28278 + Interview Questions in Maths in Class 12 Page 170 InterviewSolution

8451.	Solve -12x gt 30, when i.x is a natural number. ii.x is an integer.
Answer» ANSWER :There is no SOLUTION II. The i.solution set of INEQUALITY is {………..-6, -5, -4, -3}

Discussion

8452.	Find the number of different seven digit numbers that can be written using only the three digits, 1,2,3 with the condition that the digit 2 occurs atleast 2 times in each number.
Answer» ANSWER :`3^(7)-2^(7)-7.2^(6)`

Discussion

8453.	A variable line 'L' Passing through the origin cuts two parallel lines x-y+10=0 and x-y+20=0 at two points A and B respectively . If P is a point on line 'L' such that OA , OP, OB are in harmonic progression then the locus of P is
Answer» 3x+3y+40=0 3x+3y+20=0 2x-3y+40=0 3x-3y+20=0 Answer :C

Discussion

8454.	Integrate the following functions. int(x^(3))/(2x+1)dx
Answer» ANSWER :`(x^(3))/(6)-(x^(2))/(8)+(x)/(8)-(1)/(16)log\|2x+1\|+c`

Discussion

8455.	A: If the transformed equation of a curve is 9X^(2) + 16Y^(2) = 144 when the axes are rotated through an angle 45^(@), then the original equation is 25x^(2) - 14xy+ 25y^(2) = 288. R: If f(x,y)=0 is the transformed equation of a curve when the axes are rotate through an angle theta then the original equation of the curve is f(x cos theta + y sin theta, -x sin theta + y cos theta)=0
Answer» Both A and R are true and R is the correct EXPLANATION of A. Both A and R are true but R is not the correct explanation of A. A is true but R is FALSE A is false but R is false ANSWER :A

Discussion

8456.	int cos sqrt(x)dx=
Answer» `2 [ SQRT(X) SIN sqrt(x) + cossqrt(x) ] + c ` 2 `[ sqrt(x) sin sqrt(x) - COS sqrt(x) ] + c ` 2 `[ sqrt(x) cos sqrt(x) + sin sqrt(x) ] + c ` 2 `[ sqrt(x) cos sqrt(x) -sin sqrt(x) ] + c ` Answer :A

Discussion

8457.	If y = (a^(cos x))/( sqrt(1+ x^(2) )),then (dy)/(dx) =
Answer» ` (a^(cos x ) (( 1+x^(2) )(LOG a)(sin a )(sin x) ))/( (SQRT( 1+ x^(2)))^(3)) ` ` (-a^(cos x ) (( 1+x^(2) )(log a)(sin a )(sin x) ))/( (sqrt( 1+ x^(2)))^(3)) ` ` (a^(cos x ) (( 1+x^(2) )(log a)(sin a )(sin x) +x))/( (sqrt( 1+ x^(2)))^(3)) ` ` (-a^(cos x ) (( 1+x^(2) )(log a)(sin a )(sin x) +x))/( (sqrt( 1+ x^(2)))^(3)) ` Answer :D

Discussion

8458.	IfA_n= [ad ]A_2 =[{:( a_2, a_s),( a_4 .a_5):}], A_5 =[{:( a_6,a_7,a_8),( a_9,a_10 ,a_11),( a_12,a_13,a_14):}]= A_n =[…]and so on , where a_r= [log _2 r] where [.] denotes greatest integer function ) .Then T_r (A_10 )is equal to ,(T_r stands for trace of teh matrix )
Answer» 800 80 792 160 Answer :B

Discussion

8459.	Evaluate int_(0)^(1) x e^(x^(2))dx.
Answer» ANSWER :`1/2 (e-1)`

Discussion

8460.	The solution of linear programming problem, maximize Z=3x_(1)+5x_(2) subject to 3x_(1)+2x_(2) le 18, x_(1) le 4, x_(2) le 6, x_(1) ge 0, x_(2) ge 0 is ………..
Answer» `x_(1)=2, x_(2)=0, z=6` `x_(1)=2, x_(2)=6, z=36` `x_(1)=4, x_(2)=3, z=27` `x_(1)=4, x_(2)=6, z=42` Answer :B

Discussion

8461.	Two distinct numbers are chosen from 1,3,5,7 ……. 151,153,155 and multiplied . The probability that the product is a multiple of 5 is
Answer» `1020/3003` `1112/3003` `1011/3003` `1122/3003` ANSWER :B

Discussion

8462.	How many different numbers each of the six digit can be formed using the digit 1,2,1,2,3,3, ?
Answer» 90 92 88 94 Answer :A

Discussion

8463.	The perpendicular distance of the point (3, -4, -5) from the line (x-2)/(4)=(y+6)/(5)=(z-5)/(-3) is ….....
Answer» `1/5sqrt(1657)` `(1)/(SQRT5)SQRT(1675)` `1/5sqrt(1757)` `(1)/(sqrt5)sqrt(1667)` ANSWER :A

Discussion

8464.	A curve is defined by the condition that the sum of the x and y intercepts of its tangents is always equal to 2. Express the condition by means of a differential equation.
Answer» Answer :`X((DY)/(dx))^(2) - (x+y - 2)(dy)/(dx) +y = 0`

Discussion

8465.	int_(0)^(1) Tan^(-1) ((2x-1)/(1+x-x^(2)))dx=
Answer» 1 0 `-1` `pi/4` ANSWER :B

Discussion

8466.	If the transversal y = m_(r)x: r = 1,2,3 cut off equal intercepts on the transversal x +y = 1 then 1 +m_(1),1 +m_(2),1+m_(3) are in
Answer» A.P. G.P. H.P. None of these Solution :Solving `y = m_(r)x` and `x+y = 1`, we get `x = (1)/(1+m_(r))` and `y = (m_(r))/(1+m_(r))`. Thus the POINTS of intersection of the three lines on the TRANSVERSAL are `P ((1)/(1+m_(1)),(m_(1))/(1+m_(1))), Q ((1)/(1+m_(2)),(m_(2))/(1+m_(2)))` and `R((1)/(1+m_(3)),(m_(3))/(1+m_(3)))` According to QUESTION `PQ = QR` `((1)/(1+m_(1))-(1)/(1+m_(2)))^(2)+((m_(1))/(1+m_(1))-(m_(2))/(1+m_(2)))^(2)` `= ((1)/(1+m_(2))-(1)/(1+m_(3)))^(2) +((m_(2))/(1+m_(2))-(m_(3))/(1+m_(3)))^(2)` `rArr (m_(2)-m_(1))/(1+m_(1)) = (m_(3)-m_(2))/(1+m_(3))` `rArr (1+m_(2))/(1+m_(1)) - 1 = 1 -(1+m_(2))/(1+m_(3))` `rArr (1+m_(2))/(1+m_(1)) +(1+m_(2))/(1+m_(3)) =2` `rArr 1+m_(2) =(2(1+m_(1))(1+m_(3)))/((1+m_(1))+(1+m_(3)))` `rArr 1+m_(1), 1 +m_(2), 1 +m_(3)` are in H.P.

Discussion

8467.	Ifu = sqrt( a^2cos^2 theta+b^2 sin ^2theta ) + sqrt( a^2 sin^2 theta+b^2 cos^2theta ) then thedifferencebetweenthe maximumand manimumvaluesofu^2is givenby
Answer» `(a+b)^2` `2 SQRT(a^2 +b^2)` `2(a^2 +b^2)` `(a-b)^2` ANSWER :D

Discussion

8468.	If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
Answer» 602 603 600 601 Answer :D

Discussion

8469.	State whether the following statements are true or false, Justify. If is a commutative binary opertion on N, then a (b c) = (cb) **a
Answer»

Discussion

8470.	Integrate the following functions. int(x^(2)+a^(2))/(x^(4)+a^(4))dx
Answer» ANSWER :`(1)/(sqrt2a).TAN^(-1)((x^(2)-a^(2))/(sqrt2ax))+C`

Discussion

8471.	A and B are among 30 persons who sit at random along a round table. Find the probability that there are any six persons between A and B .
Answer» ANSWER :`(2)/(29)`

Discussion

8472.	Which of the following is CORRECT combination ?
Answer» `(II) (ii) (S) ` `(I) (i) (Q) ` `(I) (ii) (Q) ` `(III) (ii) (R ) ` SOLUTION :N/A

Discussion

8473.	Which of the following is CORRECT combination ?
Answer» `(II) (ii) (R )` `(II) (i) (R ) ` `(III) (i) (Q) ` `(IV) (i) (S) ` Solution :N/A

Discussion

8474.	Which of the following is CORRECT combination ?
Answer» `(IV) (II) (S)` `(III) (i) (Q) ` `(IV) (i) (S)` `(II) (ii) (R ) ` Solution :N/A

Discussion

8475.	Axes are co-ordinate axes, S and S^(1)are Foci, B and B^(1)are the ends of minor axis\|SBS^(1) = sin ^(-1) ((4)/(5) ) .if area of SB S^(1) B^(1)is 20sq. Units then eq. of the ellipse is
Answer» A) ` (X^(2) )/( 20 ) + ( y^(2))/( 16) =1` B) ` (x^(2))/(25) +(y^(2))/( 16)=1` C) ` (x^(2))/( 25) +(y^(2))/( 4))= 1 ` D) ` (x^(2))/( 25) +( y^(2))/( 20 ) =1 ` ANSWER :D

Discussion

8476.	Solve the following differential equation:xy(dy)/(dx)-y^2=(x+y)^2e^(-y//x)
Answer» ANSWER :`E^(y/X)((x)/(x+y))=log\|x\|+c`

Discussion

8477.	If the the angle between the circles x^2+y^2-12x-6y+41=0 andx^2+y^2+kx+6y-59=0 is 45^@ find k.
Answer» ANSWER :`+-4`

Discussion

8478.	Evaluate the following integrals (iv) int_(-1)^(1)(x^(4)+sin^(3)x)dx
Answer» ANSWER :`(2)/(5)`

Discussion

8479.	Draw the graph of y=sin^(-1)(sin x)
Answer» SOLUTION :`y = SIN^(-1) (sin X)` `rArr""sin y = sin x` `rArr""y=npi+(-1)^(n)x, n in Z` Now `y in [-pi//2, pi//2] ` so we have the following table for values for values of x and y. From the above informations, we can PLOT the graph of `y=sin^(-1)(sin x)` as shown in the following figure.

Discussion

8480.	Let C be incircle of DeltaABC. If the tangenst of lengths t_(1), t_(2) and t_(3) are drawn inside the given triangle parallel to sides a,b and c, respectively, then (t_(1))/(a )+ (t _(2))/(b)+ (t_(3))/©is equal to
Answer» 0 1 2 3 Answer :B

Discussion

8481.	Evalute the following integrals int (sin 2x)/((a + b cos x )^(2))dx
Answer» ANSWER :`-(2)/(b^(2)) [ " LOG "\|a + b cos X \| + (a)/((a + b "cos x")) ] + C `

Discussion

8482.	If n_(p_(r)) = 840 , n_(c_(r)) = 35, then n is equal to
Answer» 1 7 4 10 Answer :B

Discussion

8483.	A monopolist's demand function is p= 300 - 5x. Find the average revenue function andmarginal revenue function.
Answer» SOLUTION :N/A

Discussion

8484.	Prove that any function f(x) defined in a symmetrical interval (-l, l) can be presented as a sum of an even and an odd function. Rewrite the following functions in the form of a sum of an even and an odd function : (a) f(x)=(x+2)/(1+x^(2))""(b) y=a^x.
Answer» ANSWER :`(a) F(X)=(2)/(1+x^(2))+(x)/(1+x^(2));` (B) `a^(x)=(a^(x)+a^(-x))/(2)+(a^(x)-a^(-x))/(2)`

Discussion

8485.	Which of the following forms of haemoglobin is not present in erythrocytes ?
Answer» Methemoglobin Oxyhaemoglobin Carbon monooxyhaemoglobin Carbon dioxy haemoglobin Answer :A

Discussion

8486.	Evaluate : int (dx)/( (1 - x^(2)) sqrt( 1 + x^(2)))
Answer» ANSWER :`(1)/(2 SQRT(2)) log \|(sqrt(2) X + sqrt(1 + x^(2)))/(sqrt(2) x - sqrt(1 + x^(2)))\|`

Discussion

8487.	Let A = ((1,2,3),(0,0,0),(3,2,1)) and A^(n)=((a_(n),b_(n),c_(n)),(0,0,0),(c_(n),b_(n),a_(n))) AA n in N, If a= lim_(nrarroo)(1)/(2^(n-2))(a_(n)+b_(n)+c_(n)) then \|a+3i\|= ________
Answer» ANSWER :5

Discussion

8488.	If veca=2hati+3hatj-hatk, vecb= hati+2hatj-5hatk, vec c=3hati+5hatj-hatk, then a vector perpendicular to veca and lies in the plane containing vecb and vec c is :
Answer» `-17hati+21hatj-97hatk` `17hati+21hatj-123hatk` `-17hati-21hatj+97hatk` `-17hati-21hatj-97hatk` SOLUTION :N/A

Discussion

8489.	Find the eccentricity foci, equation of the directrices and length of the latusrectum of the hyperbola x^(3) - 4y^(2) = 4
Answer» ANSWER :1

Discussion

8490.	Differentiate the following with respect to x: (1- log x)/(1+ log x)
Answer» ANSWER :`(-2)/(X(1 + LOG x)^(2))`

Discussion

8491.	Find all the values of following . (1 - I sqrt3)^(1//3)
Answer» ANSWER :`2^(1/3)CIS(6k-1)pi/9,k=0,1,2`

Discussion

8492.	The volume generated by the region bounded by the curve y=sqrt(x) and the line x=0 and x=pi about x axis is :
Answer» `(pi^3)/(3)` `pi^3` `(2pi^3)/(3)` `(pi^2)/(2)`. ANSWER :A

Discussion

8493.	Compute the integral I _(n) = int_(0)^(1) x^(m) (I n x)^(n) dx , m gt 0,nis a natural number
Answer» ANSWER :`I_(N) = (-1)^(n) (n!)/((m +1)^(n+1))`

Discussion

8494.	Verify the Rolle's theorem for each of the function in following questions: f(x)= sin^(4)x + cos^(4)x, "in " x in [0, (pi)/(2)]
Answer» ANSWER :`(PI)/(4) in (0, (pi)/(2))`

Discussion

8495.	Vertices of an isosceles triangle of area a ^(2)are (-a,0) and (a,0). Equation of the circumcircle of the triangle is
Answer» `X ^(2) + y ^(2) + 2ax - 2ay +a ^(2)=0` `x ^(2) + y ^(2) - 2ax +2ay +a ^(2) =0` `x ^(2) + y ^(2) =a ^(2)` none of these ANSWER :C

Discussion

8496.	If\|x\|lt1thenthecoefficientofx ^ 5intheexpansion of(3x ) /((x- 2 ) ( x + 1 ))is
Answer» ` (33 )/(32)` `- (33 ) /(32 ) ` ` (31 ) /(32 ) ` `- (31 ) /( 32 ) ` SOLUTION : ` (3 x )/( (x - 2 )( x + 1 )) ` ` = (- 3 ) /(2) x ( 1 +x ) ^(-1 )(1-(x)/(2) ) ^(-1 ) ` `=(-3 ) /(2)x (1- x+x ^ 2-x ^(3 )+x ^ 4.. )(1 +(x ) /(2)+(x ^ 2 ) /(4)+(x ^ 3) /(8)+(x ^ 4 ) /(16 )+... ` `therefore ` COEFFICIENTOF`x ^5` `=( - 3 ) /(2 ) [ (1)/(16) - (1)/(8)+(1 ) /(4) - (1)/(2)+1 ] ` `= (-3)/(2) [(1 - 2+ 4 - 8 +16 )/(16)] ` `= (-3 )/(2) ((11)/(16)) ` `=(-33)/(32)`

Discussion

8497.	If R is the set of all real numbers and f : R - {2}to R is defined by f(x)=(2+x)/(2-x) for x in R - {2}
Answer» `R-{-2}` R `R-{1}` `R-{-1}` ANSWER :D

Discussion

8498.	If x+i y=(-1+i sqrt(3))^(2010), then x=
Answer» `2^(2010)` `-2^(2010)` `-1` 1 Answer :A

Discussion

8499.	The value of the expansion (sumsum)_(0 le i lt j le n) (-1)^(i+j-1)"^(n)C_(i)*^(n)C_(j)=
Answer» `"^(2n-1)C_(N)` `"^(2n)C_(n)` `"^(2n+1)C_(n)` None of these Solution :`(a)` LET the required value be `S` `sum_(j=0)^(n)sum_(i=0)^(n)(-1)^(i+j-1)'^(n)C_(i)*^(n)C_(j)=sum_(i=0)^(n)(-1)^(2i-1)('^(n)C_(i))^(2)+2S` `:.0=-sum_(i=0)^(n)('^(n)C_(i))^(2)+2S` `:.2S=^(2n)C_(n)` `:.S=^(2n-1)C_(n-1)=^(2n-1)C_(n)`

Discussion

8500.	The plane 2x-y+3z+5=0 is rotated through 90^(@) about its line of intersection with the plane 5x-4y-2z+1=0. The equation of the plane in the new position is
Answer» `6x-9y-29z-31=0` `27x-24y-26z-13=0` `43x-32y-2z+27=0` `26x-43y-151z-165=0` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Solve -12x gt 30, when i.x is a natural number. ii.x is an integer.

Find the number of different seven digit numbers that can be written using only the three digits, 1,2,3 with the condition that the digit 2 occurs atleast 2 times in each number.

A variable line 'L' Passing through the origin cuts two parallel lines x-y+10=0 and x-y+20=0 at two points A and B respectively . If P is a point on line 'L' such that OA , OP, OB are in harmonic progression then the locus of P is

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

int cos sqrt(x)dx=

If y = (a^(cos x))/( sqrt(1+ x^(2) )),then (dy)/(dx) =

IfA_n= [ad ]A_2 =[{:( a_2, a_s),( a_4 .a_5):}], A_5 =[{:( a_6,a_7,a_8),( a_9,a_10 ,a_11),( a_12,a_13,a_14):}]= A_n =[…]and so on , where a_r= [log _2 r] where [.] denotes greatest integer function ) .Then T_r (A_10 )is equal to ,(T_r stands for trace of teh matrix )

Evaluate int_(0)^(1) x e^(x^(2))dx.

The solution of linear programming problem, maximize Z=3x_(1)+5x_(2) subject to 3x_(1)+2x_(2) le 18, x_(1) le 4, x_(2) le 6, x_(1) ge 0, x_(2) ge 0 is ………..

Two distinct numbers are chosen from 1,3,5,7 ……. 151,153,155 and multiplied . The probability that the product is a multiple of 5 is

How many different numbers each of the six digit can be formed using the digit 1,2,1,2,3,3, ?

The perpendicular distance of the point (3, -4, -5) from the line (x-2)/(4)=(y+6)/(5)=(z-5)/(-3) is ….....

A curve is defined by the condition that the sum of the x and y intercepts of its tangents is always equal to 2. Express the condition by means of a differential equation.

int_(0)^(1) Tan^(-1) ((2x-1)/(1+x-x^(2)))dx=

If the transversal y = m_(r)x: r = 1,2,3 cut off equal intercepts on the transversal x +y = 1 then 1 +m_(1),1 +m_(2),1+m_(3) are in

Ifu = sqrt( a^2cos^2 theta+b^2 sin ^2theta ) + sqrt( a^2 sin^2 theta+b^2 cos^2theta ) then thedifferencebetweenthe maximumand manimumvaluesofu^2is givenby

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

State whether the following statements are true or false, Justify. If ** is a commutative binary opertion on N, then a ** (b **c) = (c**b) **a

Integrate the following functions. int(x^(2)+a^(2))/(x^(4)+a^(4))dx

A and B are among 30 persons who sit at random along a round table. Find the probability that there are any six persons between A and B .

Which of the following is CORRECT combination ?

Which of the following is CORRECT combination ?

Which of the following is CORRECT combination ?

Axes are co-ordinate axes, S and S^(1)are Foci, B and B^(1)are the ends of minor axis|SBS^(1) = sin ^(-1) ((4)/(5) ) .if area of SB S^(1) B^(1)is 20sq. Units then eq. of the ellipse is

Solve the following differential equation:xy(dy)/(dx)-y^2=(x+y)^2e^(-y//x)

If the the angle between the circles x^2+y^2-12x-6y+41=0 andx^2+y^2+kx+6y-59=0 is 45^@ find k.

Evaluate the following integrals (iv) int_(-1)^(1)(x^(4)+sin^(3)x)dx

Draw the graph of y=sin^(-1)(sin x)

Let C be incircle of DeltaABC. If the tangenst of lengths t_(1), t_(2) and t_(3) are drawn inside the given triangle parallel to sides a,b and c, respectively, then (t_(1))/(a )+ (t _(2))/(b)+ (t_(3))/©is equal to

Evalute the following integrals int (sin 2x)/((a + b cos x )^(2))dx

If n_(p_(r)) = 840 , n_(c_(r)) = 35, then n is equal to

A monopolist's demand function is p= 300 - 5x. Find the average revenue function andmarginal revenue function.

Prove that any function f(x) defined in a symmetrical interval (-l, l) can be presented as a sum of an even and an odd function. Rewrite the following functions in the form of a sum of an even and an odd function : (a) f(x)=(x+2)/(1+x^(2))""(b) y=a^x.

Which of the following forms of haemoglobin is not present in erythrocytes ?

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

Let A = ((1,2,3),(0,0,0),(3,2,1)) and A^(n)=((a_(n),b_(n),c_(n)),(0,0,0),(c_(n),b_(n),a_(n))) AA n in N, If a= lim_(nrarroo)(1)/(2^(n-2))(a_(n)+b_(n)+c_(n)) then |a+3i|= ________

If veca=2hati+3hatj-hatk, vecb= hati+2hatj-5hatk, vec c=3hati+5hatj-hatk, then a vector perpendicular to veca and lies in the plane containing vecb and vec c is :

Find the eccentricity foci, equation of the directrices and length of the latusrectum of the hyperbola x^(3) - 4y^(2) = 4

Differentiate the following with respect to x: (1- log x)/(1+ log x)

Find all the values of following . (1 - I sqrt3)^(1//3)

The volume generated by the region bounded by the curve y=sqrt(x) and the line x=0 and x=pi about x axis is :

Compute the integral I _(n) = int_(0)^(1) x^(m) (I n x)^(n) dx , m gt 0,nis a natural number

Verify the Rolle's theorem for each of the function in following questions: f(x)= sin^(4)x + cos^(4)x, "in " x in [0, (pi)/(2)]

Vertices of an isosceles triangle of area a ^(2)are (-a,0) and (a,0). Equation of the circumcircle of the triangle is

If|x|lt1thenthecoefficientofx ^ 5intheexpansion of(3x ) /((x- 2 ) ( x + 1 ))is

If R is the set of all real numbers and f : R - {2}to R is defined by f(x)=(2+x)/(2-x) for x in R - {2}

If x+i y=(-1+i sqrt(3))^(2010), then x=

The value of the expansion (sumsum)_(0 le i lt j le n) (-1)^(i+j-1)"^(n)C_(i)*^(n)C_(j)=

The plane 2x-y+3z+5=0 is rotated through 90^(@) about its line of intersection with the plane 5x-4y-2z+1=0. The equation of the plane in the new position is

State whether the following statements are true or false, Justify. If is a commutative binary opertion on N, then a (b c) = (cb) **a