A) = P(B) - P(A) `P(A^(C)cupB^(C)) = P(A^(C))+P(B^(C))` `P(AcupB)^(C) = P(A^(C)).P(B^(C))` P(A\|B) = P(A)\|P(B) ANSWER :C

Discussion

26.	After a day filled with adventures in Tehran, you now reach the bank of Hari river. There you find a box that contains the key to the boat which can help you cross the river quickly. The box can be opened only if the correct password is entered. On the top part of the box there is a number carved.“101111830140311” The box you have got can be opened by deciphering the code number given on the top of the box which would provide you the password. The password consists only English alphabets (capital). Each alphabet is coded by a three digit number in which the ones-place is given by the number of curved lines in that alphabet and the tens- place is given by the number of straight lines in the alphabet. To find the hun- dredths-place digit first place all the alphabets with the same last two digits together in their alphabetical order and interchange the first half with the second half. Now number them 1 onwards and thus the corresponding number will take the hundredths-place. Example: Let these letters (of some unknown alphabet) be the ones having one curved line and one straight line in ascending order then they will be coded as- (Consider “B” to have 2 curves and 1 straight line whereas “U” to have only a curved line. Also consider these letter as shown here: GIJQRY) What is the correct password ?
Answer» SQYWD SPIWD SQIMJ UPYMJ Solution :B The procedure has been CLEARLY described in the question. So, FIND out the 3 DIGIT alphabet corresponding to all the English alphabets. Therefore, the final answer should be SPIWD.

Discussion

27.	Find the maximum and minimum values, if any, of the functions given by f(x) = x^(3) + 1
Answer» ANSWER :NEITHER MINIMUM nor MAXIMUM VALUE

Discussion

28.	(x+1)/(2) =(y-1)/(1)=(z-9)/(-3) "and" (x-3)/(2) =(y+15)/(-7) =(z-9)/(5)
Answer» ANSWER :`4sqrt(3)" UNITS" x=y =Z`

Discussion

29.	Observe the following lists. {:("LIST - I","LIST - II"),((A) 8^(th)" term of log"_(e)^(2) " is",(1)log((n+1)/(n-1))),((B)7^(th)" term of log"_(e )(5//4)" is",(2)(-1)/(8)),((C )n^(th)" term of log"_(e )(3//2)" is",(3)(1)/(7.4^(7))),((D)(2)/(n^(2)+1)+(1)/(3)((2n)/(n^(2)+1))^(3)+.....,(4)( (-1)^(n-1))/(n.2^(n))):} The correct match for List-I from List-II is
Answer» `{:(A,B,C,D),(2,3,4,1):}` `{:(A,B,C,D),(2,3,1,4):}` `{:(A,B,C,D),(2,4,3,1):}` `{:(A,B,C,D),(3,2,4,1):}` ANSWER :A

Discussion

30.	int _(0) ^(pi) ((ax +b) sec c tan x)/(4 + tan ^(2) x ) dx (a,b gt 0)
Answer» ANSWER :`((api+ 2B)PI)/(3 SQRT3)`

Discussion

31.	The three sides of a trapezium are equal, each being 6 cm long, find the area of the trapeziumwhen it is maximum.
Answer» ANSWER :`27sqrt3` SQ. CM

Discussion

32.	For a positive constant a find (dy)/(dx), where y= a^(t+(1)/(t))," and "x=(t+(1)/(t))^(a).
Answer» ANSWER :`(a^(t+(1)/(t))LOGA)/(a(t+(1)/(t))^(a-1))`

Discussion

33.	If x^4-1=0 then x=
Answer» `(1pm i)/(SQRT2),(-1 pm i)/(sqrt2)` `(1pm i)/(2),(-1 pm i)/(sqrt2)` `(1pm i)/(sqrt2),(-1 pm i)/(2)` `pm 1, pm i` ANSWER :A

Discussion

34.	Compute the 2!^(3!)
Answer» SOLUTION :`2!^(3!)=2^6=64`

Discussion

35.	If1,-2,3are therootsofx^3 -6x^2 +9 x-4=0 then find' alpha'
Answer» ANSWER :`4`

Discussion

36.	Compute the 2^3!
Answer» SOLUTION :`2^3!=8!=40320`

Discussion

37.	Find the variance for the discrete data given below . 350,361,370,373,376,379,385,394,395
Answer» ANSWER :`9.25`

Discussion

38.	Find the projection of the point (7,-5,3) on zx-plane
Answer» SOLUTION :(7,0,3,),

Discussion

39.	Verify that y=sqrt(a^(2)-x^(2)) is a solution of the differential equation x+ydy/dx=0
Answer» Answer :`y=sqrt(a^(2)-X^(2))` is a SOLUTION for the DIFFERENTIAL equation

Discussion

40.	If g(x) =x^(2)+x-2 and 1/(2) (gof) (x) =2x^(2)-5x+2 then f(X) =........
Answer» `2x-3` `2x+3` `2x^2+3x+1` `2x^2-3x-1` SOLUTION :N/A

Discussion

41.	If AP, BQ and CR are the altitudes of acute triangleABC and 9AP+4BQ+7CR=0 Q. angleACB is equal to
Answer» `(PI)/(4)` `(pi)/(3)` `cos^(-1)((1)/(3sqrt(7)))` `cos^(-1)((1)/(sqrt(7)))` Answer :B

Discussion

42.	Evaluate the following definite integrals as limit of sums : int_(0)^(2)(e^(x)-x)dx
Answer» ANSWER :`E^(2)-3`

Discussion

43.	int sqrt(2x^(2)+3x+4)dx=
Answer» ANSWER :`=LOG[(4x+3)+2sqrt(2)SQRT(2X^(2)+3x+4)`

Discussion

44.	If f:RrarrR and g:R rarrR are two functions such that f(x)+f''(x)=-xg(x)f'(x) and g(x) gt 0 AA x in R then the function f^(2)(x)+(f'(x))^(2) has
Answer» a MAXIMA at x = 0 a MINIMA at x = 0 a point of inflection at x = 0 none of these Answer :A

Discussion

45.	How many ............
Answer» SOLUTION : [TOTAL 4 isomers of Z are POSSIBLE]

Discussion

46.	A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
Answer» ANSWER :`(25)/(216)`

Discussion

47.	Variable straight lines y=mx+c make intercepts on the curve y^2 -4ax=0 which subtend a right angle at the origin. Then the point of concurrence of these lines y=mx+c is
Answer» `(4a,0)` `(2a,0)` `(-4a,0)` `(-2a,0)` ANSWER :A

Discussion

48.	Find the projection of vec a
Answer» ANSWER :`(8)/(SQRT(17))`

Discussion

49.	If p and q are two propositions, Then ~ ( p vee q ) equiv ~ p ^^ ~ q ,is
Answer» a TAUTOLOGY a CONTRADICTION a simple statement none of these Answer :A

Discussion

50.	Let R denote the set of all real numbers and R^(+) denote the set of all positivereal numbers. For the subsets A and B of R define f : A to B by f(x)=x^(2) for x in A. Observe the two lists given below{:(,"Column I",,"Column II"),(A.,"f is one-one and onto, if",1.,A=R^(+)",B=R"),(B.,"f is one-one but not onto, if",2.,A=B=R),(C.,"f is onto but not one-one, if",3.,"A=R, "B=R^(+)),(D.,"f is neither one-one nor onto, if",4.,A=B=R^(+)):}
Answer» A-1, B-2, C-3, D-4 A-4, B-2, C-1, D-3 A-4, B-1, C-3, D-2 A-4, B-2, C-3, D-1 ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Prove that : (1)/(2) cos^(-1) ((1+ 2 cos x)/( 2+cosx) ) = tan^(-1) ((1)/(sqrt(3)) "tan" (x)/(2))

Solvetheequation 6x^4 -13 x^3 -35x^2-x+3=0 giventhat2 +sqrt(3)is a root

Let f(x) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):} If the number of points where f(x) is nonderivable in [–2, oo) is 3 then the value of |a + b| is (Note: [y] and sgn (y) denote greatest integer function and signum function of y respectively).

If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p-q),

Which of the following is correctly matched.

f(x) is a continuous and differentiable function. f'(x) ne 0 and |{:(f'(x),f(x)),(f''(x),f'(x)):}|=0.If f(0)=1 and f'(0)=2 then f(x)=....

Findproducts : [[1,0],[0,k]][[a,b],[c,d]]

A sequence a_(1),a_(2), …..a_(n)of real numbers is such that a_(1) = 0 ,|a_(2)|=|a_(1)-2|,|a_(3)|=|a_(2)-2|,---|a_(n)| = |a_(n-1)-2| . Then the maximum value of the arithmetic mean of these numbers is _____.

If the relation R on the set {1,2,3}be defined by R = {(1,2)}.Then , R is .........

The vectices of a triangle are A(1,7), B(-5, -1) and C(-1, 2). Then, the equation of a bisector of the angleABC is

Find |x|, if for a unit vector a (vecx-veca)(vecx+veca)=12

A balanced dice is thrown twice and the sum of the numbers appearing on the top face is observed to be 7. What is the conditional probability that the number 2 has appeared at least once ?

A strictly increeasing sequence of positive integers a _(1), a _(2), a _(3)… has the property that for ever positive integer k, the subsequence a _(2k -1), 2 _(2k), a _(2k +1) is geometric and the subsequence a _(2k), 2 _(2k +1), a _( 2k +2) is arithmetic. Suppose that a _(13)= 2016. Find a _(1).

Differntiate the following functions by proper substitution.cos^(-1)(2t^2-1)

Integrate the following functions: sin^-1x/(sqrt(1-x^2)

If a,b,c are linearly independent, ((a + 2b). (2b + c) xx (5c + a))/(a. (b xx c)) = k then k is

Value of int_(2)^(3)(dx)/(sqrt((a+x^(3)))) is

For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=vec(0)|vec(a)|=3,|vec(b)|=4,|vec( c )|=5, then evaluate 2(vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a)).

Freedom equation of a line is (whereare direction cosines) x = x_(1) + lr, y =y_(1) +mr, z=z_(1) + nr, where:

If G is the centroid of DeltaABC, then (AG^(2)+BG^(2)+CG^(2))/(AB^(2)+BC^(2)+CA^(2))=

If (x+iy)^(1//3)=a+ib, " then " (x)/(a)+(y)/(b) equals

Prove that the sequence x_(1)=sqrtx, x_(2)=sqrt(a+sqrta), x_(3)=sqrt(a+sqrt(+sqrt(a)), x_(n)=sqrt(a+sqrt(a+.....+sqrta)) has the limits b=(sqrt(4a+1)+1)//2

Two particles A and B move from rest along a straight line with constant accelerations f and h respectively. If A takes m seconds more than B and describes n units more than that of B acquiring the same speed, then

If (x)/(b)+ (b)/(x)=(a)/(b)+(b)/(a)then x=

Let 0 lt P(A) lt 1, 0 lt P(B) lt 1 and P(AcupB) = P(A) + P(B) - P(A) P(B). Then

Find the maximum and minimum values, if any, of the functions given by f(x) = x^(3) + 1

(x+1)/(2) =(y-1)/(1)=(z-9)/(-3) "and" (x-3)/(2) =(y+15)/(-7) =(z-9)/(5)

int _(0) ^(pi) ((ax +b) sec c tan x)/(4 + tan ^(2) x ) dx (a,b gt 0)

The three sides of a trapezium are equal, each being 6 cm long, find the area of the trapeziumwhen it is maximum.

For a positive constant a find (dy)/(dx), where y= a^(t+(1)/(t))," and "x=(t+(1)/(t))^(a).

If x^4-1=0 then x=

Compute the 2!^(3!)

If1,-2,3are therootsofx^3 -6x^2 +9 x-4=0 then find' alpha'

Compute the 2^3!

Find the variance for the discrete data given below . 350,361,370,373,376,379,385,394,395

Find the projection of the point (7,-5,3) on zx-plane

Verify that y=sqrt(a^(2)-x^(2)) is a solution of the differential equation x+ydy/dx=0

If g(x) =x^(2)+x-2 and 1/(2) (gof) (x) =2x^(2)-5x+2 then f(X) =........

If AP, BQ and CR are the altitudes of acute triangleABC and 9AP+4BQ+7CR=0 Q. angleACB is equal to

Evaluate the following definite integrals as limit of sums : int_(0)^(2)(e^(x)-x)dx

int sqrt(2x^(2)+3x+4)dx=

If f:RrarrR and g:R rarrR are two functions such that f(x)+f''(x)=-xg(x)f'(x) and g(x) gt 0 AA x in R then the function f^(2)(x)+(f'(x))^(2) has

How many ............

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

Variable straight lines y=mx+c make intercepts on the curve y^2 -4ax=0 which subtend a right angle at the origin. Then the point of concurrence of these lines y=mx+c is

Find the projection of vec a

If p and q are two propositions, Then ~ ( p vee q ) equiv ~ p ^^ ~ q ,is

For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=vec(0)|vec(a)|=3,|vec(b)|=4,|vec( c )|=5, then evaluate 2(vec(a)vec(b)+vec(b)vec( c )+vec( c )*vec(a)).