28278 + Interview Questions in Maths in Class 12

1.	If the pair of straight lines xy - y - y + 1 = 0 and the line ax + 2y - 3a = 0 are concurrent , then a equal to
Answer» 0 1 `-1` 3 Answer :B

Discussion

2.	Lines (x)/(1)=(y-2)/(2)=(z+3)/(3)" and "(x-2)/(2)=(y-6)/(3)=(z-3)/(4) are
Answer» parallel perpendicular coplanar non-coplanar Answer :C

Discussion

3.	If A is skew symmetric matrix , then A^(2) is a symmetric matrix .
Answer» ANSWER :TRUE

Discussion

4.	underset(x to 0-)"Lt" cot x=
Answer» 0 `OO` `-oo` does not exist Answer :C

Discussion

5.	Consider the followingcurves: C_(1):x^(2)+y^(2)=4," " C_(2):x^(2)-2sqrt3y=3, " " C_(3)+sqrt3, " "C_(3):x^(2)+2sqrt3y=3-sqrt3 Statement-1: Parabolas C_(2)and C_(3) have the same latusrectum, the line joining the end -points oflatusrecla of the ellipse C_(1) with negative ordinates. Statement-2: Common chord of C_(2) and C_(3) is a laturectum of C_(1).
Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT explanation for Statement-1 Statement-1 is True, Statement-2 is True, Statement -2 is not a correct explanation for Statement-1 Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True Solution :See EXAMPLE 41 on page 25.37.

Discussion

6.	Obtain the following integrals : int sqrt((a+x)/(a-x))dx
Answer» Answer :`:.I=a sin^(-1)((X)/(a))- SQRT(a^(2)-x^(2))+C`

Discussion

7.	underset(x to 0+)"Lt" cot x=
Answer» 0 `OO` `-oo` does not exist Answer :B

Discussion

8.	Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)} be a relation on the set A= {3,6,9,12} The relation is
Answer» an equialence RELATION REFLEXIVE and SYMMETRIC only reflexive and TRANSITIVE only reflexive only Answer :C

Discussion

9.	The mid point of the chord x-2y+7=0 w.r.t the circle x^(2)+y^(2)-2x-10y+1=0 is
Answer» `(7,21)` `(7/4,21/4)` `(7/5,21/5)` `((-7)/4,(-21)/4)` ANSWER :C

Discussion

10.	Using properties of determinants in Exercises prove that : {:\|( alpha , alpha ^(2) ,beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) \|:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )
Answer» ANSWER :`x=2,y=3,z=5`

Discussion

11.	A fair coin is tossed repeatedly. If tails appear on first four tosses, what is the probability of head appearing on the fifth toss ?
Answer» SOLUTION :When a FAIR coin is tossed, each toss is independent of other `therefore` (HEAD in 5th toss) =1/2

Discussion

12.	Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is
Answer» 1)`3/9` 2)`8/9` 3)`5/9` 4)`4/9` ANSWER :C

Discussion

13.	Choose the correct answer inte^(x)secx(1+tanx)dx equals
Answer» `e^(x) cos x + C` `e^(x) SEC x + C` `e^(x) SIN x + C` `e^(x) tan x + C` ANSWER :B

Discussion

14.	Vertify mean value theorem for the following functions: f(x)= x- 2 sin x, x in [-pi, pi]
Answer» ANSWER :`(PI)/(2)`

Discussion

15.	Evaluate the following integrals f x cosh^(-1)x dx
Answer» ANSWER :`(1)/(4)[(2X^(2)+1)COSH^(-1)X-xsqrt(x^(2)-1)]+c`

Discussion

16.	int((x^(2) +1))/(x^(4) + 7x^(2) + 1) dx =
Answer» `(1)/(3) tan^(-1) ((X^(2) - 1)/( 3x) )+ c ` `tan^(-1) ((x^(2) - 1)/( 3x) )+ c ` `(1)/(3) tan^(-1) ((x^(2) - 1)/( 3x) )+ c ` `(1)/(SQRT(3)) tan^(-1) ((x^(2) - 1)/( 3x) )+ c ` Answer :A

Discussion

17.	A value of k each that the straight lines y - 3kx + 4 = 0 and (2k - 1) x - (8k - 1) y - 6= 0 are perpendicular
Answer» `(1)/(6)` `-(1)/(6)` 1 0 Answer :a

Discussion

18.	Evaluate the definite integral in exercise overset(1)underset(0)int(x e^(x)+"sin"(pix)/(4))dx
Answer» ANSWER :`1+(4)/(PI)XX (2 sqrt(2))/(pi)`

Discussion

19.	If f(x)={{:(x " for"x lt 1),(x-1 " for "x ge1):} then int_(0)^(2)x^(2)f(x)dx=
Answer» `5/3` `3/5` `- 5/3` `- 3/5` ANSWER :A

Discussion

20.	The value of the integratio int_(-pi//4)^(pi//4)(lambda\|sinx\|+(mu sinx)/(1+cosx)+gamma)dx
Answer» is independent of `LAMBDA` only is independent of `mu` only is independent of `GAMMA` only depends on `lambda, mu and gamma` Answer :B

Discussion

21.	One of the methods of determining mode is
Answer» MODE = 2 MEDIAN - 3 mean mode = 2 median + 3 mean mode = 2 median - 2 mean mode = 3 median + 3 mean Answer :C

Discussion

22.	Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b). Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 externally.
Answer» ANSWER :`4bar(B)-BAR(a)`

Discussion

23.	Consider two points P ans Q with position vectors bar(OQ)=bar3(a)+bar2(b) and bar(OQ)=bar(a)+bar(b). Find the position the line joining P and Q in the ratio 2 : 1internally
Answer» ANSWER :`(5bar(a))/(3)`

Discussion

24.	If the function f(x) satisfies lim_(x rarr 1) (f(x) - 2)/(x^(2) - 1) = pi, then lim_(x rarr 1) f(x) =
Answer» 1 2 0 3 Answer :B

Discussion

25.	Three matrices are given as A = [{:( alpha ^(2) ,4,6),(9,beta ^(4) , 7),( 1,2,2gamma ^(2)):}] B= [{:( 2beta ^(2),-1,0),( 2,gamma^(2)-2gamma ,1),( 1,9,2alpha-1):}] C= [{:( gamma , 2,1),(1,alpha , 1),(2,0,beta ) :}] If Tr(A)=Tr (B) -2 and alpha, beta , gamma in Rthen det( c) can be
Answer» `-1` `2` 5 0 Answer :A::C

Discussion

26.	Differentiate cos(x^3). sin^(2)(x^5) with respect to x.
Answer» Answer :`10x^(4)sin x^(5) COSX^(5) cox^(3) -3X^(2) sinx^(3)sin^(2)x^(5)`.

Discussion

27.	If alpha and beta be the coefficients of x^4 and x^2 respectively in the expression of (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6, then :
Answer» `alpha+beta=-30` `alpha-beta=-132` `alpha+beta=60` `alpha-beta=60` ANSWER :B

Discussion

28.	Let f(x)={{:(3x^2-2x+10, x lt 1),(-2,x gt 1):} The set of values of b for which f(x) has greatest value at x=1 is
Answer» `(-6,-2)` (2,6) `(-6,-2)cup (2,6)` `(-6,6)` Solution :we have `f(x)={{:(3x^2-2x+10, x lt 1),(-2,x gt 1):}` Clealy `f(x) gt 0 for x lt 1 ` and`f(x)lt 0 for x gt 1` Thus f(x) is INCREASING for all `x lt 1` and decreasing for `x gt 1` Therfore f(x) will have grastest value at x=1 if `underset(x to 1)lim f(x)lt f(1)=underset(x to 1)limf(x)` `rArr underset(x to 1)lim -2x+log_2 (b^2-4)lt -1+10-7` `rArr-2 + LOG _2(b^2-4) lt 3` `rArrlog_2(b^2 -4)lt 5` `b^2 -36 lt 0 and b^2 -4 gt 0 ` `rArr-6 lt b lt 6and b in (-oo,-2) cup (2,oo)` `RARRB in (-6,-2) cup (2,6)`

Discussion

29.	Identify the wrong statement from the below
Answer» `~[PVV(~q)]cong(~p)^^q` `[vvq]VV(~p)` is tautology `[p^^q]^^(~p)` is a CONTRADICTION `~(PVVQ)-=(~p)vv(~q)` Answer :D

Discussion

30.	if the two circles x^2 + y^2 + 2gx + 2fy = 0 and x^2 + y^2 + 2g'x + 2 f'y = 0 touch each other then show that f'g = fg'
Answer» ANSWER :`G'F`

Discussion

31.	If f'(x)=x-(1)/(x^(2)) and f(1)=(1)/(2) then find f(x).
Answer» ANSWER :`(X^(2))/(2)+(1)/(x)-1`

Discussion

32.	The power of the point B(-1,1) with respect to the circle S equiv x^(2) + y^(2) -2x -4y + 3 = 0is p. If the length of the tangent drawn from B to the circles S = 0 is t , then the point (2, 3) with respect to circle S' = 0 having centre at (p, t^(2)) and passing through the origin.
Answer» lies inside the CIRCLE `S' = 0` lies OUTSIDE the circle `S'= 0` lies on the circle `S' = 0` is the centre of the circle `S'= 0` ANSWER :A

Discussion

33.	State which of the following statements are true (T) or false(F) The line (x-2)/3=(1-y)/4=(5-z)/1 is parallel to the plane 2x -y-2z=0.
Answer» ANSWER :F

Discussion

34.	A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30^(@), and when he moves up further a distance c metres the angle of depression of that point is 45^(@). The angle of inclination of the slope with the horizontal is (Man starts from bottom of slope)
Answer» `60^(@)` `45^(@)` `75^(@)` `30^(@)` Solution :Applying m - n THEOREM of TRIGONOMETRY we GET `(C + c) cot (THETA-30^(@))c cot 15^(@) - c cot 30^(@)` or `cot (theta -30^(@)) = 1` `= theta - 30^(@) = 45^(@)` `:. theta = 75^(@)`

Discussion

35.	The solution of the differential equation dy - (ydx)/(2x) = sqrt(x) ydy is (where , c is an arbitrary constant)
Answer» `y/(SQRTX) = y + c` `y/(sqrtx) = (y^2)/2 + c` `y = ysqrt(x) + c` `y/(sqrtx) = -y^(2)+ c` Answer :B

Discussion

36.	On a holiday, a father gave a puzzle from a newspaper to his son Ravi and his daughter Priya. The probabiliy of solving this specific puzzle independent by Ravi and Priya are (1)/(4) and (1)/(5) respectively. Based on the above information, answer the following questions. The chance that both Ravi and Priya solved the Puzzle, is
Answer» `10%` `5%` `25%` `20%` ANSWER :B

Discussion

37.	sin A + 2 sin 2 A + sin 3 Ais equal to which of the following ? 1.4sin2Acos^(2)((A)/(2)) 2.2 sin2A("sin"(A)/(2)+"cos"(A)/(2))^(2)3.8sin A cos A cos ^(2)((A)/(2))Select the correct answer using the code given below :
Answer» 1 and 2 only 2 and 3 only 1 and 3only 1 , 2 and 3 Solution :LET`A=30^(@)` `rArrsinA+2sin2A=sin3A=sin30^(@)+2sin60^(@)+sin90^(@)` `=(1)/(2)+(2sqrt(3))/(2)+1=(2sqrt(3)+3)/(2)` `(because2cos^(2)A=1+cos2A)` Now , `4sin2Acos^(2)((A)/(2))=2sin2A[1+cosA]` `=2sin60^(@)[1+COS30^(@)]=(2sqrt(3)+3)/(2)` Also ,`sin2A=2sinAcosA&SIN^(2)A+cos^(2)A=1` `2sin2A["sin"(A)/(2)+"cos"(A)/(2)]^(2)` `=2sin2A["sin"^(2)(A)/(2)"cos"^(2)(A)/(2)+2"sin"(A)/(2)"cos"(A)/(2)]` `=2sin2A[1+sinA]=2sin60^(@)[1+sin30^(@)]` `=(3sqrt(3))/(2)` & 8 sin A cos A`cos^(2)((A)/(2))` `=4sinAcosA[1+cosA]` `=4sin30^(@)cos30^(@)[1+cos30^(@)]` `=(2sqrt(3)+3)/(2)`

Discussion

38.	The radius of the circle passing through the point (6,2) and two of whose diameter are x + y = 6 and x + 2y = 4 is
Answer» `4` `6` `20` `SQRT(20)` ANSWER :D

Discussion

39.	Evaluation of definite integrals by subsitiution and properties of its : If I_(n)=int_(pi//4)^(pi//2)cot^(n)xdx, then 100(I_(99)+I_(101))=.......
Answer» 100 0 1 `-1` ANSWER :C

Discussion

40.	If the sum of first 75 terms of an A.P. is 2625, then the 38^(th) term of the A.P. is
Answer» 39 37 36 35 Answer :D

Discussion

41.	Lt_(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=
Answer» `1/2` `1/5` `1/10` `1/15` ANSWER :C

Discussion

42.	Without expanding at any stage, prove that \|(a-b,1,a),(b-c,1,b),(c-a,1,c)\| = \|(a,1,b),(b,1,c),(c,1,a)\|
Answer» ANSWER :`OO`

Discussion

43.	Shortest distance between z-axis and the line(x-2)/(3) =(y-5)/(2) =(z+1)/(-5)is
Answer» `1//SQRT(13)` ` 11//13` ` sqrt(11) //13` ` 11//sqrt(13)` ANSWER :D

Discussion

44.	If Integration using rigonometric identities : int(dx)/(sqrt(sin^(3)x(sinx+2cosx)))=f(x)+c then f((pi)/(4))=....
Answer» `-1` `-sqrt(2)` `-sqrt(3)` `-2` ANSWER :C

Discussion

45.	If the bisectors of the angles between the lines given by 3x^(2)-4xy+5y^(2)=0 and 5x^(2)+4xy+3y^(2)=0 asre same, then, the angle made by the lines in the first pair with the second is
Answer» `30^(@)` `60^(@)` `45^(@)` `90^(@)` ANSWER :D

Discussion

46.	If the roots of ax^(2)+ bx + c = 0 are equal in magnitude but opposite in sign, then
Answer» `a lt 0, C lt 0` `a lt 0, c gt 0, b gt 0` `a gt 0, b = 0, c lt 0` `a gt 0, b = 0, c gt 0` ANSWER :C

Discussion

47.	If cos x cos y=asin x+siny=b then prove that sin (x+y)=(2ab)/(a^(2)+b^(2))
Answer» ANSWER :`(2AB)/(a^(2)+B^(2))`

Discussion

48.	A special die with numbers 1, -1, 2, -2, 0 and 3 is thrown thrice. What is the probability that the total is 0.
Answer» ANSWER :`(25)/(216)`

Discussion

49.	A bag contains 5 balls the colours of which are not known. Two balls are drawn and found them to be red. Find the probability that all the balls in the bag are red.
Answer» ANSWER :`(1)/(2)`

Discussion

50.	Consider a pair of perpendicular straight lines ax^(2)+3xy-2y^(2)-5x+5y+c=0.Distance between the orthocenter and the circumcenter of triangle ABC is
Answer» 4 `9//2` `8//3` `7//4` Solution :Asthe lines are perpendicular,Coefficient of `x^(2)+` Coefficient of `y^(2)=0` `:.a-2=0` or `a=2` Also , `abc+2fgh-af^(2)-bg^(2)-ch^(2)=0` `:. C=-3` HENCE , the given pair of lines is `2x^(2)+3xy-2y^(2)-5x+5y-3=0` Factorizing , we get lines `x+2y-3=0and 2x-y+1=0` The point of INTERSECTION of the lines is C `(1//5,7//5)`. The points of intersection of the lines with the x- axis are A(3,0) and B `(-1//2,0)`. The orthocenter of triangle isC `(1//5,7//5)` and the CIRCUMCENTER is the midpoint of AB which isM `(5//4,0)`.Therefore, CM`sqrt(((5)/(4)-(1)/(5))^(2)+(49)/(25))=(7)/(4)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the pair of straight lines xy - y - y + 1 = 0 and the line ax + 2y - 3a = 0 are concurrent , then a equal to

Lines (x)/(1)=(y-2)/(2)=(z+3)/(3)" and "(x-2)/(2)=(y-6)/(3)=(z-3)/(4) are

If A is skew symmetric matrix , then A^(2) is a symmetric matrix .

underset(x to 0-)"Lt" cot x=

Obtain the following integrals : int sqrt((a+x)/(a-x))dx

underset(x to 0+)"Lt" cot x=

Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)} be a relation on the set A= {3,6,9,12} The relation is

The mid point of the chord x-2y+7=0 w.r.t the circle x^(2)+y^(2)-2x-10y+1=0 is

Using properties of determinants in Exercises prove that : {:|( alpha , alpha ^(2) ,beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) |:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )

A fair coin is tossed repeatedly. If tails appear on first four tosses, what is the probability of head appearing on the fifth toss ?

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

Choose the correct answer inte^(x)secx(1+tanx)dx equals

Vertify mean value theorem for the following functions: f(x)= x- 2 sin x, x in [-pi, pi]

Evaluate the following integrals f x cosh^(-1)x dx

int((x^(2) +1))/(x^(4) + 7x^(2) + 1) dx =

A value of k each that the straight lines y - 3kx + 4 = 0 and (2k - 1) x - (8k - 1) y - 6= 0 are perpendicular

Evaluate the definite integral in exercise overset(1)underset(0)int(x e^(x)+"sin"(pix)/(4))dx

If f(x)={{:(x " for"x lt 1),(x-1 " for "x ge1):} then int_(0)^(2)x^(2)f(x)dx=

The value of the integratio int_(-pi//4)^(pi//4)(lambda|sinx|+(mu sinx)/(1+cosx)+gamma)dx

One of the methods of determining mode is

Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b). Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 externally.

Consider two points P ans Q with position vectors bar(OQ)=bar3(a)+bar2(b) and bar(OQ)=bar(a)+bar(b). Find the position the line joining P and Q in the ratio 2 : 1internally

If the function f(x) satisfies lim_(x rarr 1) (f(x) - 2)/(x^(2) - 1) = pi, then lim_(x rarr 1) f(x) =

Three matrices are given as A = [{:( alpha ^(2) ,4,6),(9,beta ^(4) , 7),( 1,2,2gamma ^(2)):}] B= [{:( 2beta ^(2),-1,0),( 2,gamma^(2)-2gamma ,1),( 1,9,2alpha-1):}] C= [{:( gamma , 2,1),(1,alpha , 1),(2,0,beta ) :}] If Tr(A)=Tr (B) -2 and alpha, beta , gamma in Rthen det( c) can be

Differentiate cos(x^3). sin^(2)(x^5) with respect to x.

If alpha and beta be the coefficients of x^4 and x^2 respectively in the expression of (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6, then :

Let f(x)={{:(3x^2-2x+10, x lt 1),(-2,x gt 1):} The set of values of b for which f(x) has greatest value at x=1 is

Identify the wrong statement from the below

if the two circles x^2 + y^2 + 2gx + 2fy = 0 and x^2 + y^2 + 2g'x + 2 f'y = 0 touch each other then show that f'g = fg'

If f'(x)=x-(1)/(x^(2)) and f(1)=(1)/(2) then find f(x).

The power of the point B(-1,1) with respect to the circle S equiv x^(2) + y^(2) -2x -4y + 3 = 0is p. If the length of the tangent drawn from B to the circles S = 0 is t , then the point (2, 3) with respect to circle S' = 0 having centre at (p, t^(2)) and passing through the origin.

State which of the following statements are true (T) or false(F) The line (x-2)/3=(1-y)/4=(5-z)/1 is parallel to the plane 2x -y-2z=0.

The solution of the differential equation dy - (ydx)/(2x) = sqrt(x) ydy is (where , c is an arbitrary constant)

sin A + 2 sin 2 A + sin 3 Ais equal to which of the following ? 1.4sin2Acos^(2)((A)/(2)) 2.2 sin2A("sin"(A)/(2)+"cos"(A)/(2))^(2)3.8sin A cos A cos ^(2)((A)/(2))Select the correct answer using the code given below :

The radius of the circle passing through the point (6,2) and two of whose diameter are x + y = 6 and x + 2y = 4 is

Evaluation of definite integrals by subsitiution and properties of its : If I_(n)=int_(pi//4)^(pi//2)cot^(n)xdx, then 100(I_(99)+I_(101))=.......

If the sum of first 75 terms of an A.P. is 2625, then the 38^(th) term of the A.P. is

Lt_(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=

Without expanding at any stage, prove that |(a-b,1,a),(b-c,1,b),(c-a,1,c)| = |(a,1,b),(b,1,c),(c,1,a)|

Shortest distance between z-axis and the line(x-2)/(3) =(y-5)/(2) =(z+1)/(-5)is

If Integration using rigonometric identities : int(dx)/(sqrt(sin^(3)x(sinx+2cosx)))=f(x)+c then f((pi)/(4))=....

If the bisectors of the angles between the lines given by 3x^(2)-4xy+5y^(2)=0 and 5x^(2)+4xy+3y^(2)=0 asre same, then, the angle made by the lines in the first pair with the second is

If the roots of ax^(2)+ bx + c = 0 are equal in magnitude but opposite in sign, then

If cos x cos y=asin x+siny=b then prove that sin (x+y)=(2ab)/(a^(2)+b^(2))

A special die with numbers 1, -1, 2, -2, 0 and 3 is thrown thrice. What is the probability that the total is 0.

A bag contains 5 balls the colours of which are not known. Two balls are drawn and found them to be red. Find the probability that all the balls in the bag are red.

Consider a pair of perpendicular straight lines ax^(2)+3xy-2y^(2)-5x+5y+c=0.Distance between the orthocenter and the circumcenter of triangle ABC is