28278 + Interview Questions in Maths in Class 12 Page 257 InterviewSolution

12801.	Choose the correct answer. The general solution of a differential equation of the type (dx)/(dy) + P_1 x = Q_1 isa)y e^(int P_1 dy) = int (Q_1 e^(int P_1 dy))dy + cb)y e^(int P_1 dx) = int (Q_1 e^(int P_1 dx))dy + cc)x e^(int P_1 dy) = int (Q_1 e^(int P_1 dy))dy + cd)x e^(int P_1 dx) = int (Q_1 e^(int P_1 dx))dx + c
Answer» `y e^(int P_1 dy) = int (Q_1 e^(int P_1 dy))dy + c` `y e^(int P_1 dx) = int (Q_1 e^(int P_1 dx))dy + c` `x e^(int P_1 dy) = int (Q_1 e^(int P_1 dy))dy + c` `x e^(int P_1 dx) = int (Q_1 e^(int P_1 dx))dx + c` ANSWER :C

Discussion

12802.	Find the number of diagonals of a polygon having 20 sides
Answer» ANSWER :170

Discussion

12803.	Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
Answer» `0.7` `0.06` `0.14` `0.2` ANSWER :C

Discussion

12804.	If A=[{:(1,5),(7,12):}],B=[{:(9,1),(7,8):}] find a matrix C such that 3A+5B+2C is a null matrix.
Answer» ANSWER :`=[{:(-24,-10),(-28,-38):}]`

Discussion

12805.	Evaluate the following integrals (iii) int_(-1)^(2) (x^(2))/(x^(2)+2)dx
Answer» ANSWER :`3-SQRT(2)(TAN^(-1)sqrt(2)+Tan^(-1)((1)/(sqrt(2))))`

Discussion

12806.	L_(1)andL_(2) are two lines whose vector equations are L_(1):vecr=lamda((costheta+sqrt3)hati+(sqrt2sintheta)hatj+(costheta-sqrt3)hatk) L_(2):vecr=mu(ahati+bhatj+chatk), where lamdaandmu are scalars and alpha is the acute angle between L_(1)andL_(2).If the anglealpha is independent of theta then the value of alpha is
Answer» `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` Solution :Both the lines pass through the origin. Line `L_(1)` is parallel to the vector `vec(V_1)` `""vec(V_1)= (costheta+sqrt(3))HATI+ (sqrt2 sin theta)hatj + (costheta-sqrt3)hatk` and `L_(2)` is parallel to the vector `vec(V_2)` `""vec(V_2) = ahati+bhatj+chatk` `therefore ""cosalpha= (vec(V_1)*vec(V_2))/(\|vec(V_1)\|\|vec(V_2)\|)` `= (a(costheta+ sqrt3)+ (bsqrt2)sintheta+c(costheta-sqrt3))/(sqrt(a^(2)+B^(2)+c^(2))sqrt((costheta+sqrt3)^(2)+ 2sin^(2)theta+ (costheta-sqrt3)^(2)))` `((a+c)costheta+bsqrt2sintheta+ (a-c)sqrt3)/(sqrt(a^(2)+b^(2)+c^(2))sqrt(2+6))` For `cos ALPHA` to be INDEPENDENT of `theta`, we get `""a+c=0 and b=0` `therefore ""cosalpha = (2asqrt3)/(asqrt2 2sqrt2)= (sqrt3)/(2)` or `""alpha= (pi)/(6)`

Discussion

12807.	The points of intersection of the parabolas y^(2) = 5x and x^(2) = 5y lie on the line
Answer» x+y=10 x-2y=0 x-y=0 2x-y=0 Answer :C

Discussion

12808.	For 0 le theta ltpi/4,let x = sum_(n=0)^(oo)(sin theta )^(2n), y = sum_(n=0)^(oo)(cos theta)^(2n) then sum of the series {:(,P,Q,R,S),((A),2,4,1,3),((B ),3,2,4,1),((C ),1,3,2,4),((D),4,1,2,3):}
Answer» ANSWER :B

Discussion

12809.	""^4C_1 + ""^5C_2.(1/2) + ""^6C_3.(1/2)^2+….. to oo terms :
Answer» 30 40 900 15 Answer :A

Discussion

12810.	A variablecircle is drawn to touch the x-axis at the origin. The locus of the pole of the straight line l x+my+n=0 w.r.t the variable circle has the equation:
Answer» `X(my-n)-LY^(2)=0` `x(my+n)-ly^(2)=0` `x(my-n)+ly^(2)=0` None of these Answer :A

Discussion

12811.	int (cos sqrt(x))/(sqrtx) dx
Answer» ANSWER :`2sinsqrtx+C`

Discussion

12812.	A be a square matrix of order 2 with \|A\| ne 0 such that \|A+\|A\| adj (A) \| = 0 , where adj(A) is a adjoint of matrix A, then the value of \|A-\|A\| adj (A) \| is
Answer» 1 2 3 4 Answer :D

Discussion

12813.	Let f(x) be a non negative continuous and bounded function for all xge0 .If (cos x)f(x) lt (sin x- cosx)f(x) forall x ge 0, then which of the following is/are correct?
Answer» `f(6)+f(5)gt0` `x^(2)-3x+2+f(7)=0` has 2 distinct solution f(5)f(7)-f(5)=0 `underset(xrarr6)lim (f(x)-sin (PIX))/(x-6)=1` Solution :Let `g(x)=e^(x)cosxf(x)` `therefore g(x)=e^(x)cosxf(x)+e^(x)(cosx-sinx)f(x)` `=e^(x)(cosxf(x)+(cosx-sinx)f(x)` `le0` `therefore g(X)` is a NON increasing function `therefore f(6)=e^(6)cos 6 f(6)le0` `therefore f(6)le0` But given that f(x) is non negative ltbegt `therefore f(6)=0` with similar reasons f(5),f(7)=0 Thus `x^(2)-3x+2+f(7)=0` or `x^(2)-3x+2=0` l has 2 distinct solution `underset(xrarr6)lim(f(x)-sin(pix))/(x-6)` =`underset(xrarr6)limf(x)-picos(pix)/(1)` (applying L hospital rule) `=f(6)-pilt0`

Discussion

12814.	If log_(e)5,log_(e)(5^(x) - 1)and log_(e)(5^(x) - 11/5) are in A.P., then the values of x are
Answer» `log_(5)4` and `log_(5)3` `log_(3)4` and `log_(4)3` `log_(3)4` and `log_(3)5` `log_(5)6` and `log_(5)7` ANSWER :A

Discussion

12815.	Find the vector and cartesian equations of the planes :(a) that passes through the point (1, 0, -2) and the normal to the plane is hati+hatj-hatk.(b) that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk.
Answer» Answer :(a) `IMPLIES` X + y - Z = 3 (b) `therefore` x-2y+z+1=0

Discussion

12816.	Find the value of k so that the function: f(x) = [{:(kx + 1, if x le 5),(3x-5, if x gt 5):}] at x=5 is a continous function:
Answer» ANSWER :`k-9/5`

Discussion

12817.	Using elementary transformations, find the inverseof the matrices [(2,-3),(-1,2)]
Answer» ANSWER :`[(2,3),(1,2)]`

Discussion

12818.	Find the probability of getting a odd number in a single roll of the die
Answer» <P> Answer :Probability of GETTING an odd NUMBER `=P(1)+P(3)+P(5)` `1/21+ 3/21+5/21=9/21`

Discussion

12819.	A variable plane is at a distance of 6 units from the origin. If it meets the coordinate axes in A, B and C, then the equation of the locus of the centroid of the Delta ABC is
Answer» `1/x^(2)+1/y^(2)+1/Z^(2)=1/4` `x^(2)+y^(2)+z^(2)=4` `1/x^(2)+1/y^(2)+1/z^(2)=1` `1/x^(2)+1/y^(2)-1/z^(2)=1/4` ANSWER :A

Discussion

12820.	The real x and y satisfy log_(8) x + log_(4) y^(2) = 5 " and " log_(8) y + log_(4) x^(2) = 7, find xy.
Answer» ANSWER :`XY = 2^(9)`

Discussion

12821.	Determine the order and degree of the differential equation y' + 5y = 0
Answer» ANSWER :ORDER 1; DEGREE 1

Discussion

12822.	Write the projection of the point (1,2,3) on xy-plane.
Answer» SOLUTION :PROJECTION of the POINT (2,3,1) on y-axis is (0,3,0).

Discussion

12823.	The solution of (dy)/(dx) = e^(x-y) (e^(x) - e^(y)) is
Answer» `E^(y) = e^(X) -1+ CE^(-e^(x))` `e^(y) = e^(x) + 1 + ce^(-e^(x))` `e^(y) = e^(x) -1 - ce^(-e^(x))` `e^(y) = e^(x) -2 + ce^(-e^(x))` ANSWER :A

Discussion

12824.	If cosalpha=(1)/(sqrt5)(0°ltalphalt90^(@))andcosbeta=(1)/(sqrt10),(270^(@)ltbetalt360^(@)) then the value of sin(alpha+beta) is
Answer» `(1)/(SQRT2)` `(1)/(5sqrt2)` `-(3)/(5sqrt2)` `-(1)/(5sqrt2)` ANSWER :A::B

Discussion

12825.	Number of ways in which n differentprizes can be distributedamong m-persons (m lt n)if each is entitled to receive atmost (n-1) prizes is
Answer» `N^(m) - n` `m^(n)` MN `m^(n) - m` ANSWER :D

Discussion

12826.	Protein present in eye lens is :
Answer» Opsin Collagen Crystalline Rhodopsin Answer :A

Discussion

12827.	If a, b,c be the sides of a triangle ABC with right angle at C. The medians AD and BE have slopes 1 and 2 respectively. Then ab = kc where 36 k equals………
Answer» ANSWER :8

Discussion

12828.	Which of the following statement is dual of p ^^ ( q vee r ) equiv ( p ^^ q) vee ( p ^^ r)
Answer» <P>`pvee ( Q VEE r ) equiv ( p vee q ) ^^ ( p vee r ) ` `p vee ( q ^^ r ) equiv ( p vee q ) ^^ (p VV r) ` `p ^^ (q ^^ r ) equiv( p ^^ q) vv (q ^^ r)` `p ^^ ( q ^^ r ) equiv ( p ^^ q ) vee ( q ^ r)` Answer :B

Discussion

12829.	When H_(2)O_(2) is reacted with K_(2)Cr_(2)O_(7)" in dilute "H_(2)SO_(4) and then ether is added. The ether layer gets -colour
Answer» RED Yellow BLUE Green Answer :C

Discussion

12830.	I. The number of all ten digited numbers that can be formed with all the distinct digits and which ar divisble by 4 is 15 times 81. II. The number of positive integers that can be formed by using the digits 0, 1, 2, 3, 4, 5 without any repetition is 630.
Answer» Only I is true Only II is true Both I and II are true Both I and IIare false Answer :B

Discussion

12831.	A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and 2 hours on the sprayer to manufacture a shade.On any day, the sprayer is available for at the most 12 hours and the grinding/cutting machine for at the most 12 hours.The profit from the sale of a lamp is ₹ 5 and that from a shade is ₹ 3.Assuming that manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
Answer» Answer :Max.profit is ₹ 32 when 4 PEDESTAL LAMPS and 4 WOODEN shades are manufactured.

Discussion

12832.	The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking it was found that one item 8 was incorrect. If it is replaced by 12, then find the mean and variance.
Answer» ANSWER :10.2 and 3.96

Discussion

12833.	Three lines drawn from origin with direction cosines l_1,m_1,n_1 , l_2, m_2,n_2 , l_3,m_3,n_3 are coplanar iff : \|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)\|=0 since :
Answer» intersecting LINES are coplanar it is POSSIBLE to FIND a LINE perpendicular to all these lines all lines pass through origin None of these. Answer :A

Discussion

12834.	Find the area of the region given by : {(x,y): x ^(2) le y le \|x\|}. (ii) Find the area bounded by thte curves : {(x,y) : y ge x ^(2) and y= \|x\|}. (iii) Find the area of the region bounded by the parabola y = x ^(2) and y= \|x\|.
Answer» ANSWER :`(i) -(III) (1)/(3)` (sq. units).

Discussion

12835.	Numberof transformed equations ofx^3 +2x^2 +x+1=0byeliminatingthirdtermis
Answer» `X^(4) + 6x^(3) - 12X + 8 = 0 " or " x^(4) - 6x^(3) + 42x + 53 = 0 ` `x^(4) + 6x^(3) - 12x - 8 = 0 " or " x^(4) - 6x^(3) + 42x - 53 = 0 ` `x^(3) + x^(2) + 1 =0 " or " 27x^(3) - 27x^(2) + 23 = 0 ` `x^(3) - x^(2) + 1 =0 " or " 27x^(3) + 27x^(2) + 23 = 0 ` ANSWER :4

Discussion

12836.	Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x),forall x,y in R, then for some real a,
Answer» f (X) is perodic FUNCTION f (x) is a CONSTANT function `f (x)= 1/2` ` f(x) =(cos x)/(2)` Answer :A::B::C

Discussion

12837.	Foran ellipse(x^2)/(a^2) +(y^2)/(b^2) =1, a gt b, the areaenclosedby two latusrectumis ……. ( whereis theeccentricityof anellipse )
Answer» `b ( b e + a sin^(-1) 2E)` `8b (b e+ a sin^(-1) e)` `(2b ( be+ ASIN ^(-1)e)` `4b( b e+ a sin^(-1) e)` Answer :C

Discussion

12838.	Let f(x)=(sinx-cosx+sqrt2)/(x^(3//2)), " where "x in [pi/4,(5pi)/4] . Let m be the maximum value of F(x) and M be the minimum value of F(x). Then [(2M)/(5m)] is equal to ([.]) denotesthe greatest interger function
Answer» 3 2 4 6 Answer :C

Discussion

12839.	Evaluate the following definite intergrals as limit of sums. overset(4)underset(0) int (x+e^(2x))dx
Answer» ANSWER :`(E^(8)+15)/(2)`

Discussion

12840.	Expand the expression (1 - 2x)^(5).
Answer» Answer :`= 1 - 10X + 40X^(2) - 80x^(3) + 80x^(4) - 32X^(5)`

Discussion

12841.	The value of f(x).f(-x) for all x is
Answer» 4 9 12 16 Answer :B

Discussion

12842.	If A denotes the area enclosed by 3\|x\|+4\|y\|le 12 then A is equal to
Answer» ANSWER :24

Discussion

12843.	The value of the expression \|bar(a)xx bar(b)\|^(2)+(bar(a).bar(b))^(2) is …………..
Answer» ANSWER :`=\|BAR(a)\|^(2).\|bar(B)\|^(2)`

Discussion

12844.	There is a point inside an equilateral triangle ABC of side d whose distance from the vertices is 3,4,5 . Rotate the triangle and P through 60^@ about C. Let A go to A' and P to P'. The angle APB is equal to
Answer» `90^@` `120^@` `150^@` none of these Answer :C

Discussion

12845.	There is a point inside an equilateral triangle ABC of side d whose distance from the vertices is 3,4,5 . Rotate the triangle and P through 60^@ about C. Let A go to A' and P to P'. The value of d^2 is
Answer» `25+12sqrt3` `25-12sqrt3` `5 + 12 SQRT3` `25 +24 sqrt3` Answer :A

Discussion

12846.	Ifroot3(-1) = -1 , -omega, -omega^(2) , then roots of the equation(x+1)^(3) + 64 =0are
Answer» ` 1- 4omega` ` -1-4 omega^(2)` `-5` `-4` ANSWER :A::B::C

Discussion

12847.	If X is a Poisson veriate with P(X = 0) = 0.8 , then the veriance of X is .
Answer» ` log_(e) 20` `log_(10) 20` `log_(e) 5//4 ` `0 ` Answer :C

Discussion

12848.	Solve the given equations: x +y +z=0 x^(3) + y^(3) +z^(3)=18 x^(7) + y^(7) + z^(7) = 2058 where x,y,z in R
Answer» ANSWER :(x, y, Z) = (2, -1, - 3), (2, - 3, - 1) (1-3,-2) (1-2,-3), (3,-1,-2), (3,-2.-1)

Discussion

12849.	From the following data, find (i) regression coefficients (ii) regression equations
Answer» Answer :`b_(yx-0.65,b_(XY)=-1.3` REGRESSION equation of y on x;y=-0.65x+11.9 Regression equation of x on `y:x=-1.3y+16.4`

Discussion

12850.	Find the locus of the point P(x,y) such that the area of the triangle PAB is 5, where A is the point (1,-1) and B is the point (5,2).
Answer» <P> SOLUTION : `THEREFORE` AREA of the triangle PAB is 1/2{x(-1-2) + 1(2-y) + 5(y+1)} = 1/2 (-3x+2-y+5y+5) 1/2(-3x+4y+7) = 1/2 (-3x+4y+7) = 5 or, -3x+4y+7 = 10 or, 3x-4y+3 = 0 which is the locus of the point P(x,y).

Discussion

Explore topic-wise InterviewSolutions in .

Find the number of diagonals of a polygon having 20 sides

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

If A=[{:(1,5),(7,12):}],B=[{:(9,1),(7,8):}] find a matrix C such that 3A+5B+2C is a null matrix.

Evaluate the following integrals (iii) int_(-1)^(2) (x^(2))/(x^(2)+2)dx

The points of intersection of the parabolas y^(2) = 5x and x^(2) = 5y lie on the line

For 0 le theta ltpi/4,let x = sum_(n=0)^(oo)(sin theta )^(2n), y = sum_(n=0)^(oo)(cos theta)^(2n) then sum of the series {:(,P,Q,R,S),((A),2,4,1,3),((B ),3,2,4,1),((C ),1,3,2,4),((D),4,1,2,3):}

""^4C_1 + ""^5C_2.(1/2) + ""^6C_3.(1/2)^2+….. to oo terms :

A variablecircle is drawn to touch the x-axis at the origin. The locus of the pole of the straight line l x+my+n=0 w.r.t the variable circle has the equation:

int (cos sqrt(x))/(sqrtx) dx

A be a square matrix of order 2 with |A| ne 0 such that |A+|A| adj (A) | = 0 , where adj(A) is a adjoint of matrix A, then the value of |A-|A| adj (A) | is

Let f(x) be a non negative continuous and bounded function for all xge0 .If (cos x)f(x) lt (sin x- cosx)f(x) forall x ge 0, then which of the following is/are correct?

If log_(e)5,log_(e)(5^(x) - 1)and log_(e)(5^(x) - 11/5) are in A.P., then the values of x are

Find the vector and cartesian equations of the planes :(a) that passes through the point (1, 0, -2) and the normal to the plane is hati+hatj-hatk.(b) that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk.

Find the value of k so that the function: f(x) = [{:(kx + 1, if x le 5),(3x-5, if x gt 5):}] at x=5 is a continous function:

Using elementary transformations, find the inverseof the matrices [(2,-3),(-1,2)]

Find the probability of getting a odd number in a single roll of the die

A variable plane is at a distance of 6 units from the origin. If it meets the coordinate axes in A, B and C, then the equation of the locus of the centroid of the Delta ABC is

The real x and y satisfy log_(8) x + log_(4) y^(2) = 5 " and " log_(8) y + log_(4) x^(2) = 7, find xy.

Determine the order and degree of the differential equation y' + 5y = 0

Write the projection of the point (1,2,3) on xy-plane.

The solution of (dy)/(dx) = e^(x-y) (e^(x) - e^(y)) is

If cosalpha=(1)/(sqrt5)(0°ltalphalt90^(@))andcosbeta=(1)/(sqrt10),(270^(@)ltbetalt360^(@)) then the value of sin(alpha+beta) is

Number of ways in which n differentprizes can be distributedamong m-persons (m lt n)if each is entitled to receive atmost (n-1) prizes is

Protein present in eye lens is :

If a, b,c be the sides of a triangle ABC with right angle at C. The medians AD and BE have slopes 1 and 2 respectively. Then ab = kc where 36 k equals………

Which of the following statement is dual of p ^^ ( q vee r ) equiv ( p ^^ q) vee ( p ^^ r)

When H_(2)O_(2) is reacted with K_(2)Cr_(2)O_(7)" in dilute "H_(2)SO_(4) and then ether is added. The ether layer gets -colour

I. The number of all ten digited numbers that can be formed with all the distinct digits and which ar divisble by 4 is 15 times 81. II. The number of positive integers that can be formed by using the digits 0, 1, 2, 3, 4, 5 without any repetition is 630.

The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking it was found that one item 8 was incorrect. If it is replaced by 12, then find the mean and variance.

Three lines drawn from origin with direction cosines l_1,m_1,n_1 , l_2, m_2,n_2 , l_3,m_3,n_3 are coplanar iff : |(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)|=0 since :

Find the area of the region given by : {(x,y): x ^(2) le y le |x|}. (ii) Find the area bounded by thte curves : {(x,y) : y ge x ^(2) and y= |x|}. (iii) Find the area of the region bounded by the parabola y = x ^(2) and y= |x|.

Numberof transformed equations ofx^3 +2x^2 +x+1=0byeliminatingthirdtermis

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x),forall x,y in R, then for some real a,

Foran ellipse(x^2)/(a^2) +(y^2)/(b^2) =1, a gt b, the areaenclosedby two latusrectumis ……. ( whereis theeccentricityof anellipse )

Let f(x)=(sinx-cosx+sqrt2)/(x^(3//2)), " where "x in [pi/4,(5pi)/4] . Let m be the maximum value of F(x) and M be the minimum value of F(x). Then [(2M)/(5m)] is equal to ([.]) denotesthe greatest interger function

Evaluate the following definite intergrals as limit of sums. overset(4)underset(0) int (x+e^(2x))dx

Expand the expression (1 - 2x)^(5).

The value of f(x).f(-x) for all x is

If A denotes the area enclosed by 3|x|+4|y|le 12 then A is equal to

The value of the expression |bar(a)xx bar(b)|^(2)+(bar(a).bar(b))^(2) is …………..

There is a point inside an equilateral triangle ABC of side d whose distance from the vertices is 3,4,5 . Rotate the triangle and P through 60^@ about C. Let A go to A' and P to P'. The angle APB is equal to

There is a point inside an equilateral triangle ABC of side d whose distance from the vertices is 3,4,5 . Rotate the triangle and P through 60^@ about C. Let A go to A' and P to P'. The value of d^2 is

Ifroot3(-1) = -1 , -omega, -omega^(2) , then roots of the equation(x+1)^(3) + 64 =0are

If X is a Poisson veriate with P(X = 0) = 0.8 , then the veriance of X is .

Solve the given equations: x +y +z=0 x^(3) + y^(3) +z^(3)=18 x^(7) + y^(7) + z^(7) = 2058 where x,y,z in R

From the following data, find (i) regression coefficients (ii) regression equations

Find the locus of the point P(x,y) such that the area of the triangle PAB is 5, where A is the point (1,-1) and B is the point (5,2).