28278 + Interview Questions in Maths in Class 12 Page 155 InterviewSolution

7701.	A ball thrown by one player reaches the other in 2 seconds. The maximum height attained by the ball above the point of projection will be :- (g = 10 m//s^(2))
Answer» 10 m. 7.5 m 5 m 2.5 m Answer :A

Discussion

7702.	The sumS_n = n^3+3n^2+ 5n +3isdivisibleby
Answer» `3AA N in N` `4AAn in N` ` 5 AA n in N` can'tbedetermined ANSWER :A

Discussion

7703.	I : If \|a + b\| = \|a - b\| then (a,b) = pi//2 II : If a,b, a+ b are unit vectors then (a,b) = 2 pi//3
Answer» only I is ture Only II is ture both I and II are true Neither I nor II are true Answer :C

Discussion

7704.	f(x)= int_(0)^(x) ln ((1-t)/(1+t))dt rArr
Answer» `f(X)` is an even FUNCTION `f(x)` is an ODD function `f(x)` is neither even nor odd `f(x)` cannot be a function Answer :A

Discussion

7705.	The value of (tan59^@+1) (cot76^@ -1) is :-
Answer» 1 -1 2 -2

Discussion

7706.	(1 + Delta)^(n) f(a) is equal to
Answer» f(a+ h) f(a + 2H) f(a + nh) f(a + (n-1) h) SOLUTION :`(1 + DELTA)^(n) f(a) = E^(n) f(a)` `= f(a + nh)`

Discussion

7707.	Find the rank of the following matrices by row reduction method.[[1,1,1,3],[2,-1,3,4],[5,-1,7,11]]
Answer» ANSWER :`RHO (E ) = 2`

Discussion

7708.	If f( 2010) = pi //2, f(2x) = f(x)AA x in R and f(x) is continuous for x in R, then the value of underset( x rarr0 ) ( "lim") ( cos (f(x) )-root3(cos(f(x))))/(sin^(2)x) is underset( x rarr pi //2)("Lim") [(x-(pi)/(2))/(cos x ) ] is
Answer» `1//4` 1 0 None of these Answer :C

Discussion

7709.	A plane passes through a fixed point (alpha,beta,gamma). The locus of the foot of the perpendiculars to the plane from the origin is
Answer» a PLANE inclined at a angle `(PI)/(3)` with the given plane a straight LINE a plane PERPENDICULAR to the given plane none of these Answer :D

Discussion

7710.	lim_(n to oo) (1)/(n) [ 1+ (n^2)/( n^2+ 1^2)+ (n^2)/( n^2+ 2^2) + …+ (n^2)/( n^(2) + (n-1)^(2) ) ] is equal to
Answer» `pi/2` `pi/3` `pi/4` `pi/6` ANSWER :C

Discussion

7711.	Integrate the following : int1/(xsqrtx)dx
Answer» SOLUTION :`intdx/(xsqrtx)`=`intx^(-3/2)DX` `X^(-3/2+1)/(-3/2+1`)+C`=`x^(-1/2)/(-1/2)+C`=`-2x^(-1/2)`+C

Discussion

7712.	If A, B are two mutually exclusive and exhaustive events such that 2P(B) = 3P(A) find odds infavour of A.
Answer» ANSWER :`2 : 3`

Discussion

7713.	int_(0)^(pi) sin^(8) . x/2 dx=
Answer» `(35pi)/(128)` `(5PI)/(128)` `(25pi)/(128)` `(3PI)/(128)` ANSWER :A

Discussion

7714.	Statement I: cos 52^(@)+cos68^(@)+cos172^(@)=1/2 Statement II: 4sin Acos^(3)A-4cosAsin^(3)A=cos4A Which of the above statements is correct?
Answer» only I only II Both I and II Neither I nor II Answer :D

Discussion

7715.	If A is square matrix of order 3 and \|A\|=4,then find \|adj A\|
Answer» ANSWER :16

Discussion

7716.	Probability distribution of random variable X is as follows : Then variance of g(X) = 2X + 3 ……….
Answer» 6 36 4 8 Answer :C

Discussion

7717.	Let z be any non-zero complex number. Then arg (z) + arg (barz) is equal to
Answer» `PI` `-pi` 0 `pi//2` ANSWER :C

Discussion

7718.	If f(x) ={{:((1-\|x\|)/(1+x), x ne -1),(1, x =-1):}, then f([2x]) is (where [*] represent greatest integer function)
Answer» CONTINOUS at `x=-1` continous at x=0 discontinous at `x=1//2` all of these ANSWER :D

Discussion

7719.	L is a line passing through the point A(1, 0, -3) and parallel to a line having direction rations 0, 1, -2, P is a point on the line L which is at a minimum distance from the plane 2x + 3y + 5z =1. Then, the equation of the plane through P and perpendicular to AP is
Answer» `y+ 2z =12` `y-2z + 4=0` `X + y -2z = 12` `2y -Z =16` ANSWER :B

Discussion

7720.	In how many ways 3 different numbers which are in A.P. can be selected from 1, 2, 3, ... 10
Answer» ANSWER :100

Discussion

7721.	Let A = {x_(1),x_(2),x_(3),x_(4), x_(5), x_(6),x_(7), x_(8)}, B= { y_(1), y_(2), y_(3), y_(4) } .The total number of functionf : A to Bthat are onto and there are exactly three elements x in A such thatf(x) = y_(1)is :
Answer» 11088 10920 13608 None of these Answer :D

Discussion

7722.	If z_(r)=sin(2pir)/11-icos(2pir)/11, then sum_(r=0)^(10)z_(r)=
Answer» `-1` 0 i `-i` ANSWER :B

Discussion

7723.	If the regions A and B are given by A={(x,y)// : y gt x}B={(x,y):y lt 2-x^(2)} then the area of A nn B is
Answer» `(1)/(3)` `(9)/(2)` `(2)/(5)` `(3)/(4)` Answer :B

Discussion

7724.	If vec(C) is the midpoint of vec(AB)andvec(P) is any point outside vec(AB)," then "vec(PA)+vec(PB)=
Answer» `VEC(PC)` `vec(2PC)` `vec(-PC)` `2vec(OP)` ANSWER :B

Discussion

7725.	Find the number of terms free of radical sign in (5^(1//2) +7^(1//5))^(220). Also find the number of irrational terms.
Answer» SOLUTION :N/A

Discussion

7726.	If alpha,beta are the ends of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1then its eccentricity e is
Answer» `(1+TAN(ALPHA)/(2)tan(BETA)/(2))/(1-tan (alpha)/(2)tan (beta)/(2))` `(1-tan(alpha)/(2)tan(beta)/(2))/(1+tan (alpha)/(2)tan (beta)/(2))` `(tan(alpha)/(2)tan(beta)/(2)+1)/(tan(alpha)/(2)tan (beta)/(2)-1)` `(tan(alpha)/(2)tan(beta)/(2)-1)/(tan (alpha)/(2)tan (beta)/(2)+1)` ANSWER :A

Discussion

7727.	Evaluation of definite integrals by subsitiution and properties of its : int_(pi//8)^(3pi//8)(1)/(1+sqrt(tanx))dx=.........
Answer» `(PI)/(4)` `(pi)/(8)` `(pi)/(2)` 0 Answer :B

Discussion

7728.	Evalute \|(cos 15^(@) sin 15^(@)),(sin 75^(@) cos 75^(@))\|
Answer» 3 2 0 1 Answer :C

Discussion

7729.	Evaluate the following integrals intsin^(5)xcos^(4)xdx
Answer» Answer :`-(sin^(4)XCOS^(5)x)/(9)-(4SIN^(2)xcos^(5)x)/(63)-(8cos^(5)x)/(315)+c`

Discussion

7730.	intcot^4thetad theta
Answer» SOLUTION :`intcot^4thetad THETA=intcot^2theta.cot^2thetad theta` =`intcot^2(cosec^2theta-1)d theta` =`intcot^2.cosec^2theta d theta-intcot^2thetad theta` =`intcot^2.cosec^2theta d theta-int(cosec^2theta-1)d theta` =`-1/3cot^3theta+cottheta+theta+C`

Discussion

7731.	Differentiate cos(sinx)w.r.t.x
Answer» SOLUTION :LET y=cos(sin.x). Then `dy/dx=-sin(SINX)d/dxsinx=-cosxsin(sinx)`

Discussion

7732.	Let bar(a)=bar(i)+2bar(j)+3bar(k)andbar(b)=3bar(i)+bar(j).. Finda unit vector in the direction of bar(a)+bar(b)
Answer» Answer :`(1)/(sqrt(34))(4bar(i)+3BAR(J)+3bar(k))`

Discussion

7733.	The vector a=alpha hati+2hatj+betahatk lies in the plane of the vectors b=hati+hatj and c = hatj+hatk and bisects the angle between b and c. Then, which one of the following gives possible value of alpha and beta?
Answer» `alpha=1, beta=1` `alpha=2, beta=2` `alpha=1, beta=2` `alpha=2,beta=1` Solution :Since, a, b, and C are coplanar. `implies \|(alpha,2,beta),(1,1,0),(0,1,1)\|=0` `implies alpha (1-0)-2(1-0)+beta (1-0)=0` `implies alpha +beta =2` which is POSSIBLE for `alpha=1, beta =1`.

Discussion

7734.	lim_(x to pi/6)(Sin(x-pi/6))/(sqrt(3)/2-cosx)=
Answer» 0 1 2 `1/2` ANSWER :C

Discussion

7735.	If the straight line 2x + 3y + 1 = 0 bisects the angle between a pair of lines, one of which in this pair is 3x + 2y + 4 = 0, then the equation of the other line in that pair of lines is
Answer» `3X + 4y -9 = 0` `6x-7y-14=0` `9x + 46y -28 = 0` `9x-23y - 12 = 0` Answer :C

Discussion

7736.	Number of ways of arranging4 boys and 3 girls so that no boy is in between any two girls
Answer» 360 720 180 90 Answer :B

Discussion

7737.	Find (veca+3vecb)*(2veca-vecb). If veca=hati+hatj+2hatk, hatb=2hati+2hatj-hatk
Answer» ANSWER :`-15`

Discussion

7738.	Find the number of ways of permuting the letters of the word PICTURE so that the relative positions of vowels and consonants are not distributed.
Answer» ANSWER :144

Discussion

7739.	If ("5x1")((4),(2),(7))=(35), then x = _________.
Answer» ANSWER :4

Discussion

7740.	Evaluate the following inegrals int(1)/(1+e^(-x))dx
Answer» Answer :`LOG(E^(x)+1)+c`

Discussion

7741.	The equation of the circle radius is 5 and which touches the circle x^(2)+y^(2)-2x-4y-20=0" at this point (5,5) is"
Answer» `(X-9)^(2)+(y-8)^(2)=5` `(x-9)^(2)+(y+8)^(2)=25` `x^(2)+y^(2)=25` `(x-9)^(2)+(y-8)^(2)=25` ANSWER :D

Discussion

7742.	f:RrarrR and g:[0,oo]rarrRis defined by f(x)=x^(2) and g(x)=sqrtx. Which one of the following is not true?
Answer» 1)`fog(2)=2` 2)`gof(4)=4` 3)`gof(-2)=2` 4)`fog(-4)=4` Answer :D

Discussion

7743.	int (dx)/(x^(2)sqrt(4+x^(2)))=
Answer» Answer :`(-1)/(4x)SQRT(4+x^(2))+C`

Discussion

7744.	Express the 3+2i points geometrically in the Argand plane.
Answer» SOLUTION :`3+2i=(3,2)`

Discussion

7745.	If f(x) is differentiate in [a,b], then prove that there exists at least one c in (a,b)"such that"(a^(2)-b^(2))f'(c)=2c(f(a)-f(b)).
Answer»

Discussion

7746.	IfS_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!) then lim_(n rarr infty)S_(n) is equal to
Answer» 3e 5e 7e 9e Answer :C

Discussion

7747.	What concentration of Ag^(+) ions will be in equilibrium with a saturated solution containing a precipitate of Ag_(2)CrO_(4) and CrO_(4)-ion concentration of 0.40 moles per litre. Given K_(SP)" of "Ag_(2)CrO_(4) = 1. 1 xx 10^(-11 )
Answer» `5.24xx10^(-6)` MOLES PER LITRE `2.5xx10^(-6)` moles per litre `7.5xx10^(-6)` moles per litre `5.9xx10^(-6)` moles per litre Answer :a

Discussion

7748.	Evaluate int cos(6x) sqrt(1+sin(6x))dx.
Answer» ANSWER :`(1)/(9)(1+sin 6x)^((3)/(2))+C`

Discussion

7749.	If (1)/((x-a)(x^(2)+b))=(A)/(x-a)+(Bx+C)/(x^(2)+b) then (1)/((x-a)(x^(2)+b)^(2))=
Answer» `A^(2)/(X-a)+(A(Bx+C))/(x^(2)+B)+(Bx+C)/(x^(2)+b)^(2)` `A^(2)/(x+a)+(A(Bx-C))/(x^(2)+b)+(Bx+C)/(x^(2)-b)^(2)` `A^(2)/(x+a)+(A(Bx+C))/(x^(2)+b)+(Bx-C)/(x^(2)+b)^(2)` `A^(2)/(x-a)+(A(Bx-C))/(x^(2)-b)+(Bx+C)/(x^(2)-b)^(2)` ANSWER :A

Discussion

7750.	Find the equation of the ellipse whose foci are (0pm 3) and e=3/4
Answer» Answer :(i) `9x^(2)-16y^(2)=144` (II) `y^(2)/(25)-(x^(2))/(144)=1` (III) `(9x^(2))/(20)-(9y^(2))/(16)+1=0` (iv) `x^(2)-y^(2)=32`

Discussion

Explore topic-wise InterviewSolutions in .

A ball thrown by one player reaches the other in 2 seconds. The maximum height attained by the ball above the point of projection will be :- (g = 10 m//s^(2))

The sumS_n = n^3+3n^2+ 5n +3isdivisibleby

I : If |a + b| = |a - b| then (a,b) = pi//2 II : If a,b, a+ b are unit vectors then (a,b) = 2 pi//3

f(x)= int_(0)^(x) ln ((1-t)/(1+t))dt rArr

The value of (tan59^@+1) (cot76^@ -1) is :-

(1 + Delta)^(n) f(a) is equal to

Find the rank of the following matrices by row reduction method.[[1,1,1,3],[2,-1,3,4],[5,-1,7,11]]

If f( 2010) = pi //2, f(2x) = f(x)AA x in R and f(x) is continuous for x in R, then the value of underset( x rarr0 ) ( "lim") ( cos (f(x) )-root3(cos(f(x))))/(sin^(2)x) is underset( x rarr pi //2)("Lim") [(x-(pi)/(2))/(cos x ) ] is

A plane passes through a fixed point (alpha,beta,gamma). The locus of the foot of the perpendiculars to the plane from the origin is

lim_(n to oo) (1)/(n) [ 1+ (n^2)/( n^2+ 1^2)+ (n^2)/( n^2+ 2^2) + …+ (n^2)/( n^(2) + (n-1)^(2) ) ] is equal to

Integrate the following : int1/(xsqrtx)dx

If A, B are two mutually exclusive and exhaustive events such that 2P(B) = 3P(A) find odds infavour of A.

int_(0)^(pi) sin^(8) . x/2 dx=

Statement I: cos 52^(@)+cos68^(@)+cos172^(@)=1/2 Statement II: 4sin Acos^(3)A-4cosAsin^(3)A=cos4A Which of the above statements is correct?

If A is square matrix of order 3 and |A|=4,then find |adj A|

Probability distribution of random variable X is as follows : Then variance of g(X) = 2X + 3 ……….

Let z be any non-zero complex number. Then arg (z) + arg (barz) is equal to

If f(x) ={{:((1-|x|)/(1+x), x ne -1),(1, x =-1):}, then f([2x]) is (where [*] represent greatest integer function)

L is a line passing through the point A(1, 0, -3) and parallel to a line having direction rations 0, 1, -2, P is a point on the line L which is at a minimum distance from the plane 2x + 3y + 5z =1. Then, the equation of the plane through P and perpendicular to AP is

In how many ways 3 different numbers which are in A.P. can be selected from 1, 2, 3, ... 10

Let A = {x_(1),x_(2),x_(3),x_(4), x_(5), x_(6),x_(7), x_(8)}, B= { y_(1), y_(2), y_(3), y_(4) } .The total number of functionf : A to Bthat are onto and there are exactly three elements x in A such thatf(x) = y_(1)is :

If z_(r)=sin(2pir)/11-icos(2pir)/11, then sum_(r=0)^(10)z_(r)=

If the regions A and B are given by A={(x,y)// : y gt x}B={(x,y):y lt 2-x^(2)} then the area of A nn B is

If vec(C) is the midpoint of vec(AB)andvec(P) is any point outside vec(AB)," then "vec(PA)+vec(PB)=

Find the number of terms free of radical sign in (5^(1//2) +7^(1//5))^(220). Also find the number of irrational terms.

If alpha,beta are the ends of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1then its eccentricity e is

Evaluation of definite integrals by subsitiution and properties of its : int_(pi//8)^(3pi//8)(1)/(1+sqrt(tanx))dx=.........

Evalute |(cos 15^(@) sin 15^(@)),(sin 75^(@) cos 75^(@))|

Evaluate the following integrals intsin^(5)xcos^(4)xdx

intcot^4thetad theta

Differentiate cos(sinx)w.r.t.x

Let bar(a)=bar(i)+2bar(j)+3bar(k)andbar(b)=3bar(i)+bar(j).. Finda unit vector in the direction of bar(a)+bar(b)

The vector a=alpha hati+2hatj+betahatk lies in the plane of the vectors b=hati+hatj and c = hatj+hatk and bisects the angle between b and c. Then, which one of the following gives possible value of alpha and beta?

lim_(x to pi/6)(Sin(x-pi/6))/(sqrt(3)/2-cosx)=

If the straight line 2x + 3y + 1 = 0 bisects the angle between a pair of lines, one of which in this pair is 3x + 2y + 4 = 0, then the equation of the other line in that pair of lines is

Number of ways of arranging4 boys and 3 girls so that no boy is in between any two girls

Find (veca+3vecb)*(2veca-vecb). If veca=hati+hatj+2hatk, hatb=2hati+2hatj-hatk

Find the number of ways of permuting the letters of the word PICTURE so that the relative positions of vowels and consonants are not distributed.

If ("5x1")((4),(2),(7))=(35), then x = _________.

Evaluate the following inegrals int(1)/(1+e^(-x))dx

The equation of the circle radius is 5 and which touches the circle x^(2)+y^(2)-2x-4y-20=0" at this point (5,5) is"

f:RrarrR and g:[0,oo]rarrRis defined by f(x)=x^(2) and g(x)=sqrtx. Which one of the following is not true?

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

Express the 3+2i points geometrically in the Argand plane.

If f(x) is differentiate in [a,b], then prove that there exists at least one c in (a,b)"such that"(a^(2)-b^(2))f'(c)=2c(f(a)-f(b)).

IfS_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!) then lim_(n rarr infty)S_(n) is equal to

What concentration of Ag^(+) ions will be in equilibrium with a saturated solution containing a precipitate of Ag_(2)CrO_(4) and CrO_(4)-ion concentration of 0.40 moles per litre. Given K_(SP)" of "Ag_(2)CrO_(4) = 1. 1 xx 10^(-11 )

Evaluate int cos(6x) sqrt(1+sin(6x))dx.

If (1)/((x-a)(x^(2)+b))=(A)/(x-a)+(Bx+C)/(x^(2)+b) then (1)/((x-a)(x^(2)+b)^(2))=

Find the equation of the ellipse whose foci are (0pm 3) and e=3/4