28278 + Interview Questions in Maths in Class 12 Page 162 InterviewSolution

8051.	Findthe areaof theregionboundedby thecurvey^2 = 4xandx^2 = 4y
Answer» ANSWER :`16/3` SEQ. UNIT

Discussion

8052.	Evaluate the following integrals. inttan^(4)xsec^(2)x dx
Answer» ANSWER :`(TAN^(5))/(5) + C`

Discussion

8053.	If the point z = (1+i) (1+2i)(1+3i)…(1+10i) lies on a circle with centre at origin and radius r, then r^(2) =
Answer» 10! `2 xx 3 xx 4 xx …… xx 10` `2 xx 5 xx 10 xx … xx 101` 11! Answer :c

Discussion

8054.	Evaluate the following: intx^2e^(ax)dx
Answer» Solution :`intx^2e^(AX)DX` [CHOOSE `x^2` as first and `e^(ax)` as second function] =`x^2.e^(ax)/a-int2x.e^(ax)/a dx` =`1/a x^2e^(ax)-2/a{x.e^(ax)/a-int1.e^(ax)/a dx}` =`1/ax^2e^(ax)-2/a^2 xe^(ax)+2/a^3.e^(ax)+C`

Discussion

8055.	int sec^(4)x dx=
Answer» `(1)/(3) Sec^(2) X " tanx" - (2)/(3) ` tan x + C `(1)/(3) Sec^(2) x " tanx" + (2)/(3) ` tan x + c `(1)/(3) Sec^(2) x " tanx" - (1)/(3) ` tan x + c `(1)/(3) Sec^(2) x " tanx" - (1)/(3) `x + c Answer :B

Discussion

8056.	Using quantifiers AA,EE convert the following open statement into true statement. 'x + 5 = 8 , x in N'
Answer» `AA x in N, x + 5 = 8` For EVERY ` x in N, x + 5 gt 8` `EE x in N` such thatx+5 = 8 For every `x in N, x + 5 lt 8` Answer :C

Discussion

8057.	Let n be a positive integer and a complex number with unit modulus is a solution of the equation Z^n+Z+1=0 , then the value of n can be
Answer» 62 155 221 196 Answer :A::B::C

Discussion

8058.	The roots of the equation (x -1 )^(3) + 8 = 0 are
Answer» `-1,1+2omega,1+2omega^(2)` `-1,1-2omega,1-2omega^(2)` `2,2omega,2omega^(2)` `2,1+2omega,1+2omga^(2)` ANSWER :B

Discussion

8059.	If A and B are two events such that P(A) = (1)/(3), P(B) = (1)/(4) and P(A cap B) = (1)/(5) , then P(A' \| B') = ………..
Answer» `(37)/(40)` `(37)/(45)` `(23)/(40)` `(8)/(45)` Answer :B

Discussion

8060.	Find the area of the region enclosed by the circle x^(2)+y^(2)=a^(2) by integration method.
Answer» ANSWER :`PIA^(2)`

Discussion

8061.	OX and OY are two coordinate axes . On OY is taken a fixed point P on OX any point Q. On PQ an equilateral triangle is described, its vertex R being on the side of PQ away from O, then the lacus of R will be,
Answer» STRAIGHT LINE CIRCLE ellipse parabola Answer :A

Discussion

8062.	IfP(X) = (3)/( 10) , P(Y) = (2)/(5) and P(X cupY) = (3)/(5) , "then " P((Y)/(X))+ P ((X)/(Y)) equals
Answer» `(1)/(4)` `(1)/(3)` `(5)/(12)` `(7)/(12)` ANSWER :D

Discussion

8063.	The mean weight of 150 students in a certain class is 60 kilograms. The mean weight of boys in the class is 70 kilograms and that of the girls is 55 kilograms, then the number of boys and girls are
Answer» 100,50 50100 75,75 60, 90 Answer :B

Discussion

8064.	If the constant due to which it is displaced from a point on a particle due to which it is displaced from a point A(4, -3, -2) to a point B (6, 1, -3) then the work done by the forces is
Answer» 10 units `-10` units `-15` units `-9` units Solution :Resultant FORCE, `F=(2hati-5hatj+6hatk)+(-hati+2hatj-hatk)=hati-3hatj+5hatk` and displacement `d=(6hati+hatj-3hatk)-(4hati-3hatj-2hatk)=2hati+4hatj-hatk` `:.""`Work DONE W `= F* d=( hati-3hatj+5hatk)*(2hati+4hatj-hatk)=-15` `=-15` units[ NEGLECTING- ve sign]

Discussion

8065.	Evaluate : int(cosx+3sinx+7)/(cosx+sinx+1)dx.
Answer» ANSWER :`2x-log\|cosx+1\|+5log\|1+tan""(X)/(2)\|_k`

Discussion

8066.	Prove that the points : (x_1,y_1),(x_2,y_2),(x_3,y_3) are collinear if [[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]]=0
Answer» SOLUTION :From geometry, we know that, if the POINTS A,B,C, are collinear, then the area of the traingle ABC with vertices`(x_1,y_1),(x_2,y_2)` and `(x_3,y_3)` is zero . `[[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]]`=0

Discussion

8067.	Let veca, vecb, vecc be three vectors such that 3veca + 4vecb + 5vecc=0. Then which of the following statements is true?
Answer» `VECA` is parallel to `VECB` `veca` is perpendicular to `vecb` `veca` is neither parallel nor perpendicular to `vecb` None of these Answer :B

Discussion

8068.	Evaluate : int_(0)^(a)x^(5//2)sqrt(a-x)dx
Answer» Solution :`{:("Put" x = a sin^(2)theta,rArr,dx=2asinthetacostheta d theta),("Lower LIMIT" : x = 0, rArr, theta = 0),("Upper limit" x = a , rArr, theta = pi/2):}` `underset(0)OVERSET(pi)intx^(5//2)SQRT(a-x)dx=underset(0)overset(pi/2)int2a^(4)sin^(6)theta d theta = 2a^(4) xx (pi)/(2).((5.31)(1))/(8.64.2) = (5pia^(4))/(128)`

Discussion

8069.	Find the equation of a curve passing through the point (0,2), given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.
Answer» ANSWER :`y = 4 - X - 2 E^(x)`

Discussion

8070.	Evaluate the definite integrals int_(0)^(pi/4)cosecxdx
Answer»

Discussion

8071.	If rational a, b, c, d are in G.P., then roots of equation (a-c)^(2) x^(2)+(b-c)^(2)x +(b-d)^(2)=(a-d)^(2) are necessarily
Answer» IMAGINARY IRRATIONAL RATIONAL REAL and distinct Answer :C

Discussion

8072.	Length of the common chord of the circles (x -1) ^(2) + (y + 1)^(2) = c ^(2) and (x +1) ^(2) + (y-1) ^(2) =c^(2) is
Answer» `1/2 SQRT (C^(2) -2)` `sqrt (c ^(2) -2)` `2 sqrt ( c ^(2) -2)` `c + 2` ANSWER :C

Discussion

8073.	intcot^(-1)(1-x+x^2)dx=
Answer» `xtan^(-1)X+(1-x)TAN^(-1)(1-x)+(1)/(2)log\|1+x^2\|+(1)/(2)log\|1+(1-x^2)\|+c` `xtan^(-1)x-(1-x)tan^(-1)(1-x)+(1)/(2)log\|1+x^2\|+(1)/(2)log\|1+(1-x^2)\|+c` `xtan^(-1)x-(1-x)tan^(-1)(1-x)-(1)/(2)log\|1+x^2\|+(1)/(2)log\|1+(1-x^2)\|+c` `xtan^(-1)x-(1-x)tan^(-1)(1-x)+(1)/(2)log\|1+x^2\|-(1)/(2)log\|1+(1-x^2)\|+c` ANSWER :C

Discussion

8074.	{{:(6x+3y=18),(qx -y/3=-2):} In the system of linear equations above, q is a constant. If the system has infinitely many solutions, what is the value of q?
Answer» `-9` `-2.3` `2.3` 9 Solution :A SYSTEM of equations that has infinitely many solutions DESCRIBES a single line. Therefore, MANIPULATION of one equation will yield the other. Look at the constant terms: to turn the 18 into `1-2,` DIVIDED the first equation by `-9:` `((6x+3y=18))/(-9)to - 6/9x - 3/9y=-2` `to -2/3x -1/3 y =-2` The y terms and constants in the second equation now match those in the first, all that's left is to SET the coefficients of x equal to each other : `q =-2/3.` Choice (B) is correct. Note that you could also write each equation in slopeintercept form and set the slopes equal to each other to solve for q.

Discussion

8075.	Discuss the continuity of the function f defined by f(x)= {(x+2",","if" x le 1),(x-2",","if" x gt 1):}
Answer» ANSWER :x=1

Discussion

8076.	Let M=[(a,b,c),(d,e,f),(1,1,1)] and N=(M^(2))/(2). If (a-b)^(2)+(d-e)^(2)=36, (b-c)^(2)+(e-f)^(2)=64, (a-c)^(2)+(d-f)^(2)=100, then value of \|N\| is equal to
Answer» 1152 48 144 288 Answer :D

Discussion

8077.	The value of a, for which the points A, B and C with position vectors 2hati-hatj+hatk, hati-3hatj-5hatk and a hati-3hatj+hatk respectively are the vertices of a right angled triangle with C=(pi)/(2) are
Answer» `-2 and -1` `-2 and 1` `2 and -1` 2 and 1 Solution :Given, POSITIONVECTORS of A,B, C are `2hati -hatj + hatk`,`HATI -3hatj - 5hatk`and `AHATI - 3hatj + hatk`,RESPECTIVELY. Now, `AC = (ahati- 3hatj + hatk) - (2hati - hatj + hatk) = (a-2)hati - 2hatj` and `BC = (ahati - 3hatj +hatk) - (hati - 3hatj - 5hatk) = (a-1)hati + 6hatk` Since, the `DeltaABC`is rightangledat C, therefore `AC.BC = 0` `rArr {(a-2)hati- 2hatj}.{(a-1)hati + 6hatk} = 0` `rArr (a-2)(a-1)= 0` `:. a = 1` and `2`

Discussion

8078.	Find the maximum and the minimum values, if any, of the function f given by f(x)=x^(2), x in R.
Answer» Answer :MAXIMUM value of the function f does not exists and MINIMUM value is ZERO.

Discussion

8079.	Evaluate the following integrals. intxsqrt(4x+3)dx
Answer» ANSWER :`(1)/(40)(4x+3)^(5//2)-(1)/(8)(4x+3)^(3//2)+C`

Discussion

8080.	Evaluate int(x^(6)-1)/(x^(2)+1)dx
Answer» ANSWER :`(X^(5))/(5)-(x^(3))/(3)+x-2tan^(1-)x+c`

Discussion

8081.	If I_(1), I_(2), I_(3) are the centers of escribed circles of Delta ABC, show that the area of Delta I_(1) I_(2) I_(3) is (abc)/(2r)
Answer» Solution :AREA `= (I_(1) I_(2) xx I_(3)I_(2) xx I_(1) I_(3))/(4R')` where R' = Circumradius of `Delta I_(1) I_(2) I_(3)` `= ((4R cos.(A)/(2)) (4R cos.(B)/(2))(4R cos.(C)/(2)))/(8R)`(`:' Delta ABC` is pedal TRIANGLE for `Delta I_(1), I_(2), I_(3)`) `=8R^(2) cos.(A)/(2) cos.(B)/(2) cos.(C)/(2)` `= (R^(2) sin A sin B sin C)/(sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))` `= (R^(2) abc)/(8R^(3) sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))` `= (abc)/(2(4R sin.(A)/(2) sin.(B)/(2) sin.(C)/(2)))` `= (abc)/(2r)`

Discussion

8082.	If theta is eliminated from the equations a sec theta-x tan theta=y" and "b sec theta+y tan theta=x (a and b are constants), then :
Answer» the DIRECTOR circle of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` auxiliary circle of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` director circle of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` director circle of the circle `x^2+y^2=(a^2+b^2)/(2)` ANSWER :C::D

Discussion

8083.	If sec theta =x+1/(2x) , then the value of sec theta +tan thetawill be
Answer» 2x X `2/(x)` `1/x` ANSWER :A::C

Discussion

8084.	If n in N , then the number (2+sqrt3)^n+(2-sqrt3)^n is
Answer» an INTEGER for all values of n an integer if n is EVEN an integer if n is ODD ALWAYS an IRRATIONAL number Answer :A

Discussion

8085.	If ax^(2) + bx + c, a, b, c in R, a ne 0 has real zero and a - b + c lt 0 , then value of ac is
Answer» positive zero negative non-negative Answer :A

Discussion

8086.	Write{x:x =is an odd integer} set in the form of lists?
Answer» SOLUTION :`{+- 1,+- 3, +-5, …………}`

Discussion

8087.	The tangent to curve y_(1)=ax^(2)+bx+7/2 at (1,2)is parallel to normal at point (-2,2) on curve y_(2)=x^(2)+6x+10 then value of (a-2b) is
Answer» Solution :(1,2) LIES on `y_(1)` `2=a+b+7/2impliesa+b=-3/2`……………1 `((dy_(1))/(dx))_((1,2))=-1/(((dy_(2))/(dx))_((-2,2)))` `2a+b=-1/2` `a-2b=6`

Discussion

8088.	In the matrix A=[[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]] Write: The number of elements
Answer» SOLUTION :The NUMBER of ELEMENTS in `A=3xx4=12`

Discussion

8089.	Integrate the following functions. int(x+2)/((x^(2)+3x+2)sqrt(x+1))dx
Answer» Answer :`(2)/(SQRT3)tan^(-1)((X)/(sqrtxsqrt(x+1)))+c`

Discussion

8090.	Letf(x) = ax^(2) + bx + c,where a, b, c in R . Suppose \|f (x) \|le 1 AA x in [0,1] ,then \|a\| cannot exceed
Answer» 5 6 7 8 Answer :D

Discussion

8091.	Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X ?
Answer» ANSWER :0, 2, 4 and 6.

Discussion

8092.	A park has the shape and dimensions in blocks given below. A water fountain is located halfway between point B and point D. Which of the following is the location of the water fountain from point A? (Note: The park's borders run east-west or north-south.)
Answer» `3 1/2` blocks east and 6 blocks NORTH 5 blocks east and `4 1/2` blocks north 5 blocks east and 6 blocks north `8 1/2` BLOCK east and `4 1/2` block north Answer :D

Discussion

8093.	A binary sequence of length n is a sequence of length n such that each of its terms is either 0 or 1. How many binary words of length 10 begin with three 0's
Answer» ANSWER :`2^(7)`

Discussion

8094.	A binary sequence of length n is a sequence of length n such that each of its terms is either 0 or 1. How many end with two l's.
Answer» ANSWER :`2^(8)`

Discussion

8095.	f : N to N : f (x) =x^(2) + x+ 1is
Answer» ONE-one and onto one - one and into many -one and onto many -one and into Answer :B

Discussion

8096.	If y=(Cot^(-1)x^(3))^(2) then find dy/dx.
Answer» ANSWER :`(-6X^(2)Cot^(-1)X^(3))/(1+x^(6))`

Discussion

8097.	Find the number of 4 letter words that can be formed using the letters of the word 'ARTICLE' in which atleast one letter is repeated.
Answer» ANSWER :`7^4-""^7P_4`

Discussion

8098.	Is the function [x] differentiable at x=0?
Answer» SOLUTION :[X] is not DIFFERENTIABLE at x=0.

Discussion

8099.	The upper three-quarters of a vertical pole subtends an angle tan^(-1) (3//5) at a point in the horizontal plane through its foot and distant 40 m from it. The height of the pole is
Answer» 80 m 100 m 160 m 200 m ANSWER :C

Discussion

8100.	IF""^((2n-1))P_(n-1): ""^((2n-1))P_n= 3:5then n=
Answer» 4 7 8 9 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Findthe areaof theregionboundedby thecurvey^2 = 4xandx^2 = 4y

Evaluate the following integrals. inttan^(4)xsec^(2)x dx

If the point z = (1+i) (1+2i)(1+3i)…(1+10i) lies on a circle with centre at origin and radius r, then r^(2) =

Evaluate the following: intx^2e^(ax)dx

int sec^(4)x dx=

Using quantifiers AA,EE convert the following open statement into true statement. 'x + 5 = 8 , x in N'

Let n be a positive integer and a complex number with unit modulus is a solution of the equation Z^n+Z+1=0 , then the value of n can be

The roots of the equation (x -1 )^(3) + 8 = 0 are

If A and B are two events such that P(A) = (1)/(3), P(B) = (1)/(4) and P(A cap B) = (1)/(5) , then P(A' | B') = ………..

Find the area of the region enclosed by the circle x^(2)+y^(2)=a^(2) by integration method.

OX and OY are two coordinate axes . On OY is taken a fixed point P on OX any point Q. On PQ an equilateral triangle is described, its vertex R being on the side of PQ away from O, then the lacus of R will be,

IfP(X) = (3)/( 10) , P(Y) = (2)/(5) and P(X cupY) = (3)/(5) , "then " P((Y)/(X))+ P ((X)/(Y)) equals

The mean weight of 150 students in a certain class is 60 kilograms. The mean weight of boys in the class is 70 kilograms and that of the girls is 55 kilograms, then the number of boys and girls are

If the constant due to which it is displaced from a point on a particle due to which it is displaced from a point A(4, -3, -2) to a point B (6, 1, -3) then the work done by the forces is

Evaluate : int(cosx+3sinx+7)/(cosx+sinx+1)dx.

Prove that the points : (x_1,y_1),(x_2,y_2),(x_3,y_3) are collinear if [[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]]=0

Let veca, vecb, vecc be three vectors such that 3veca + 4vecb + 5vecc=0. Then which of the following statements is true?

Evaluate : int_(0)^(a)x^(5//2)sqrt(a-x)dx

Find the equation of a curve passing through the point (0,2), given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

Evaluate the definite integrals int_(0)^(pi/4)cosecxdx

If rational a, b, c, d are in G.P., then roots of equation (a-c)^(2) x^(2)+(b-c)^(2)x +(b-d)^(2)=(a-d)^(2) are necessarily

Length of the common chord of the circles (x -1) ^(2) + (y + 1)^(2) = c ^(2) and (x +1) ^(2) + (y-1) ^(2) =c^(2) is

intcot^(-1)(1-x+x^2)dx=

{{:(6x+3y=18),(qx -y/3=-2):} In the system of linear equations above, q is a constant. If the system has infinitely many solutions, what is the value of q?

Discuss the continuity of the function f defined by f(x)= {(x+2",","if" x le 1),(x-2",","if" x gt 1):}

Let M=[(a,b,c),(d,e,f),(1,1,1)] and N=(M^(2))/(2). If (a-b)^(2)+(d-e)^(2)=36, (b-c)^(2)+(e-f)^(2)=64, (a-c)^(2)+(d-f)^(2)=100, then value of |N| is equal to

The value of a, for which the points A, B and C with position vectors 2hati-hatj+hatk, hati-3hatj-5hatk and a hati-3hatj+hatk respectively are the vertices of a right angled triangle with C=(pi)/(2) are

Find the maximum and the minimum values, if any, of the function f given by f(x)=x^(2), x in R.

Evaluate the following integrals. intxsqrt(4x+3)dx

Evaluate int(x^(6)-1)/(x^(2)+1)dx

If I_(1), I_(2), I_(3) are the centers of escribed circles of Delta ABC, show that the area of Delta I_(1) I_(2) I_(3) is (abc)/(2r)

If theta is eliminated from the equations a sec theta-x tan theta=y" and "b sec theta+y tan theta=x (a and b are constants), then :

If sec theta =x+1/(2x) , then the value of sec theta +tan thetawill be

If n in N , then the number (2+sqrt3)^n+(2-sqrt3)^n is

If ax^(2) + bx + c, a, b, c in R, a ne 0 has real zero and a - b + c lt 0 , then value of ac is

Write{x:x =is an odd integer} set in the form of lists?

The tangent to curve y_(1)=ax^(2)+bx+7/2 at (1,2)is parallel to normal at point (-2,2) on curve y_(2)=x^(2)+6x+10 then value of (a-2b) is

In the matrix A=[[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]] Write: The number of elements

Integrate the following functions. int(x+2)/((x^(2)+3x+2)sqrt(x+1))dx

Letf(x) = ax^(2) + bx + c,where a, b, c in R . Suppose |f (x) |le 1 AA x in [0,1] ,then |a| cannot exceed

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X ?

A park has the shape and dimensions in blocks given below. A water fountain is located halfway between point B and point D. Which of the following is the location of the water fountain from point A? (Note: The park's borders run east-west or north-south.)

A binary sequence of length n is a sequence of length n such that each of its terms is either 0 or 1. How many binary words of length 10 begin with three 0's

A binary sequence of length n is a sequence of length n such that each of its terms is either 0 or 1. How many end with two l's.

f : N to N : f (x) =x^(2) + x+ 1is

If y=(Cot^(-1)x^(3))^(2) then find dy/dx.

Find the number of 4 letter words that can be formed using the letters of the word 'ARTICLE' in which atleast one letter is repeated.

Is the function [x] differentiable at x=0?

The upper three-quarters of a vertical pole subtends an angle tan^(-1) (3//5) at a point in the horizontal plane through its foot and distant 40 m from it. The height of the pole is

IF""^((2n-1))P_(n-1): ""^((2n-1))P_n= 3:5then n=