28278 + Interview Questions in Maths in Class 12

1.	(i) Find the area bounded by x^(2)+y^(2)-2x=0 and y = sin'(pix)/(2) in the upper half of the circle. (ii) Find the area bounded by the curve y = 2x^(4)-x^(2), x-axis and the two ordinates cooreponding to the the minima to the function. (iii) Find area of the curve y^(2) = (7-x)(5+x) above x-axis and between the ordinates x = - 5 and x = 1.
Answer» SOLUTION :N//A

Discussion

2.	If x - coordinateof a point P on theline joining the [points Q(2,2,1) and R (5,1,-2)is 4 , then the z - cossrdinate of P is
Answer» `-2` `-1` 1 2 Answer :B

Discussion

3.	Find the sum of n-terms of the series 2.5 + 5.8 + 8.11 +……..
Answer» Answer :`=3N (n +1) ^(2) - 2n`

Discussion

4.	Evaluate the following integrals (vi) int_(0)^(1)e^(x) sin h x dx.
Answer» ANSWER :`(E^(2)-3)/(4)`

Discussion

5.	The solution of (dy)/(dx) + (3x^(2) y)/(1 + x^(3)) = (1+ x^(2))/(1 + x^(3)) is
Answer» `y(1+X^(3)) = x+(x^(3))/(3)+C` `y(1-x^(3)) = x+(x^(3))/(3)+c` `y(1+x^(3)) = x-(x^(3))/(3)+c` `y(1-x^(3)) = x-(x^(3))/(3)+c` ANSWER :A

Discussion

6.	Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).
Answer» ANSWER :`3/2`

Discussion

7.	1+3/(1!) +5/(2!) + (7)/(3!) + ......oo=
Answer» E `2E` 3 e 4e Answer :C

Discussion

8.	Determine if the set A ={-1,1,3}is a proper subset of the set B={x:x in R and x^3-2x^2-x+2=0}
Answer» SOLUTION :Solving `x^3-2x^2-c+2=0` we have `x^2(x-2)-1(x-2)=0` or, `(x-2)(x^2-1)=0` `:.`x=1,-1,2` `:. B ={-1,1,2}` `:.`A is not a subset of B.

Discussion

9.	From the point A(0,3) on the circle x^(2)+4x+(y-3)^(2)=0, a chord AB is drawn and extended to a point P, such that AP=2AB. The locus of P is
Answer» `X^(2)+4X+(y-3)^(2)=0` `x^(2)+8x+(y-3)^(2)=0` `x^(2)+4x-(y-3)^(2)=0` `x^(2)+8x-(y-3)^(2)=0` Answer :B

Discussion

10.	Compute the product A = Z, B = phi
Answer» SOLUTION :A = Z , B = `PHI THEREFORE A xx B = phi`

Discussion

11.	For all values of A, B, C and P, Q, R \|(cos(A-P), cos(A-Q),cos(A-R)),(cos(B-P), cos(B-Q), cos(B-R)),(cos(C-P), cos(C-Q), cos(C-R))\|=
Answer» `COS A cos B cos C` `cos PcosQ cos R` 0 1 Answer :C

Discussion

12.	A man running on a race course notices that the sum of the distances of the two flag posts from him is always 10m and the distance between the flag posts is 8m. Find the equation of the race course traced by the man.
Answer» ANSWER :`x^2/25+y^2/9=1`

Discussion

13.	Find dy/dx, if sin^(2)x+cos^(2)y=1.
Answer» ANSWER :`thereforedy/dx=(SIN2X)/(sin2y)`

Discussion

14.	intsqrt(1-sin2xdx),x in[-(3pi)/(4),(pi)/(4)]
Answer» ANSWER :`-(sinx+cosx)+C`

Discussion

15.	If the chord of contact of tangents from a point to a given circle passes through Q , then the circle on PQ as diameter
Answer» CUTS the given CIRCLE orthogonally TOUCHES the given circle externally touches the given circle internally none ANSWER :A

Discussion

16.	Let omega=-(1)/(2)+i (sqrt(3))/(2), then the value of [[1,1,1],[1,-1-omega^(2),omega^(2)],[1,omega^(2),omega^(4)]] is
Answer» `3OMEGA` `3omega(omega-1)` `3omega^2` `3omega(1-omega)` ANSWER :B

Discussion

17.	If [(alpha,beta),(gamma,-alpha)] is square root of identity matrix of order 2 then-
Answer» `1+ALPHA^(2)+betagamma=0` `1+alpha^(2)-betagamma=0` `1-alpha^(2)+betagamma=0` `alpha^(2)+betagamma=1` ANSWER :D

Discussion

18.	If the first three terms in the expansion of (1 -ax)^n where n is a positive integer are 1,-4x and 7x^2 respectively then a =
Answer» `1//5` `1//4` `1//3` `1//2` ANSWER :D

Discussion

19.	Find the slope of the tangent to the curve y = x^(3) –3x + 2 at the point whose x-coordinate is 3.
Answer» ANSWER :24

Discussion

20.	The solutionof(dy)/(dx)=( x+y)/(x-y) is
Answer» `tan ^(-1) ((y)/(x))= logsqrt(x^2+y^2)+C` `tan ^(-1) ((y)/(x))= LOG sqrt((x^2-y^2 )+ c ` `sin ^(-1)((y)/(x)) log sqrt(x^2 +y^2) + c` `cos ^(-1)((y)/(x))= logsqrt(x^2 - y^2) + C` ANSWER :A

Discussion

21.	If -2-i is a root of the equation ax^(2)+12x+b=0 (where a and b are real), then the value of ab is equal to
Answer» `45` `15` `-15` `-45` ANSWER :A

Discussion

22.	The equation of parabola whose latus rectum isthe line segment joining the points (-3,1) , (1,1) is
Answer» ANSWER :`2X^(2)=10(2y+3) (or) 2x^(2)=-10(2y-7)`

Discussion

23.	Find P^(-1), if the exists, given P=[(10,-2),(-5,1)]
Answer» <P> ANSWER :`P^(-1)` does not EXIST.

Discussion

24.	If x=sinh^(-1)[log(1+sqrt(y)], " then "(dy)/(dx)=
Answer» `2(y+sqrt(y))SINHX` `2(y+sqrt(y))sqrt(1-(LOG(1+sqrt(y)))^(2))` `2(y+sqrt(y))(coshx` `2(y+sqrt(y))log(1+sqrt(y))` ANSWER :C

Discussion

25.	Out of 52 cards 4 are drawn at random without replacement. What is the probability that (i) they belong to different suits (i.e., one from each suit) (ii) they belong to different denominations
Answer» ANSWER :`(i) (13^(4))/(.^(52)C_(4))` `(ii) ((.^(13)C_(4))xx4^(4))/(.^(52)C_(4))`

Discussion

26.	1/2.""^10C_0 -""^10C_1 +2.""^10C_2 - 2^2.""^10C_3+…..+2^9. ""^10C_10 =
Answer» `1//2` `1//4` `3//2` `1//3` ANSWER :A

Discussion

27.	Which of the following is noth the number of ways of selecting n objects from 2n objects of which n objects are identical
Answer» `2^(n)` `("^(2n+1)C_(0)+^(2n+1)C_(1)+...+^(2n+1)C_(n))^(1//2)` the number of POSSIBLE subsets `{a_(1),a_(2),….,a_(n)}` None of these Solution :`(d)` We can take `0` indentical and `n` distinct , `1` IDENTICAL and `n-1` distinct , `2` identical and `n-2` distinct and so on… `:.` Total no. of solutions `=sum_(r=0)^(n).^(n)C_(r )=2^(n)` No. of possible subsets of a set containing `n` elements is `2^(n)` and `.^(2n+1)C_(0)+^(2n+1)C_(1)+^(2n+1)C_(2)+...+^(2n+1)C_(n)=2^(2n)`

Discussion

28.	Let A, B, C, D, E represent vertices of a regular pentagon ABCDE. Given the position vector of these vertices be veca, veca + vecb, vecb, lamda veca andlamda vecb, respectively. AD divides EC in the ratio
Answer» `cos""(2pi)/(5) : 1` `cos""(3pi)/(5) : 1` `1 : 2 cos""(2pi)/(5)` `1 : 2` Solution :Given ABCDE is a regular pentagon Let position vector of POINT A and C be `VECA and veb`, respectively. `AD` is parallel to BC and AB is parallel to EC. Therefore, AOCB is a PARALLELOGRAM and position vector of B is `veca + VECB` The position vectors of E and D are `lamdavecb and lamda veca`respectively. Also `OA = BC = AB= OC =1` (let) Therefore, AOCB is rhombus. `angle ABC = angle AOC = (3pi)/(5)` and `angleOAB = angle BCO = pi - (3pi)/(5) = (2pi)/(5)` Further `OA = AE = 1 and OC = CD = 1 ` Thus, `DeltaEAO and Delta OCD` are isosceles. In `Delta OCD`, using sine rule we get `(OC)/(sin""(2pi)/(5))= (OD )/( sin""(pi)/(5))` `rArr OD = (1)/( 2 cos ""(pi)/(5)) = OE` `rArr AD = OA + OD = 1 + (1)/(2 cos ""(pi)/(2))` `rArr (AD)/(BC) =1 + (1)/(2 cos""(pi)/(5)) = (1 +2 cos""(pi)/(5))/( 2 cos""(pi)/(5))` And `(OE)/( OC) = (1)/( 2cos ""(pi)/(5))`

Discussion

29.	Let A, B, C, D, E represent vertices of a regular pentagon ABCDE. Given the position vector of these vertices be veca, veca + vecb, vecb, lamda veca andlamda vecb, respectively. The ratio (AD)/(BC) is equal to
Answer» `1-cos""(3pi)/(5) : cos""(3pi)/(5)` `1+ 2cos""(2pi)/(5): cos ""(PI)/(5)` `1 + 2 cos""(pi)/(5) : 2 cos""(pi)/(5)` None of these Solution :Given ABCDE is a regular pentagon Let position vector of point A and C be `veca and veb`, respectively. `AD` is parallel to BC and AB is parallel to EC. THEREFORE, AOCB is a parallelogram and position vector of B is `veca + vecb` The position vectors of E and D are `lamdavecb and lamda veca`respectively. Also `OA = BC = AB= OC =1` (let) Therefore, AOCB is rhombus. `angle ABC = angle AOC = (3pi)/(5)` and `angleOAB = angle BCO = pi - (3pi)/(5) = (2pi)/(5)` Further `OA = AE = 1 and OC = CD = 1 ` Thus, `DeltaEAO and Delta OCD` are isosceles. In `Delta OCD`, using SINE RULE we get `(OC)/(sin""(2pi)/(5))= (OD )/( sin""(pi)/(5))` `rArr OD = (1)/( 2 cos ""(pi)/(5)) = OE` `rArr AD = OA + OD = 1 + (1)/(2 cos ""(pi)/(2))` `rArr (AD)/(BC) =1 + (1)/(2 cos""(pi)/(5)) = (1 +2 cos""(pi)/(5))/( 2 cos""(pi)/(5))` And `(OE)/( OC) = (1)/( 2cos ""(pi)/(5))`

Discussion

30.	A line makes an angle alpha,beta and gamma with axes repectively, The values of alpha, beta and gamma are respectively theta, 60^@ and 30^@ then sin theta = .............
Answer» 1 `-2` `0` `1/2` ANSWER :A

Discussion

31.	Find the order and degree (if defined) of the following differential equations. (d^2y)/(dx^2) = cos 3x + sin 3x
Answer» Solution :The ORDER of the highest order derivative in the DIFFERENTIAL EQUATION = 2. `therefore` The order of the differential equation = 2 . Since the degree of `(d^2y)/(dx^2)` is 1, the degree of the differential equation = 1.

Discussion

32.	If lim_(x to 0) [cot (pi//4 + x)]^(1//x) =Ae^2 then the value of A is
Answer» `E^2` `e^(-4)` `e` `e^3` ANSWER :B

Discussion

33.	If \|{:(2x,5),(8,x):}\|=\|{:(6,-2),(7,3):}\|, then value of x is "........."
Answer» 3 `+-3` `+-6` 6 Answer :C

Discussion

34.	A curve C has the property that if the tangent drawn at any point 'P' on C meets the coordinate axes at A and B, and P is midpoint of AB. If the curve passes through the point (1,1) then the equation of the curve is
Answer» XY = 2 xy = 3 xy = 1 xy = 4 Answer :C

Discussion

35.	If x^(2)+y^(2)=1 then minimum and maximum values of (x+y) are
Answer» `-SQRT(2),sqrt(2)` `-1,1` `-(1)/(sqrt(2)),(1)/(sqrt(2))` `-(1)/(sqrt(2)),2` ANSWER :A

Discussion

36.	If A+B+C=180^@" then " 4 cos""((pi-A)/(4)) cos""((pi-B)/(4)) cos""((pi-C)/(4))=
Answer» `cos A + cos B + cos C ` `cos""(A)/(2) + cos""(B)/(2) + cos""(C)/(2) ` `SIN A + sin B + sin C ` `sin""(A)/(2)+sin"(B)/(2) + sin""(C)/(2) ` ANSWER :B

Discussion

37.	Angle between the asymptotes of a hyperbola is x^(2)-3y^(2)=1 is
Answer» `15^(@)` `45^(@)` `60^(@)` `30^(@)` Answer :C

Discussion

38.	Evaluate the following:lim_(ntoinfty) n/(n+1)
Answer» SOLUTION :`lim_(ntoinfty) N/(n+1)` `=lim_(ntoinfty)1/(1+1/n)=1`

Discussion

39.	The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2)-2t-5 at the point (2,-1) is
Answer» 1)`(22)/(7)` 2)`(6)/(7)` 3)`(7)/(6) 4)`(-6)/(7)` ANSWER :B

Discussion

40.	Find the values of x for which \|(x,2),(18,x)\|=\|(6,2),(18,6)\|
Answer» ANSWER :`RARR X= PM 6`

Discussion

41.	Let f(x) = 1 + 4x - x^(2), AA x in Rg(x) = max {f(t), x le t le (x + 1), 0 le x lt 3min {(x + 3), 3 le x le 5} Verify conntinuity of g(x), for all x in [0, 5]
Answer» ANSWER :`X = [0, 3) UU (3, 5]`

Discussion

42.	Find the area of the triangle formed by three points on the ellipse x^2/a^2+y^2/b^2=1 whose eccentric angles are alpha, beta and gamma.
Answer» ANSWER :`SIN((gamma-alpha)/2)`

Discussion

43.	If int (x^(2) + 2)/((x^(2) + 1)(x^(2) + 4))dx = A tan^(-1) x + B tan^(-1)""(x)/(2)+ c then (A, B) =
Answer» ANSWER :`(1/3,1/3)`

Discussion

44.	1/(1!) +(1+3)/(2!) + (1+3+5)/(3!)+......oo =
Answer» e 2e `SQRTE` `e/2` ANSWER :B

Discussion

45.	Find the equation of the circum circle of the triangle formed by the lines x+ 3y =1, x+y + 1=0, 2x + 3y -4=0
Answer» ANSWER :` X^(2) + y^(2) +12X +12Y +7=0 `

Discussion

46.	Consider the expansion of (2x-1)^(15)
Answer» ALGEBRAICALLY least coefficient is `T_(5)` Algebraically greatest coefficient is `T_(5)` Numerically greatest coefficient is `T_(6)` Numerically least coefficient is `T_(16)` SOLUTION :`RLE(n+1)/(1+\|(x)/(y)\|)` `rle(16)/(1+\|(2x)/(-1)\|)` `rle(16)/(3)=5` `impliesT_(6)` gives numerically greatest coefficient `T_(6)= .^(15)C_(5)(-1)^(5)(2)^(10)(x)^(10)` `N.G.C= .^(15)C_(5)(2)^(10)` `N.I.C=1` `A.L.C= .^(15)C_(4)(2)^(10)` `A.G.C= .^(15)C_(4)(2)^(11)`

Discussion

47.	""^15C_2 + 2.""^15C_3 + 3. ""^15C_4 + …..+ 14.""^15C_15 =
Answer» `13.2^14 - 1` `13.2^14 + 1` `12^14 + 1` `12^14 - 1` ANSWER :B

Discussion

48.	Definite integration as the limit of a sum : lim_(ntooo)sum_(r=1)^(n)(1)/(n)e^(r/(n))=.............
Answer» e e-1 1-e e+1 Answer :B

Discussion

49.	(1 + e^(x/y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0
Answer» ANSWER :`YE^(X)/(y) + x = C`

Discussion

50.	If x^(2) is divisible by 216, what is the smallest possible value for positive integer x?
Answer» ANSWER :36

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If x - coordinateof a point P on theline joining the [points Q(2,2,1) and R (5,1,-2)is 4 , then the z - cossrdinate of P is

Find the sum of n-terms of the series 2.5 + 5.8 + 8.11 +……..

Evaluate the following integrals (vi) int_(0)^(1)e^(x) sin h x dx.

The solution of (dy)/(dx) + (3x^(2) y)/(1 + x^(3)) = (1+ x^(2))/(1 + x^(3)) is

Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).

1+3/(1!) +5/(2!) + (7)/(3!) + ......oo=

Determine if the set A ={-1,1,3}is a proper subset of the set B={x:x in R and x^3-2x^2-x+2=0}

From the point A(0,3) on the circle x^(2)+4x+(y-3)^(2)=0, a chord AB is drawn and extended to a point P, such that AP=2AB. The locus of P is

Compute the product A = Z, B = phi

For all values of A, B, C and P, Q, R |(cos(A-P), cos(A-Q),cos(A-R)),(cos(B-P), cos(B-Q), cos(B-R)),(cos(C-P), cos(C-Q), cos(C-R))|=

A man running on a race course notices that the sum of the distances of the two flag posts from him is always 10m and the distance between the flag posts is 8m. Find the equation of the race course traced by the man.

Find dy/dx, if sin^(2)x+cos^(2)y=1.

intsqrt(1-sin2xdx),x in[-(3pi)/(4),(pi)/(4)]

If the chord of contact of tangents from a point to a given circle passes through Q , then the circle on PQ as diameter

Let omega=-(1)/(2)+i (sqrt(3))/(2), then the value of [[1,1,1],[1,-1-omega^(2),omega^(2)],[1,omega^(2),omega^(4)]] is

If [(alpha,beta),(gamma,-alpha)] is square root of identity matrix of order 2 then-

If the first three terms in the expansion of (1 -ax)^n where n is a positive integer are 1,-4x and 7x^2 respectively then a =

Find the slope of the tangent to the curve y = x^(3) –3x + 2 at the point whose x-coordinate is 3.

The solutionof(dy)/(dx)=( x+y)/(x-y) is

If -2-i is a root of the equation ax^(2)+12x+b=0 (where a and b are real), then the value of ab is equal to

The equation of parabola whose latus rectum isthe line segment joining the points (-3,1) , (1,1) is

Find P^(-1), if the exists, given P=[(10,-2),(-5,1)]

If x=sinh^(-1)[log(1+sqrt(y)], " then "(dy)/(dx)=

Out of 52 cards 4 are drawn at random without replacement. What is the probability that (i) they belong to different suits (i.e., one from each suit) (ii) they belong to different denominations

1/2.""^10C_0 -""^10C_1 +2.""^10C_2 - 2^2.""^10C_3+…..+2^9. ""^10C_10 =

Which of the following is noth the number of ways of selecting n objects from 2n objects of which n objects are identical

Let A, B, C, D, E represent vertices of a regular pentagon ABCDE. Given the position vector of these vertices be veca, veca + vecb, vecb, lamda veca andlamda vecb, respectively. AD divides EC in the ratio

Let A, B, C, D, E represent vertices of a regular pentagon ABCDE. Given the position vector of these vertices be veca, veca + vecb, vecb, lamda veca andlamda vecb, respectively. The ratio (AD)/(BC) is equal to

A line makes an angle alpha,beta and gamma with axes repectively, The values of alpha, beta and gamma are respectively theta, 60^@ and 30^@ then sin theta = .............

Find the order and degree (if defined) of the following differential equations. (d^2y)/(dx^2) = cos 3x + sin 3x

If lim_(x to 0) [cot (pi//4 + x)]^(1//x) =Ae^2 then the value of A is

If |{:(2x,5),(8,x):}|=|{:(6,-2),(7,3):}|, then value of x is "........."

A curve C has the property that if the tangent drawn at any point 'P' on C meets the coordinate axes at A and B, and P is midpoint of AB. If the curve passes through the point (1,1) then the equation of the curve is

If x^(2)+y^(2)=1 then minimum and maximum values of (x+y) are

If A+B+C=180^@" then " 4 cos""((pi-A)/(4)) cos""((pi-B)/(4)) cos""((pi-C)/(4))=

Angle between the asymptotes of a hyperbola is x^(2)-3y^(2)=1 is

Evaluate the following:lim_(ntoinfty) n/(n+1)

The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2)-2t-5 at the point (2,-1) is

Find the values of x for which |(x,2),(18,x)|=|(6,2),(18,6)|

Let f(x) = 1 + 4x - x^(2), AA x in Rg(x) = max {f(t), x le t le (x + 1), 0 le x lt 3min {(x + 3), 3 le x le 5} Verify conntinuity of g(x), for all x in [0, 5]

Find the area of the triangle formed by three points on the ellipse x^2/a^2+y^2/b^2=1 whose eccentric angles are alpha, beta and gamma.

If int (x^(2) + 2)/((x^(2) + 1)(x^(2) + 4))dx = A tan^(-1) x + B tan^(-1)""(x)/(2)+ c then (A, B) =

1/(1!) +(1+3)/(2!) + (1+3+5)/(3!)+......oo =

Find the equation of the circum circle of the triangle formed by the lines x+ 3y =1, x+y + 1=0, 2x + 3y -4=0

Consider the expansion of (2x-1)^(15)

""^15C_2 + 2.""^15C_3 + 3. ""^15C_4 + …..+ 14.""^15C_15 =

Definite integration as the limit of a sum : lim_(ntooo)sum_(r=1)^(n)(1)/(n)e^(r/(n))=.............

(1 + e^(x/y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0

If x^(2) is divisible by 216, what is the smallest possible value for positive integer x?