28278 + Interview Questions in Maths in Class 12

1.	A particle moves a distance x in time t according to equation x^(2) = 1 + t^(2) . The acceleration of the particle is
Answer» ACC. VARIES as `s^3` acc.varies as `1/s` acc.varies as `1/s^3` acc. Varies as `1/s^2` ANSWER :C

Discussion

2.	If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =
Answer» `E^(-y)` `1+e^(-y)` `1-e^(-y)` 1 Answer :C

Discussion

3.	The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are
Answer» `(r-p)/(q-r),1` `(p-q)/(q-r),1` `(p-r)/(q-r),2` `(q-r)/(p-q),2` ANSWER :B

Discussion

4.	{:(" " Lt),(n rarroo):}(pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)pi)/(2n))=
Answer» -1 1 `- 1/2` `1/2` ANSWER :B

Discussion

5.	Let the sequences x_n and y_n diverge. Can one assert that the sequences x_n+y_n, x_ny_n diverge too?
Answer» ANSWER :(a) No, EXAMPLE `;x_(N) =n; y_(n)=-n+1; (B) No`

Discussion

6.	The solution set of the inequation (x^(2) + 6x-7)/(\|x+4\|) lt 0 is ______
Answer» 1)`(-7, -4) UU (4,1)` 2)`(-7, -4)uu(-4,1)` 3)`(-7, -4)` 4)`(-7, 1)` Answer :B

Discussion

7.	If x^(2) + y^(2) + z ^(2) =r^(2), thentan^(-1) ((xy)/(zr)) + tan ^(-1) ((yz)/(xr)) + tan ^(-1) ((zx)/(yr))= ?
Answer» `(pi)/(4)` `(pi)/(6)` `(pi)/(2)` `pi` ANSWER :C

Discussion

8.	If L,M,N are the three points on the parabola y^(2) = 4axwhose ordinates are in G.P then the tangents at L and N meet on the
Answer» parabola abscissa of M ORDINATE of M none Answer :B

Discussion

9.	Let z_1, z_2 be two complex numbersrepresented by points on the circle \|z_1\|=1 and \|z_2\|=2 respectively then
Answer» MAX `\|2z_1 + z_2\|=4` MIN `\|z_1 - z_2\|=1` `\|z_2 + (1)/(z_1)\| GE 3` NONE of these Answer :A::B::C

Discussion

10.	The sum of all the numbers greater than 10000 formed by using digits 0, 2, 4, 6, 8, no digit being repeated in any number, is equal to
Answer» 5199960 5209960 5199980 5299960 Answer :A

Discussion

11.	Find the angle between the following pairs of lines.(x)/2=(y)/2=(z)/1and (x-5)/4=(y-2)/1=(z-3)/8
Answer» Answer :Here, a_1, b_1, c_1 are 2, 2, 1 and a_2, b_2, c_2 are 4, 1, 8 respectively `therefore COSTHETA = (8+2+8)/(sqrt(4+4+1)sqrt(16+1+64)) = (18)/(3xx9) = 2/3 rArr theta = cos^(-) (2/3)`

Discussion

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

Discussion

13.	Evaluate the following integrals (ix) int_(0)^(1)(x)/(1+sqrt(x))dx
Answer» 0 1 `2(5/6 + LN 2)` `(5/6 - ln 2)` ANSWER :D

Discussion

14.	In the group G = { 1, 2, 3, 4, 5 } under addition modulo 6, (3 + 5^(-1))^(-1) is
Answer» 0 1 2 3 Answer :C

Discussion

15.	Let vecr=sinx (veca xx vecb)+cosy(vecb xx vec c)+2(vec c xx veca), where veca, vecb are non-collinear and vec c, vecd are also non-collinear then :
Answer» `pi^(2)` `(5pi^(2))/(4)` `(35pi^(2))/(4)` `(37pi^(2))/(4)` ANSWER :B::D

Discussion

16.	If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=
Answer» `(a^(3))/((C-b)(c-a))` `(a^(3))/((b-c)(b-a))` `(a^(3))/((a-b)(a-c))` `(1)/((a-b)(a-c))` ANSWER :C

Discussion

17.	Solve the matrix equation[x" "1] [{:( 1,0),(-2,-3):}] [{:(x),(5):}] =0
Answer» ` X = - 5or 3` ` x= 5 or -3` ` x=0 or 5` ` x=-3 or 0 ` ANSWER :B

Discussion

18.	Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4hatkFind a vector vecd whichis perpendicular to both vecaandvecb,andvecc*vecd=15.
Answer» ANSWER :`(1)/(3)(160hati-5hatj+70hatk)`

Discussion

19.	Integrate the functions ((1+logx)^(2))/x
Answer» ANSWER :`1/3(1+logx)^(3)+C`

Discussion

20.	Find the equation of the parabola whose focus is S (1,-7) and vertex is A(1,-2).
Answer» ANSWER :`(x-1)^(2)=-20(y+2)`

Discussion

21.	A vertical pole stands at a point A on the boundary of a circular park of radius 2 km and subtends an angle 60^(@) at another point B on the boundary. If the chord AB subtends the same angle 60^(@) at the centre of the park, the height of the pole is
Answer» `2 sqrt(3)` KM `sqrt(3)` km `2//sqrt(3)` KMM 1 km ANSWER :A

Discussion

22.	Letthe functionf: [-7,9] to Rbecontinuouson[-7,0]anddifferentialon (-7,0). Iff(-7) =-3andf'(x) le 2, forallx in(-7,0) , thenfor allsuch functionf,f(-1)+ f(0)liesintheinterval :
Answer» `[-6,20]` `[-OO ,20]` `[-oo,11]` `[-3,11]` ANSWER :B

Discussion

23.	(1+costheta-isintheta)^4=
Answer» `2^4cos^4(theta/2)cis2theta` `2^4cos^4(theta/2)CIS(-2THETA)` `2^4sin^4(theta/2)cis2theta` `2^4sin^4(theta/2)cis(-2theta)` ANSWER :B

Discussion

24.	Let f(x)=In (2x-x^2)sin"(pix)/2. Then
Answer» GRAPH of is symmetrical about the LINE x=1 Graph of is symmetrical about the line x=2 Maximum VALUE of f(x) is 1 Minimum value of f(x) does not EXITS Answer :A:C::D

Discussion

25.	Evaluate the integrals by using substitution int_(0)^(pi/2)sqrt(sinphi)cos^(5)phidphi
Answer» ANSWER :`64/231`

Discussion

26.	If ""^nC_(12)=""^nC_8 , then n is equal to :
Answer» 26 12 6 20 Answer :D

Discussion

27.	The centroid of the triangle formed by the points (1,2,3),(3,-1,5),(4,0,-3) is
Answer» RIGHT angled TRIANGLE isosceles triangle equilateral triangle right angled isosceles triangle ANSWER :A

Discussion

28.	Integrate the following function : int(1)/(4x^(2)+9)dx
Answer» ANSWER :`(1)/(6)TAN^(-1)""(2x)/(3)+C`

Discussion

29.	The solution set \|x-2\| lt \|2x-1\| is
Answer» a. `(-OO,-1)` b. `(1,oo)` c. `(-oo, -1) UU (1,oo)` d. `(-1,1)` Answer :C

Discussion

30.	int_(0)^(pi) x f (sin x) dx is equal to
Answer» `pi/2 LN 2` `(-pi^(2))/(2) ln 2` `- pi/2 ln 2` `- 2pi ln 2` Answer :B

Discussion

31.	bar(a),bar(b) and bar( c ) are non zero vectors. \|(bar(a)xx bar(b))*bar( c )\|=\|bar(a)\|\|bar(b)\|\|bar( c )\| then ……………
Answer» `BAR(a)bar(B)=0,bar(b)bar( C )=0` `bar(b)bar( c )=0,bar( c )bar(a)=0` `bar( c )bar(a)=0,bar(a)bar(b)=0` `bar(a)bar(b)=bar(b)bar( c )=bar( c )*bar(a)=0` ANSWER :D

Discussion

32.	Ifunderset0oversetaintf(x)dx=lambda and underset0oversetaintf(2a-x)dx=mu then underset0overset(2a)intf(x)dx=_______
Answer» SOLUTION :`underset0overset(2A)INTF(X)dx=underset0oversetaintf(x)dx+underset0oversetaintf(2a-x)dx=lambda+mu`

Discussion

33.	If f (n) = 1/n [(n +1) (n+2) (n+3)…(2n) ]^(1/n), then lim _( n to oo) f (n)=
Answer» `4/E` `LOG ((4)/(e))` `2/e` `log ((2)/(e))` ANSWER :A

Discussion

34.	Discuss the continuity of the following functions: f(x)= sin x. cos x
Answer» ANSWER :`F(X)= SIN x.cos x`

Discussion

35.	Discuss the continuity of the following functions: f(x)= sin x - cos x
Answer» ANSWER :`F(X)= SIN x - COS x`

Discussion

36.	Discuss the continuity of the following functions: f(x)= sin x + cos x
Answer» ANSWER :`F(X)= SIN x + COS x`

Discussion

37.	If int(dx)/(5-4sinx+3cosx) is equal to (1)/(2+f(x)) + C then f(x) is equal to
Answer» TAN X `tan^(x)/(2)` `-tan (x)/(2)` `tan x - tan^(2) x` ANSWER :C

Discussion

38.	The values of lamda for which the system of equations (lamda+5)x+(lamda-4)y+z=0 (lamda-2)x+(lamda+3)y+z=0 lamdax+lamday+z=0 has a non trivial solution is (are)
Answer» `-1,2` `0,-1` `0` NONE of these Answer :D

Discussion

39.	If p is any· logical statement, then
Answer» <P>p `^^ (~p)` is a TAUTOLOGY `p VEE (~p)` is a CONTRADICTION `p ^^ p = p ` `p vee (~p) = p ` Answer :C

Discussion

40.	Select the CORRECT order of bond energy ?
Answer» I-I GT F-F CL -Cl gt Br-Br F-F gt Cl -Cl F-F gt Br-Br

Discussion

41.	Find the values of x and y so that the vectors 2overset^^i+3overset^^j "and" xoverset^^i+yoverset^^j are equal.
Answer» Solution :The GIVEN vectors are EQUAL if and only x=2 and y=3. HENCE, the required values of x and y are 2 and 3 RESPECTIVELY.

Discussion

42.	Let be a binary opertion on the set Q of rational numbers as follows: (i)a b =a -b (ii) a * b =a^(2) + b ^(2) (iii)a b =a + ab (iv)a b = (a-b) ^(2) (v) a b = (ab)/(4) (vi) a b =ab ^(2) Find which of the binary opertions are commutative and which are associative.
Answer» ANSWER :(ii) , (IV) ,(V) are commutative; (v) is ASSOCIATIVE.

Discussion

43.	Integrate the functions sqrt(ax+b)
Answer» ANSWER :`( :.t=ax+b)`

Discussion

44.	The values of alpha and beta such that lim_( xtooo) [(x^2+1)/(x-1) -alpha x -2beta]=3/2 are
Answer» `alpha=-1,BETA=3/4` `alpha=1,beta=-1/4` `alpha=-1,beta=5/4` `alpha=1,beta=(-3)/4` ANSWER :B

Discussion

45.	Matchthe following :
Answer» a,B,C,d b,c,d,a c,d,a,b d,a,c,b Answer :C

Discussion

46.	Matchthe following :
Answer» a,B,C,d b,c,d,a c,d,a,b d,a,c,b Answer :A

Discussion

47.	{{:(3x+2y=15),(2x+3y=10):} Given the system of equations above, what is the value of 5x+5y ?
Answer» SOLUTION :Often, when the SAT asks for a sum of difference of VARIABLES, solbing by combination yields the answer very quickly. Add the equations: `2x + 3Y =15` ` (+ 3x + 2y =10)/(5x + 5y=25)` Grid in 25 and move on.

Discussion

48.	If E and F are two events such that 0 ltP(F)lt 1, then
Answer» <P>P(E\|F')+P(E'\|F')=1 P(E\|F)+P(E\|F')=1 P(E'\|F)+P(E\|F')=1 none of these Answer :A

Discussion

49.	Find the values of the following integrals intsqrt(1-cos2x)dxin[0,pi]
Answer» ANSWER :`-SQRT(2) cosx+c`

Discussion

50.	Find (dy)/(dx) of each of the functions expressed in parametric form:x= (1 + log t)/(t^(2)), y= (3 + 2 log t)/(t)
Answer» ANSWER :t

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A particle moves a distance x in time t according to equation x^(2) = 1 + t^(2) . The acceleration of the particle is

If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

{:(" " Lt),(n rarroo):}(pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)pi)/(2n))=

Let the sequences x_n and y_n diverge. Can one assert that the sequences x_n+y_n, x_ny_n diverge too?

The solution set of the inequation (x^(2) + 6x-7)/(|x+4|) lt 0 is ______

If x^(2) + y^(2) + z ^(2) =r^(2), thentan^(-1) ((xy)/(zr)) + tan ^(-1) ((yz)/(xr)) + tan ^(-1) ((zx)/(yr))= ?

If L,M,N are the three points on the parabola y^(2) = 4axwhose ordinates are in G.P then the tangents at L and N meet on the

Let z_1, z_2 be two complex numbersrepresented by points on the circle |z_1|=1 and |z_2|=2 respectively then

The sum of all the numbers greater than 10000 formed by using digits 0, 2, 4, 6, 8, no digit being repeated in any number, is equal to

Find the angle between the following pairs of lines.(x)/2=(y)/2=(z)/1and (x-5)/4=(y-2)/1=(z-3)/8

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

Evaluate the following integrals (ix) int_(0)^(1)(x)/(1+sqrt(x))dx

In the group G = { 1, 2, 3, 4, 5 } under addition modulo 6, (3 + 5^(-1))^(-1) is

Let vecr=sinx (veca xx vecb)+cosy(vecb xx vec c)+2(vec c xx veca), where veca, vecb are non-collinear and vec c, vecd are also non-collinear then :

If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

Solve the matrix equation[x" "1] [{:( 1,0),(-2,-3):}] [{:(x),(5):}] =0

Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4hatkFind a vector vecd whichis perpendicular to both vecaandvecb,andvecc*vecd=15.

Integrate the functions ((1+logx)^(2))/x

Find the equation of the parabola whose focus is S (1,-7) and vertex is A(1,-2).

A vertical pole stands at a point A on the boundary of a circular park of radius 2 km and subtends an angle 60^(@) at another point B on the boundary. If the chord AB subtends the same angle 60^(@) at the centre of the park, the height of the pole is

Letthe functionf: [-7,9] to Rbecontinuouson[-7,0]anddifferentialon (-7,0). Iff(-7) =-3andf'(x) le 2, forallx in(-7,0) , thenfor allsuch functionf,f(-1)+ f(0)liesintheinterval :

(1+costheta-isintheta)^4=

Let f(x)=In (2x-x^2)sin"(pix)/2. Then

Evaluate the integrals by using substitution int_(0)^(pi/2)sqrt(sinphi)cos^(5)phidphi

If ""^nC_(12)=""^nC_8 , then n is equal to :

The centroid of the triangle formed by the points (1,2,3),(3,-1,5),(4,0,-3) is

Integrate the following function : int(1)/(4x^(2)+9)dx

The solution set |x-2| lt |2x-1| is

int_(0)^(pi) x f (sin x) dx is equal to

bar(a),bar(b) and bar( c ) are non zero vectors. |(bar(a)xx bar(b))*bar( c )|=|bar(a)||bar(b)||bar( c )| then ……………

Ifunderset0oversetaintf(x)dx=lambda and underset0oversetaintf(2a-x)dx=mu then underset0overset(2a)intf(x)dx=_______

If f (n) = 1/n [(n +1) (n+2) (n+3)…(2n) ]^(1/n), then lim _( n to oo) f (n)=

Discuss the continuity of the following functions: f(x)= sin x. cos x

Discuss the continuity of the following functions: f(x)= sin x - cos x

Discuss the continuity of the following functions: f(x)= sin x + cos x

If int(dx)/(5-4sinx+3cosx) is equal to (1)/(2+f(x)) + C then f(x) is equal to

The values of lamda for which the system of equations (lamda+5)x+(lamda-4)y+z=0 (lamda-2)x+(lamda+3)y+z=0 lamdax+lamday+z=0 has a non trivial solution is (are)

If p is any· logical statement, then

Select the CORRECT order of bond energy ?

Find the values of x and y so that the vectors 2overset^^i+3overset^^j "and" xoverset^^i+yoverset^^j are equal.

Let ** be a binary opertion on the set Q of rational numbers as follows: (i)a ***b =a -b (ii) a ** b =a^(2) + b ^(2) (iii)a **b =a + ab (iv)a ** b = (a-b) ^(2) (v) a **b = (ab)/(4) (vi) a **b =ab ^(2) Find which of the binary opertions are commutative and which are associative.

Integrate the functions sqrt(ax+b)

The values of alpha and beta such that lim_( xtooo) [(x^2+1)/(x-1) -alpha x -2beta]=3/2 are

Matchthe following :

Matchthe following :

{{:(3x+2y=15),(2x+3y=10):} Given the system of equations above, what is the value of 5x+5y ?

If E and F are two events such that 0 ltP(F)lt 1, then

Find the values of the following integrals intsqrt(1-cos2x)dxin[0,pi]

Find (dy)/(dx) of each of the functions expressed in parametric form:x= (1 + log t)/(t^(2)), y= (3 + 2 log t)/(t)

Let be a binary opertion on the set Q of rational numbers as follows: (i)a *b =a -b (ii) a b =a^(2) + b ^(2) (iii)a b =a + ab (iv)a b = (a-b) ^(2) (v) a b = (ab)/(4) (vi) a **b =ab ^(2) Find which of the binary opertions are commutative and which are associative.