28278 + Interview Questions in Maths in Class 12 Page 200 InterviewSolution

9951.	Resolve into partial fractions (x^(4)+3x+1)/(x^(3)(x+1)).
Answer» ANSWER :`:.(X^(4)+3x+1)/(x^(3)(x+1))=(-2)/(x)+(2)/(x^(2))+(1)/(x^(3))+(1)/(x+1)+1`

Discussion

9952.	STATEMENT-1 : A hyperbola and its conjugate hyperbola have the same asymptotes. and STATEMENT-2 : in a second degree curve, equation of asymptotes, if exists differ by constant only.
Answer» STATEMENT-1 is true, statement-2 is true, Statement -2 is a correct explanation for Statement -1 Statement -1 is true, Statement-2 is true , Statement-2 is NOT a correct explanation for statement-1 Statement-1 is true, Statement-2 is False Statement-1 is False, Statement-2 is true ANSWER :A

Discussion

9953.	The point 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

9954.	Proceeding from the definition, compute the integralint_(0)^(1) x dx
Answer» ANSWER :`Deltax_(i) = x_(i+1) - x_(i)`

Discussion

9955.	The range of the function defined as f(x) = log_(3)((1)/(sqrt([cosx] - [sin x]))),where [ ] represents the greatest integer function, is
Answer» {0} `[-(PI)/(2), 0]` [0, 1] {1} ANSWER :A

Discussion

9956.	Evaluate the following integrals. int(9cosx-sinx)/(5cosx+4sinx)dx
Answer» ANSWER :`x+log\|5cosx+4sinx\|+c`

Discussion

9957.	An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of he closed pipe is found to be higher by 100 Hx than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
Answer» `200 Hz` `300 Hz` `240 Hz` `480 Hz` ANSWER :A

Discussion

9958.	If p/a + q/b + r/c=1 and a/p + b/q + c/r=0, then the value of p^(2)/a^(2) + q^(2)/b^(2) + r^(2)/c^(2) is:
Answer» ANSWER :1

Discussion

9959.	Find the general value of x if the expression (sin ""(x)/(2) + cos"" (x)/(2) + itan x)/( 1 + 2isin "" (x)/(2)) is real .
Answer» `NPI" or " npipi/4` `2NPI" or " npipi/4` `npi" or " npipi/2` NONE ANSWER :B

Discussion

9960.	If f(x) {(mx + 1,x le (pi)/(2)),((sin x)+ n,x gt (pi)/(2)):} is continuous at x= (pi)/(2), then …...
Answer» `m=1, n= 0` `m= (n pi)/(2 ) + 1` `n= (m pi)/(2)` `m = n = (pi)/(2)` ANSWER :C

Discussion

9961.	If the pair of lines joining the origin and the points of intersection of the line ax +by = 1and the curve x^(2) +y^(2) - x - y - 1 = 0are at right angles , then the locus of he point (a,b) is a circle of radius
Answer» 2 `SQRT((3)/(2))` `sqrt((5)/(2))` `(sqrt(5))/(2)` Answer :C

Discussion

9962.	Let f : R rarr Rbe the function defined by f(x) = 1/(2-cosx),AA x inR. Then , find the range of f .
Answer» SOLUTION :N/A

Discussion

9963.	If sin alpha and cos alpha are the roots of the equation px^(2)+qx+r=0, then
Answer» `p^(2)-Q^(2)+2pr =0` `( p+R)^(2)=q^(2)-r^(2)` `p^(2)+q^(2)-2pr=0` `(p-r)^(2)=q^(2)+r^(2)` Answer :a

Discussion

9964.	Degree of differential (d^2y)/dx^2-2(dy/dx)+3y=0 is
Answer» 3 2 1 0 Answer :C

Discussion

9965.	There an n persons sitting around a circular table. Each person shakes hands with everybody except the person sitting on both sides of him. The total number of hand shakes are 90. Then find n.
Answer» ANSWER :n=15

Discussion

9966.	The solution of (x^(2)-y^(2)x^(2))(dy//dx) +(y^(2)+x^(2)y^(2)) = 0 is
Answer» `X+(1)/(x) + y + (1)/(y) +C = 0` `x-(1)/(x) + y - (1)/(y) = c` `x+(1)/(x) - y -(1)/(y) + c = 0` `x-(1)/(x)-y-(1)/(y) = c` ANSWER :D

Discussion

9967.	Evaluate the definite integrals int_(0)^(pi/4)e^(3x)sinxdx
Answer»

Discussion

9968.	Determine P(E\|F) A coinis tossed three times, where E : at least two heads, F : at most two heads
Answer» ANSWER :`(3)/(7)`

Discussion

9969.	The points 7hat(i)-11hat(j)+hat(k),5hat(i)+3hat(j)-2hat(k)and12hat(i)-8hat(j)-hat(k) forms
Answer» `"EQUILATERAL "Delta` `"isosceles "Delta` `"RIGHT ANGLED "Delta` collinear Answer :C

Discussion

9970.	Assertion (A) :If 1,2,3are therootsofax^3 + bx ^2 +cx+d=0then therootsofax^3+2bx^2 + 4 cx+ 8d =0 are=0are2,4,6 Reason(R ) :theequationwhoserootsare ktimestherootsof theequationf(x)=0isf((x )/(k ))=0
Answer» BOTHA and RaretrueR ISTHE correctexplanationof A both AandRare TRUEAND RIS notcorrectexplanationof A AIS trueand Risfalse A isfalseand Ristrue Answer :A

Discussion

9971.	If A=[{:(1,-1),(0,2),(2,3):}]andB=[{:(1,0),(-1,7):}]then find AB. Also find BA if it exists ?
Answer» Answer :`AB=[{:(2,-7),(-2,14),(-1,21):}]`BA does not EXIST .

Discussion

9972.	The value of int_(0)^(pi//2) sqrt( sin 2 theta) sin theta d theta is
Answer» `1` `0` `pi//2` `pi//4` ANSWER :D

Discussion

9973.	If the system of linear equations x + 2ay + az = 0,x + 3by + bz = 0,x + 4cy + cz = 0 has a non-zero solution, then a, b, c
Answer» are in G.P are in H.P satisfy `a + 2B + 3C = 0` are in A.P Answer :B

Discussion

9974.	Evaluate the integerals.int e ^(ax) sin bx dx on R, a, b, in R.
Answer» `(e^(ax))/(a^(2)-B^(2))(a sin BX- b COS bx)+C` `(e^(ax))/(a^(2)-b^(2))(a sin bx- b cos bx)+c` `(e^(ax))/(a^(2)-b^(2))(a sin bx+ b cos bx)+c` `(e^(ax))/(a^(2)-b^(2))(b sin bx+ a cos bx)+c` Answer :B

Discussion

9975.	There are 10 lamps in a hall. Each one of them can be switched on independently. No. of ways in which the hall can be illuminated is
Answer» `2^(10)-1` `2^(9)-1` `2^(10)` `2^(9)` ANSWER :A

Discussion

9976.	I : If z = barz " then " zis purely imaginary II: If \|z_1+z_2\|=\|z_1\|+\|z_2\|" then " agz_1-argz_2" is " pi//2 II: If z_1 and z_2 are two complex numbers such that \|z_1z_2\|=1 and argz_1 -argz_2=pi//2" then " bar(z)_1,bar(z)_2-i
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II are true ANSWER :C

Discussion

9977.	Find the values of the following integrals int(sinx)/(1+sinx)dx
Answer» ANSWER :`x-tanx+secx+c`

Discussion

9978.	Find the area of the region bounded by y= e^(x), y= 0, x= 0 and x= l n 2
Answer» ANSWER :1

Discussion

9979.	{{:(-x^(2)+4x+a","xle3,),(ax+b","3ltxlt4,),(-(b)/(4)x+6","xge4,):} If x=4 is the only point of maxima in its neighbourhood but x=3 is neither a point of maxima nor a point of minima thenwhich of thefollowing is true ?
Answer» `alt0,BGT0` `AGT0,blt0` `agt0,bgt0` not possible Answer :D

Discussion

9980.	Differentiate the following w.r.t.x sqrt(e^sqrtx),xgt0
Answer» SOLUTION :`d/dx(SQRT(e^SQRTX)=1/(2sqrt(e^sqrtx))d/dx(e^sqrtx)=1/(2sqrt(e^sqrtx))e^sqrtxd/dx(sqrtx)=1/2sqrte^sqrtx1/(2sqrtx)=sqrte^sqrtx/(4sqrtx)`

Discussion

9981.	Equation of the parabola with focus (3,0) and the directrix x + 3 = 0 is
Answer» `y^2 = 3X` `y^2 = 2X` `y^2 = 12x` `y^2 = 6x` ANSWER :C

Discussion

9982.	State which of the followingstatement is true ?
Answer» if a linear programminghas at leasttwo optimalfeasible solutoin then there are INFINTE number of optimalsolution in a linearprogramming problemthe decisionvaribalescan TAKE any real VALUES in any problem it is possible to express both the OBJECTIVE function andthe constraints in linear from the objective function iof a linear programming problemwith decisionvariablesx and y is of the form ax + by +cwhere a,b and c are real constants Answer :A

Discussion

9983.	X~B(n,p) and mean and variance of X are (15)/(2) and (15)/(4). Find n and p.
Answer» ANSWER :`15, 1//2`

Discussion

9984.	Statement I: The circle with the points of intersectionof the line 3x+4y=12 with axes as extremities ofa diameter is x^(2)+y^(2)-4x-3y=0 Statement II: The circle passing through (0,0) and making intercepts 8 and 6 on x,y axes, has its is (-4,2). Which of above statement is false?
Answer» only I only II both I and II neigther I nor II Answer :B

Discussion

9985.	Evaluate int(x^(2))/(sqrt(x+5))dx
Answer» Answer :`(2)/(5)(x+5)^(5//2)-(20)/(3)(x+5)^(3//2)+50sqrt(x+5)+C`

Discussion

9986.	If lim_( x to 2) (A sin (x-2) +B cos (x-2) +5)/(x^2-4)=1 , then \|A-B\| is equal to
Answer» ANSWER :`9.00`

Discussion

9987.	The value of the expression ((26),(4))+((31),(4))+((30),(4))+((29),(4))+((28),(4))+((27),(4))+((26),(5)) equal
Answer» `((32),(4))` `((32),(5))` `((32),(5))` `((31),(5))` ANSWER :B

Discussion

9988.	int_(0)^(pi) cos^(8) x dx=
Answer» `(5pi)/(16)` `(35 PI)/(128)` `(5pi)/(18)` `(5pi)/(8)` ANSWER :B

Discussion

9989.	int_(-1)^(2) (-1)^([x])(x-[x])dx=
Answer» `-1//2` `1//2` `-1` 1 Answer :1

Discussion

9990.	A fair coin is tossed 9 times the probability that at least 5 consecutive heads occurs is :
Answer» `5/64` `3/32` `""^9C_5 (1/2)^9` NONE of these SOLUTION : REQUIRED PROBABILITY `(1/2)^5 + (1/2)^6 + (1/2)^6 +(1/2)^6 + (1/2)^6 = 3/32 `

Discussion

9991.	Let [-1,1] to R and g : R to R be two functions defined by f(x)=sqrt(1-x^(2)) and g(x)=x^(3)+1. Find the function f+g, f-g,fg and f//g.
Answer» Answer :The DOMAIN of each of `f+g`, `f-g` and `FG` is `[-1,1]` and that of `f//g` is `{xin [-1,1] : g(X) ne 0}=(-1,1]`

Discussion

9992.	Which one of the following is a valid inference? (I) The state Government can be inferred as employing the highest number of Employees per establishment only because the percentage Employment it provides is the highest . The number of Establishments is not important. (II) The State Government can be inferred as employing the highest number of Employees per Establishment since it has the least number of organizations and offers the highest Employment. (III) The state Government can be inferred as employing the highest number of Employees per Establishment since it has the least number of organizations and offers the highest Percentage of Employment.
Answer» I only II only III only II and III Answer :D

Discussion

9993.	Which part of the ear is influenced by movements ?
Answer» CRISTA MACULA ORGAN of corti Both 1 and 2 Answer :A

Discussion

9994.	Evaluate the following integrals intsqrt(e^(x)-4)dx
Answer» ANSWER :`2sqrt(E^(x)-4)-tan^(-1)((SQRT(e^(x)-4))/(2))+c`

Discussion

9995.	Check the injectivity and surjectivity of the following functions . f : R rarr R , f(x) = x^3
Answer» SOLUTION :N/A

Discussion

9996.	Prove that (.^(2n)C_(0))^(2) - (.^(2n)C_(1))^(2) + (.^(2n)C_(2))^(2) - …. + (.^(2n)C_(2n))^(2) = (-1)^(n) .^(2n)C_(n)
Answer» Solution :`(1+x)^2N(1-(1)/(x))^2n` `=(.^2nC_0 -(.^2n C_1)x+(.^2nC_2)x62+.....+(.^2nC_2n)x^2n]` `xx[.^2nC_0 -(.^2nC_1)(1)/(X)+(.^2n C_2)(1)/(x^2)+.....+(.^2n C_2n)(1)/(x^2n)]` Independent TERMS of x on RHS `=(.^2n C_0)^2-(.^2n C_1)^2+(.^2nC_2)^2 -......+(.^2n C_2n)^2`. LHS `=(1+x)^2n((x-1)/(x))^2n =(1)/(x^2n)(1-x^2)^2n`. Independent term of x on the LHS `=(-1)^n .^2n C_n`.

Discussion

9997.	The point of intersection of normals to the parabola y^(2) = 4x at the points whose ordinates are 4 and 6 is
Answer» `(30,-21)` `(21,-30)` `(17,-19)` `(19,-18)` Answer :B

Discussion

9998.	Evaluate the following integrals. int(1)/(4cosx+3sinx)dx
Answer» ANSWER :`(1)/(5)log\|((1+ 2tan""(X)/(2))/(4-2tan""(x)/(2)))\|+C`

Discussion

9999.	If f(x)= {((x^(2))/(a)-a",",x lt a),(0",",x=a),(a-(x^(2))/(a)",",x gt 0):} then, ………
Answer» `underset(x RARR a^(+))("LIM") F(x)= a` `underset(x rarr a)("lim") f(x)= -a` f is continuous at x=a f is DIFFERENTIABLE at x=a Answer :C

Discussion

10000.	If overline(a), overline(b), overline(c) are non-coplanar and the vectors overline(p)=3overline(a)+overline(b)+4overline(c), overline(q)=2overline(a)+2overline(b)+3overline(c),overline(r)=overline(a)+3overline(b)+moverline(c) are collinear then m=
Answer» `3` `-3` `5` `-5` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Resolve into partial fractions (x^(4)+3x+1)/(x^(3)(x+1)).

STATEMENT-1 : A hyperbola and its conjugate hyperbola have the same asymptotes. and STATEMENT-2 : in a second degree curve, equation of asymptotes, if exists differ by constant only.

The point of intersection of the parabolas y^2=5x and x^2=5y lie on the line

Proceeding from the definition, compute the integralint_(0)^(1) x dx

The range of the function defined as f(x) = log_(3)((1)/(sqrt([cosx] - [sin x]))),where [ ] represents the greatest integer function, is

Evaluate the following integrals. int(9cosx-sinx)/(5cosx+4sinx)dx

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of he closed pipe is found to be higher by 100 Hx than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

If p/a + q/b + r/c=1 and a/p + b/q + c/r=0, then the value of p^(2)/a^(2) + q^(2)/b^(2) + r^(2)/c^(2) is:

Find the general value of x if the expression (sin ""(x)/(2) + cos"" (x)/(2) + itan x)/( 1 + 2isin "" (x)/(2)) is real .

If f(x) {(mx + 1,x le (pi)/(2)),((sin x)+ n,x gt (pi)/(2)):} is continuous at x= (pi)/(2), then …...

If the pair of lines joining the origin and the points of intersection of the line ax +by = 1and the curve x^(2) +y^(2) - x - y - 1 = 0are at right angles , then the locus of he point (a,b) is a circle of radius

Let f : R rarr Rbe the function defined by f(x) = 1/(2-cosx),AA x inR. Then , find the range of f .

If sin alpha and cos alpha are the roots of the equation px^(2)+qx+r=0, then

Degree of differential (d^2y)/dx^2-2(dy/dx)+3y=0 is

There an n persons sitting around a circular table. Each person shakes hands with everybody except the person sitting on both sides of him. The total number of hand shakes are 90. Then find n.

The solution of (x^(2)-y^(2)x^(2))(dy//dx) +(y^(2)+x^(2)y^(2)) = 0 is

Evaluate the definite integrals int_(0)^(pi/4)e^(3x)sinxdx

Determine P(E|F) A coinis tossed three times, where E : at least two heads, F : at most two heads

The points 7hat(i)-11hat(j)+hat(k),5hat(i)+3hat(j)-2hat(k)and12hat(i)-8hat(j)-hat(k) forms

Assertion (A) :If 1,2,3are therootsofax^3 + bx ^2 +cx+d=0then therootsofax^3+2bx^2 + 4 cx+ 8d =0 are=0are2,4,6 Reason(R ) :theequationwhoserootsare ktimestherootsof theequationf(x)=0isf((x )/(k ))=0

If A=[{:(1,-1),(0,2),(2,3):}]andB=[{:(1,0),(-1,7):}]then find AB. Also find BA if it exists ?

The value of int_(0)^(pi//2) sqrt( sin 2 theta) sin theta d theta is

If the system of linear equations x + 2ay + az = 0,x + 3by + bz = 0,x + 4cy + cz = 0 has a non-zero solution, then a, b, c

Evaluate the integerals.int e ^(ax) sin bx dx on R, a, b, in R.

There are 10 lamps in a hall. Each one of them can be switched on independently. No. of ways in which the hall can be illuminated is

I : If z = barz " then " zis purely imaginary II: If |z_1+z_2|=|z_1|+|z_2|" then " agz_1-argz_2" is " pi//2 II: If z_1 and z_2 are two complex numbers such that |z_1z_2|=1 and argz_1 -argz_2=pi//2" then " bar(z)_1,bar(z)_2-i

Find the values of the following integrals int(sinx)/(1+sinx)dx

Find the area of the region bounded by y= e^(x), y= 0, x= 0 and x= l n 2

{{:(-x^(2)+4x+a","xle3,),(ax+b","3ltxlt4,),(-(b)/(4)x+6","xge4,):} If x=4 is the only point of maxima in its neighbourhood but x=3 is neither a point of maxima nor a point of minima thenwhich of thefollowing is true ?

Differentiate the following w.r.t.x sqrt(e^sqrtx),xgt0

Equation of the parabola with focus (3,0) and the directrix x + 3 = 0 is

State which of the followingstatement is true ?

X~B(n,p) and mean and variance of X are (15)/(2) and (15)/(4). Find n and p.

Statement I: The circle with the points of intersectionof the line 3x+4y=12 with axes as extremities ofa diameter is x^(2)+y^(2)-4x-3y=0 Statement II: The circle passing through (0,0) and making intercepts 8 and 6 on x,y axes, has its is (-4,2). Which of above statement is false?

Evaluate int(x^(2))/(sqrt(x+5))dx

If lim_( x to 2) (A sin (x-2) +B cos (x-2) +5)/(x^2-4)=1 , then |A-B| is equal to

The value of the expression ((26),(4))+((31),(4))+((30),(4))+((29),(4))+((28),(4))+((27),(4))+((26),(5)) equal

int_(0)^(pi) cos^(8) x dx=

int_(-1)^(2) (-1)^([x])(x-[x])dx=

A fair coin is tossed 9 times the probability that at least 5 consecutive heads occurs is :

Let [-1,1] to R and g : R to R be two functions defined by f(x)=sqrt(1-x^(2)) and g(x)=x^(3)+1. Find the function f+g, f-g,fg and f//g.

Which part of the ear is influenced by movements ?

Evaluate the following integrals intsqrt(e^(x)-4)dx

Check the injectivity and surjectivity of the following functions . f : R rarr R , f(x) = x^3

Prove that (.^(2n)C_(0))^(2) - (.^(2n)C_(1))^(2) + (.^(2n)C_(2))^(2) - …. + (.^(2n)C_(2n))^(2) = (-1)^(n) .^(2n)C_(n)

The point of intersection of normals to the parabola y^(2) = 4x at the points whose ordinates are 4 and 6 is

Evaluate the following integrals. int(1)/(4cosx+3sinx)dx

If f(x)= {((x^(2))/(a)-a",",x lt a),(0",",x=a),(a-(x^(2))/(a)",",x gt 0):} then, ………

If overline(a), overline(b), overline(c) are non-coplanar and the vectors overline(p)=3overline(a)+overline(b)+4overline(c), overline(q)=2overline(a)+2overline(b)+3overline(c),overline(r)=overline(a)+3overline(b)+moverline(c) are collinear then m=