28278 + Interview Questions in Maths in Class 12 Page 535 InterviewSolution

26701.	The solution of (dy)/(dx) + x sin 2y = x^(3) cos^(2) y is
Answer» `Tan y = (x^(2))/(2) + (1)/(2) + C e^(-x^(2))` `Tan y = (x^(2))/(2) - (1)/(2) + c e^(-x^(2))` `Tan y = (x^(2))/(2) - (1)/(2) + c e^(x^(2))` `COS y = (x^(2))/(2) - (1)/(2) + c e^(-x^(2))` Answer :B

Discussion

26702.	Which of the following is not square planar ?
Answer» `[PtCl_(4)]^(-2)` `[Pt(CN)_(4)]^(-2)` `[NiCl_(4)]^(-2)` `[PdCl_(4)]^(-2)` Solution :`[NiCl_(4)]^(-2)`has `sp^(3)` hybridised state due weak field nature of `Cl^(-)ion` but `Pt^(2+)andPd^(2+)(4^(TH)and5^(th)` trasition series) pairing of electron TAKES place irrespective of nature of ligand resulting in square planar complexes.]

Discussion

26703.	The number of ways in which 7 players can be selected from a batch of 12 players so that 3 particular players are always included and 2 particular players are always excluded is
Answer» 35 46 51 63 Answer :A

Discussion

26704.	A square of side a lies above the X- axis and has one vertex at the origin . The side passing through the origin makes an angle pi//6 with the positive direction of X-axis .The equation of its diagonal not passing through the origin is
Answer» `y(SQRT(3)-1)-x(1-sqrt(3))=2a` `y(sqrt(3)+1) +x(1-sqrt(3))=2a` `y(sqrt(3)+1)+x(1+sqrt(3)) =2a` `y(sqrt(3)+1)+x(sqrt(3)-1)=2a` ANSWER :D

Discussion

26705.	{:("Quantity A","Quantity B"),("The median of x-4,x+1, and 4x","The mean of x-4,x+1, and 4x"):}
Answer» ANSWER :QUANTITY B is GREATER.

Discussion

26706.	If alpha and beta are the roots of x^(2)-2x+2=0 the prove that alpha^(n)-beta^(n)=i2^(n+1)sin((npi)/(3)) .Here find alpha^(9)-beta^(9).
Answer» ANSWER :`0`

Discussion

26707.	If vec(a) and vec(b) are non-collinear vectors find the value of x for which vectors vec(alpha)=(x-2)vec(a)+vec(b) and vec(beta)=(3+2x)vec(a)-2vec(b) are collinear.
Answer» ANSWER :`X=(1)/(4)`

Discussion

26708.	Evaluate the product (3vec(a)-5vec(b)).(2vec(a)+7vec(b)).
Answer» ANSWER :`6\|veca\|^(2)+11veca,vecb-35\|vecb\|^(2)`

Discussion

26709.	(vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )). If vec(a)*vec( c ) ……………
Answer» has angle `(PI)/(6)` are perpendicular VECTORS are PARALLEL vectors has angle `(pi)/(3)` ANSWER :C

Discussion

26710.	Translate the given statements in symbolic form and determine the truth value of each statement : (1) 2 is a rational number and it is the only even prime number. (2) sqrt(3) is a rational number or 3+ i is a complex number. (3) Neither 21 is a prime number nor it is divisible by 3. (4) 3+5gt7if and only if 4+6lt10.
Answer» SOLUTION :(1) Let p: `sqrt5` is an irrational number. q: `3+sqrt5` is a complex number. Then the symolic form of the given statement is `p^^q`. The truth value of p and q are T and F respectively. `:.` the truth value of `p^^q` is F. (2) Let p: Two triangles have equal areas. q: They are similar. Then the symbolic form of the given statement is `ptoq`. If the truth VALUES of p is T, then the truth value of q is F. `:.` the truth value of `ptoq` is F. ........ `[TtoF-=]` (3) Let p: `-2lt-1`. q: i is a real number. Then the symbolic form of the given statement is `p""iffq` The truth values of of p and q are T and F respectively. `:.` the truth value of `p""iffq` is F. (4) `EEninN` such that`n+5gt10` is a true statement because any `ngt6` satisfies `n+5gt10`. Hence, the truth value of the given statement is T. (5) Let p: `AAninN,n^(2)+n` is an even number. q: `AAninN,n^(2)-n` is an odd number. Then the symbolic form of the given statement is `p^^q`. The truth value of p and q are T and F respectively. `:.` the truth value of `p^^q` is F. "".....`[A^^F-=F]`

Discussion

26711.	If z(x,y) =x tan^(-1)(xy), x=t^(2), y=se^(t), s, t in R, Find (del z)/(del s) and (del z)/(del t) at s=t=1.
Answer» ANSWER :`(3E)/(1+e^2)+2 tan^(-1)e`

Discussion

26712.	Find the equations of the circles passing through (1,-1) touching the lines 4c+3y+5=0 and 3x-4y-10=0
Answer» ANSWER :`-2`

Discussion

26713.	A plane passing through (-1,2,3) and whose normal makes equal angles with the coordinate axesis
Answer» `x+y+z+4=0` `x-y+z+4=0` `x+y+z-4=0` `x+y+z=0` ANSWER :C

Discussion

26714.	Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(k) and overset(to)(b) = hat(i) + hat(j) + hat(k)
Answer» ANSWER :`THETA = COS^(-1) ((1)/(3))`

Discussion

26715.	If A is skew symmetric then kA is a ……. (k is any scalar)
Answer» ANSWER :`KA`

Discussion

26716.	If 3p^(2)=5p+2" and "3q^(2)= 5q+2, where p ne q, then the equationwhose roots are 3p-2q" and "3q-2p is
Answer» `3X^(2)-5X-100=0` `5x^(2)+3x+100=0` `3x^(2)-5x+100=0` `3x^(2)+5x-100=0` ANSWER :A

Discussion

26717.	If sqrt(x)+sqrt(y) = sqrt(a), find (d^(2)y)/(dx^(2)) at x = a.
Answer» SOLUTION :N/A

Discussion

26718.	If cot alpha equals the integral solution of inequality 4x ^(2)-16x+15 le 0 and sin beta equals to the slope of the bisector of the first quadrant, then sin (alpha+ beta) sin (alpha - beta)is equal to:
Answer» `-3/5` `-4/5` `(2)/(SQRT2)` `3` ANSWER :B

Discussion

26719.	Length of the tangent drawn from an end of the latus rectum of the parabola y^(2)=4ax to the circle of radius a touching externally the parabola at the vertex is
Answer» `SQRT3A` `2A` `sqrt7a` 3a Answer :C

Discussion

26720.	Find order and degree of given differential equation y' + y = e^(x)
Answer» ANSWER :ORDER 1; DEGREE 1

Discussion

26721.	Evaluate the following inegrals int(dx)/(cos^(2)x+sin2x)
Answer» ANSWER :`(1)/(2)log\|1+2tanx\|+c`

Discussion

26722.	Find the odd man one with respect to the eccentricity of the following:
Answer» `(1)/(SQRT(2))` `(4)/(5)` 7 2.5 Answer :D

Discussion

26723.	Show that the circles x^(2) + y^(2)-4x-6y-12=0 and x^(2) +y^(2) + 6x + 18 y + 26 = 0touch each other. Also find the point of contact and common tangent at this point of contact.
Answer» ANSWER :`((1)/(13),(-21)/(13)), 5X +12y +19=0`

Discussion

26724.	If the 4th term in the expansion of (2+3x//8)^10 has the maximum numerical value, then the range of values of x for which this will be true is
Answer» `(64)/(21) LT x lt -2` `(21)/(64) lt x lt 2` `-(64)/(21) lt x lt 2` `-(21)/(64) lt x lt 2` Answer :A

Discussion

26725.	Find the values of k so that the function f is continuous at the indicated pointf(x) = {(3x-8",","if" x le 5),(2k",","if" x gt 5):} at x= 5
Answer» ANSWER :`K= (7)/(2)`

Discussion

26726.	………… term of the G.P. 3, 3sqrt(3),9 ...... is 2187
Answer» 15 14 13 19 Answer :C

Discussion

26727.	If the function f(x)={{:(ax+b, -ooltxle2),(x^(2)-5x+6,2ltxlt3),(px^(2)+qx+1,3lexleoo):} is differentiable in (-oo,oo), then :
Answer» `a=-1,p=-(4)/(9)` `b=2,Q=(5)/(3)` a=1, b=2 `a=-1, q=-(5)/(3)` SOLUTION :Differentiable `implies` continuous Continuouns at `x=2implies2a+b=0` Continuous at x=3 `0=9p+3q+1` Differntiable at x=2 `a=2xx2-5impliesa=-1` Differentiable at x=3 `2xx3-5=2pxx3+qimplies6p+q=1` `a=-1,b=2,p=(4)/(9),q=-(5)/(3)`

Discussion

26728.	bar(b)=3hatj+4hatk,bar(a)=hati+hatj. If bar(b_(1)) and bar(b_(2)) are component of bar(b) and bar(b_(1))=(3)/(2)hati+(3)/(2)hatj,bar(b_(2)) is perpendicualr to bar(a) then bar(b_(2)) = ………………..
Answer» `(3)/(2)HATI+(3)/(2)hatj+4hatk` `-(3)/(2)hati+(3)/(2)hatj+4hatk` `-(3)/(2)hati+(3)/(2)hatj` NONE of these ANSWER :B

Discussion

26729.	Differentiate the following w.r.t.x. sin^(-1)((2^(x+1))/(1+4^(x)))
Answer» ANSWER :`=(2^(X+1)LOG 2)/(1+4^(x))`

Discussion

26730.	vec(r )=(hat(i) +hat(j)) +lambda(2hat(i) -hat(j) +hat(k)) vec(r )=(2hat(i) +hat(j) -hat(k)) + mu (3hat(i) -5hat(j) +2hat(k))
Answer» ANSWER :`(10)/(SQRT(59))` UNITS

Discussion

26731.	Solve 6x^6-35x^5+56x^4-56x^2+35x-6=0
Answer» ANSWER :`1,1+sqrt2,1-sqrt2`

Discussion

26732.	Correct combination for the parts of thorasic cavity and their position is :- {:((A),"Ribs",(i),"Ventral"),((b),"Diaphragm",(ii),"Dorsal"),((c),"vertebral column",(iii),"Lower side"),((D),"Sternum",(iv),"Upper side"),((E),"Collar bone",(v),"Lateral"):}
Answer» A-(iii), B-(i), C-(V), D-(IV), E-(ii) A-(v), B-(iv), C-(i), D-(ii), E-(iii) A-(v), B-(iii), C-(ii), D-(iv), E-(i) A-(v), B-(iii), C-(ii), D-(i), E-(iv) Answer :A

Discussion

26733.	f : R rarr R , f(x) ={{:(2x,xgt3),(x^2,1ltxle3),(3x,xle1):}then find f (-1) + f(2) + f(4) .
Answer» 9 14 5 None of these SOLUTION :N/A

Discussion

26734.	Simplifiy i^(2)+i^(4)+i^(6)+.....+(2n+1) terms
Answer» ANSWER :A

Discussion

26735.	int ((x^2+1))/(x^2+7x^2 +1)dx=
Answer» `(1)/(3) tan^(-1) ((X^2-1)/(3X))+c` `tan^(-1)((x^2-1)/(x))+c` `(1)/(3) tan^(-1)((x^2-1)/(x))+c` `(1)/(SQRT(3))tan^(-1)((x^2-1)/(x))+c` Answer :A

Discussion

26736.	The rate of increase of f(x)=x^(3)-5x^(2)+5x+25 is twice the rate of increase of x for x = ………..
Answer» `-3,-(1)/(3)` `3,(1)/(3)` `-3,(1)/(3)` `3,-(1)/(3)` ANSWER :B

Discussion

26737.	Given the total cost function for x units of a commodity asC(x) =1/3 x^3+x^(2)-8x+5, find slope of average cost function.
Answer» ANSWER :`(2X)/3+1-5/x^2`

Discussion

26738.	How many integers between 1 and 1000 have the sum of the digits equal to 6.
Answer» ANSWER :28

Discussion

26739.	If (3, 6) is vertex and (4, 5) is focus of parabola then equation of directrix is
Answer» X + y + 5 = 0 x + y - 5 = 0 X - y - 5 = 0 X - y + 5 = 0 ANSWER :B

Discussion

26740.	Find the value of k, if(iii) (x^(2)8)/((x^(2)+2^(2)))=(1)/(x^(2)+2)+(k)/((x^(2)+2)^(2))
Answer» ANSWER :6

Discussion

26741.	A homogeneous differential equation of the from (dx)/(dy) = h((x)/(y)) can be solved bymaking the substitution.
Answer» y = vx v = yx x = vy x = v Answer :C

Discussion

26742.	Which of thefollowingoptions is the onlyCORRECT combination ?
Answer» <P>` (III) (iii) (R) ` `(IV) (iv) (S)` `(II) (ii) (Q)` `(I) (i) (P)` ANSWER :C

Discussion

26743.	The solution of (dy)/(dx) = (y^(2))/(xy - x^(2)) is
Answer» `E^(y//x) = KX` `e^(y//x) = KY` `e^(-y//x) = kx` `e^(-y//x) = ky` ANSWER :B

Discussion

26744.	The term independent of x (x gt 0 , x ne 1) in the expansion of[((x+1))/((x^(2//3) -x^(1//3)+1))-((x-1))/((x-sqrtx))]^10 is
Answer» 105 210 315 420 Answer :B

Discussion

26745.	Show that the locus of a point such that the ratio of distance of it from two given points is constant k (ne pm 1) is a circle.
Answer» ANSWER :`x^(2) + y^(2) - 2 ((1+k^(2) )/(1-k^(2)) ) ax +a^(2) =0` which REPRESENTS a CIRCLE. (Here K NE PM 1)

Discussion

26746.	Find the number of positive integral solutions of x_(1)x_(2)x_(3)=30.
Answer» ANSWER :108

Discussion

26747.	The vertex of the parabola x^(2)+12x-9y=0 is . . .
Answer» `(6,-4)` `(-6,4)` `(6,4)` `(-6,-4)` ANSWER :D

Discussion

26748.	Prove that{:[( a,a+b,a+b+c) ,( 2a,3a+2b,4a+3b+2c),( 3a,6a+3b,10a+6b+3c)]:}=a^(3)
Answer» ANSWER :` =a (a^(2) -0) =a ( a^(2) )= a^(3) `

Discussion

26749.	If P and Q are conjugate points w.r.t a circle S=x^2+y^2+2gx+2fy+c=0 , then prove that the circle PQ as diameter cuts the circles S=0 orthogonallly.
Answer» ANSWER :ORTHOGONALLY.

Discussion

26750.	If the normal at theta on the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1 meets the transverse axis at G, prove that AG, A'G=a^(2) (e^(4) sec^(2) theta-1). Where A and A' are the vertices of the hyperbola.
Answer» ANSWER :`(-a + AE^(2) sec theta) (a + ae^(2) sec theta) = a^(2) (e^(4) sec^(2) theta -1)`

Discussion

Explore topic-wise InterviewSolutions in .

The solution of (dy)/(dx) + x sin 2y = x^(3) cos^(2) y is

Which of the following is not square planar ?

The number of ways in which 7 players can be selected from a batch of 12 players so that 3 particular players are always included and 2 particular players are always excluded is

A square of side a lies above the X- axis and has one vertex at the origin . The side passing through the origin makes an angle pi//6 with the positive direction of X-axis .The equation of its diagonal not passing through the origin is

{:("Quantity A","Quantity B"),("The median of x-4,x+1, and 4x","The mean of x-4,x+1, and 4x"):}

If alpha and beta are the roots of x^(2)-2x+2=0 the prove that alpha^(n)-beta^(n)=i2^(n+1)sin((npi)/(3)) .Here find alpha^(9)-beta^(9).

If vec(a) and vec(b) are non-collinear vectors find the value of x for which vectors vec(alpha)=(x-2)vec(a)+vec(b) and vec(beta)=(3+2x)vec(a)-2vec(b) are collinear.

Evaluate the product (3vec(a)-5vec(b)).(2vec(a)+7vec(b)).

(vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )). If vec(a)*vec( c ) ……………

If z(x,y) =x tan^(-1)(xy), x=t^(2), y=se^(t), s, t in R, Find (del z)/(del s) and (del z)/(del t) at s=t=1.

Find the equations of the circles passing through (1,-1) touching the lines 4c+3y+5=0 and 3x-4y-10=0

A plane passing through (-1,2,3) and whose normal makes equal angles with the coordinate axesis

Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(k) and overset(to)(b) = hat(i) + hat(j) + hat(k)

If A is skew symmetric then kA is a ……. (k is any scalar)

If 3p^(2)=5p+2" and "3q^(2)= 5q+2, where p ne q, then the equationwhose roots are 3p-2q" and "3q-2p is

If sqrt(x)+sqrt(y) = sqrt(a), find (d^(2)y)/(dx^(2)) at x = a.

If cot alpha equals the integral solution of inequality 4x ^(2)-16x+15 le 0 and sin beta equals to the slope of the bisector of the first quadrant, then sin (alpha+ beta) sin (alpha - beta)is equal to:

Length of the tangent drawn from an end of the latus rectum of the parabola y^(2)=4ax to the circle of radius a touching externally the parabola at the vertex is

Find order and degree of given differential equation y' + y = e^(x)

Evaluate the following inegrals int(dx)/(cos^(2)x+sin2x)

Find the odd man one with respect to the eccentricity of the following:

Show that the circles x^(2) + y^(2)-4x-6y-12=0 and x^(2) +y^(2) + 6x + 18 y + 26 = 0touch each other. Also find the point of contact and common tangent at this point of contact.

If the 4th term in the expansion of (2+3x//8)^10 has the maximum numerical value, then the range of values of x for which this will be true is

Find the values of k so that the function f is continuous at the indicated pointf(x) = {(3x-8",","if" x le 5),(2k",","if" x gt 5):} at x= 5

………… term of the G.P. 3, 3sqrt(3),9 ...... is 2187

If the function f(x)={{:(ax+b, -ooltxle2),(x^(2)-5x+6,2ltxlt3),(px^(2)+qx+1,3lexleoo):} is differentiable in (-oo,oo), then :

bar(b)=3hatj+4hatk,bar(a)=hati+hatj. If bar(b_(1)) and bar(b_(2)) are component of bar(b) and bar(b_(1))=(3)/(2)hati+(3)/(2)hatj,bar(b_(2)) is perpendicualr to bar(a) then bar(b_(2)) = ………………..

Differentiate the following w.r.t.x. sin^(-1)((2^(x+1))/(1+4^(x)))

vec(r )=(hat(i) +hat(j)) +lambda(2hat(i) -hat(j) +hat(k)) vec(r )=(2hat(i) +hat(j) -hat(k)) + mu (3hat(i) -5hat(j) +2hat(k))

Solve 6x^6-35x^5+56x^4-56x^2+35x-6=0

Correct combination for the parts of thorasic cavity and their position is :- {:((A),"Ribs",(i),"Ventral"),((b),"Diaphragm",(ii),"Dorsal"),((c),"vertebral column",(iii),"Lower side"),((D),"Sternum",(iv),"Upper side"),((E),"Collar bone",(v),"Lateral"):}

f : R rarr R , f(x) ={{:(2x,xgt3),(x^2,1ltxle3),(3x,xle1):}then find f (-1) + f(2) + f(4) .

Simplifiy i^(2)+i^(4)+i^(6)+.....+(2n+1) terms

int ((x^2+1))/(x^2+7x^2 +1)dx=

The rate of increase of f(x)=x^(3)-5x^(2)+5x+25 is twice the rate of increase of x for x = ………..

Given the total cost function for x units of a commodity asC(x) =1/3 x^3+x^(2)-8x+5, find slope of average cost function.

How many integers between 1 and 1000 have the sum of the digits equal to 6.

If (3, 6) is vertex and (4, 5) is focus of parabola then equation of directrix is

Find the value of k, if(iii) (x^(2)8)/((x^(2)+2^(2)))=(1)/(x^(2)+2)+(k)/((x^(2)+2)^(2))

A homogeneous differential equation of the from (dx)/(dy) = h((x)/(y)) can be solved bymaking the substitution.

Which of thefollowingoptions is the onlyCORRECT combination ?

The solution of (dy)/(dx) = (y^(2))/(xy - x^(2)) is

The term independent of x (x gt 0 , x ne 1) in the expansion of[((x+1))/((x^(2//3) -x^(1//3)+1))-((x-1))/((x-sqrtx))]^10 is

Show that the locus of a point such that the ratio of distance of it from two given points is constant k (ne pm 1) is a circle.

Find the number of positive integral solutions of x_(1)x_(2)x_(3)=30.

The vertex of the parabola x^(2)+12x-9y=0 is . . .

Prove that{:[( a,a+b,a+b+c) ,( 2a,3a+2b,4a+3b+2c),( 3a,6a+3b,10a+6b+3c)]:}=a^(3)

If P and Q are conjugate points w.r.t a circle S=x^2+y^2+2gx+2fy+c=0 , then prove that the circle PQ as diameter cuts the circles S=0 orthogonallly.

If the normal at theta on the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1 meets the transverse axis at G, prove that AG, A'G=a^(2) (e^(4) sec^(2) theta-1). Where A and A' are the vertices of the hyperbola.