14949 + Interview Questions in Maths in Class 11 Page 57 InterviewSolution

2801.	Simplify the following (20)/(sqrt(-5))
Answer» ANSWER :`-4 sqrt5i`

Discussion

2802.	Find the slope of the time passing through the points (3,-2) and ( -1,4)
Answer» ANSWER :`- 3/2`

Discussion

2803.	If the ratio of the sums of m terms and n terms of an A.P. be m^(2) : n^(2), prove that the ratio of its m^(th) and n^(th) terms is (2m-1) : (2n-1).
Answer» ANSWER :`= (2m-1)/(2n-1)`

Discussion

2804.	Evaluate the following limits : Lim_(x to a) (xsqrt(x)-asqrt(a))/(x-a)
Answer» ANSWER :`3/2 SQRT(a)`

Discussion

2805.	If.^(n)C_(12) =^(n)C_(8)then n = . . . . .
Answer» 12 6 4 20 Answer :B::D

Discussion

2806.	If bara,barb,barc " are three mutually perpendicular vectors such that " absbara = absbarb = absbarc, " then " (bara+barb+barc,bara)=
Answer» `pi//3` `COS^(-1)(1//3)` `cos^(-1)(1//sqrt3)` `cos^(-1)(2//3)` ANSWER :C

Discussion

2807.	If bar(a), bar(b)&bar(c) are non-coplanar vectors and if bar(d) is such that bar(d)=1/x(bar(a)+bar(b)+bar(c)) and bar(d)=1/y(bar(b)+bar(c)+bar(d)) where x and y are non-zero real numbers, then 1/(xy)(bar(a)+bar(b)+bar(c)+bar(d))=
Answer» `3BAR(c)` `-BAR(a)` `bar(0)` `2BAR(a)` Answer :C

Discussion

2808.	3sinx+4cosx-6=0 then the general solution of x =
Answer» `NPI+(-1)^(n)(pi)/(6)` `npi+(-1)^(n)(pi)/(4)` `npi+(-1)^(n)(pi)/(3)` no solution Answer :D

Discussion

2809.	Find (x + 1)^6 + (x-)^6. Hence or otherwise evaluate (sqrt2 + 1)^6 + (sqrt2 - 1)^6.
Answer» ANSWER :2(`x^6` + `15x^4` + 1), 198

Discussion

2810.	A coin is tossed twice, what is the probability that at least one tail occurs?
Answer» ANSWER :`(3)/(4)`

Discussion

2811.	What is the number of terms in the expansion of the following? (6x- (1)/(x^3) )^(17)
Answer» ANSWER :18

Discussion

2812.	Solve: \|x-1\|le5,\|x\|ge2
Answer» Answer :`x LT [-4,-2 ] UU [2,6]`

Discussion

2813.	If the real part of (barz+2)/(barz-1) is 4 then show that the locus of the point representing z in the complex plane is circle.
Answer» ANSWER :HENCE Z LIES on the CIRCLE.

Discussion

2814.	Express (3-i)^2/(2+i) in the form x+iy
Answer» ANSWER :2 - 4I

Discussion

2815.	If one angle of a triangle is 30^(@) and the lengths of the sides adjacent to it are 40 and 40sqrt(3), then the triangle is
Answer» EQUILATERAL RIGHT angled isosceles scalene ANSWER :C

Discussion

2816.	The set of all x for which sin x lex is
Answer» `(0,(PI)/(2))` `((-pi)/(2),pi)` `(-(pi)/(2),0)` `((-pi)/(2),(pi)/(2))` ANSWER :A

Discussion

2817.	If the 4^(th) and 7^(th) term of a G.P. are 27 and 729 respectively, then find the G.P.
Answer» ANSWER :1,3,9,…..

Discussion

2818.	If f: R rarr R is a function such that f(x +y) =f(x) +f(y) forall x,y in R then f is continuous on R if it is continuous at a single point in R.
Answer» ANSWER :x=0

Discussion

2819.	Find the area of the triangle formed by the lines y-x =0, x+y=0 and x-k=0.
Answer» ANSWER :`=0 and X -K =0` is `k^(2)` SQ. UNIT.

Discussion

2820.	Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and (x+3)/(-3)=(y+7)/(2)=(z-6)/(4)
Answer» `sqrt30` `2sqrt30` `5sqrt30` `3sqrt30` ANSWER :D

Discussion

2821.	Find the derivative of the following functions: 5sin x-6 cosx+7
Answer» ANSWER :5 COS x+6 SINX

Discussion

2822.	Statement- I The soluton of the system of equations 2x-y+3z=9,x+y+z=6,x-y+z=2 is x=1,y=2,z=3 Statement- II : The solution of the system of equations x+2y-z=3,3x=y+2z=1, 2x-2y+3z=2 is x=-1,y=4,z=4 Which of the above Statement(s) is true ?
Answer» only I is TRUE only II is true Both I, II are true NEITHER I nor II are true ANSWER :C

Discussion

2823.	A straight line through the point (3,4) in the first quadrant meets the axes at A and B . The minimum area of the triangle OAB is
Answer» 42 64 48 24 Answer :D

Discussion

2824.	A plane which passes through the point (3,2,0) and the line (x-4)/(1) = (y-7)/(5) = (z-4)/(4) is
Answer» `X - y + Z=1` `x + y + z=5` `x - 2y - z = 1 ` `2x - y + z=5` ANSWER :A

Discussion

2825.	(2n+7) lt (n+3)^(2)
Answer» Solution :For n=1 L.H.S `=2xx1+7=9` R.H.S. `=(1+3)^(2)=16` `:. ""L.H.S. LT R.H.S.` `RARR` Given statement is true for n=1 LET given statement be true for n=k `:. ""2k+7 lt (k+3)^(2)` for n=K+1 `2(k+1)+7 =(2k+7)+2` `lt (k+3)+2` [From inequation (1)] `=K^(2)+6k+11` `lt (k^(2)+6K+11)+(2k+5)` `lt K^(2)+8K+16lt (k+4)^(2)` ` rArr 2(k+1) +7 lt (K+4)^(2)` `rArr` Given statement is also true for n=K+1 HENCE from the principle of mathematical induction P (n) is true for all natural numbes n.

Discussion

2826.	Differentiate from first principles: 4. (1)/( sqrtx)
Answer» ANSWER :`(-1)/( 2X^(3//2) )`

Discussion

2827.	Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) prove that(1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)
Answer» SOLUTION :`sqrt2-1`

Discussion

2828.	d/(dx)[tanh^(-1)((2x)/(1+x^2))]=
Answer» `2/(1-x^2)` `2/(x^2-1)` `2/(1+x^2)` `(-2)/(x^2+1)` ANSWER :A

Discussion

2829.	A window is in the shap of a rectangle surmounted by a semicircle. If the perimeter of the window is 20 ft, find the maximum area.
Answer» ANSWER :`(200)/(PI + 4)`

Discussion

2830.	The plane which passes through the point (3,2,0) and the line (x-3)/(1) = (y-6)/(5) = (z-4)/(4) is
Answer» `X - y + z =1` `x + y + z=5` `x + 2Y - z =1` `2X - y + z=5` ANSWER :A

Discussion

2831.	Express each of the following in the form (a + ib) : {:((i),(1)/((4+3i)),(ii),((3+4i))/((4-5i)),(iii),((5+sqrt(2)i))/((1-sqrt(2)i))),((iv),((-2+5i))/((3-6i)),(v),((3-4i))/((4-2i)(1+i)),(vi),((2-2i)(2+3i))/((1+2i)(2-i))),((vii),((2+3i))/((2-i)),(viii),((1-i)^(3))/((1-i^(3))),(ix),((1+2i)^(3))/((1+i)(2-i))):}
Answer» ANSWER :`{:((i),((4)/(25)-(3)/(25)i),(ii),((-8)/(41)+(31)/(41)i),(iii),(1+2 sqrt(2)i),"(IV)",((-4)/(5)+(1)/(15)i)),((v),((1)/(4)-(3)/(4)i),(vi),((63)/(25)-(16)/(25)i),(vii),((-22)/(5)+(19)/(5)i),"(vii)",(-2+0i)),((ix),((-7)/(2)+(1)/(2)i),,,,,,):}`

Discussion

2832.	Find the direction in which a straight line must be drawn through the point (-1,2) so that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.
Answer» Solution : Let the slope of REQUIRED line PASSING through the point `(-1,2)` is `m`. `,.` Equation of line is, `y-2=m(x+1)` `impliesmx-y=-2-m`…….`(1)` Given line is, `x+y=4`……..`(2)` Solving we get `x=(2-m)/(m+1)` and `y=(5m+2)/(m+1)` `:.` Point of intersection is , `B=((2-m)/(m+1),(5m+2)/(m+1))` Given that `AB=3` units `impliessqrt(((2-m)/(m+1)+1)^(2)+((5m+2)/(m+1)-2)^(2))=3` `impliessqrt(((3)^(2)+(3m)^(2))/((m+1)^(2)))=3` `implies 3^(2)+9m^(2)=9(m+1)^(2)` `implies 9+9m^(2)=9m^(2)+18m+9` `implies 4m+18m=0` `impliesm=0` Now, `m=0` then `TAN theta=0impliestheta=0^(@)` `implies` Line is parallel to `x`-axis.

Discussion

2833.	Assertion (A): tan40^(@) + tan 80^(@) - sqrt(3)tan 40^(@) tan80^(@)=-sqrt(3) Reason( R): tan( A + B) =tan A + tan B + tan(A + B) tan A tan B
Answer» A is TRUE, R is true and R is correct EXPLANATION of A A is true, R is true and R is not correct explanation of A A is true, R is FALSE A is false, R is true. Answer :A

Discussion

2834.	Find the valueof r , if the coefficients of (2r+4)th and (r-2) th terms in the expansion of (1+x)^(18) are equal .
Answer» ANSWER :` :. R = 6`

Discussion

2835.	if a_(n) = sqrt(7+sqrt(7+sqrt(7 +n….))) times, then which one of the following is true ?
Answer» `a_(n) gt 7, AA n GE 1` `a_(n) LT 2, AA n ge 1` `a_(n) lt 7, AA n ge 1` `a_(n) gt 13, AA n ge 1` Answer :C

Discussion

2836.	If the pair of lines x^2+2xy+ay^2=0 and ax^2+2xy+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by
Answer» `3x^2+8xy-3y^2=0` `3x^2+10xy+3y^2=0` `3x^2+2xy-3y^2=0` `x^2+2xy-3y^2=0` ANSWER :B

Discussion

2837.	The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by.
Answer» ` 6! XX 5! ` ` 30 ` ` 5! Xx 4!` ` 7! Xx 5! ` ANSWER :A

Discussion

2838.	If f(x) satisfies Rolle's theorem for f(x) in [a,b] then int_(a)^(b) f'(x) dx =
Answer» `F(B) + f(a)` `f(a)` f(b) 0 Answer :D

Discussion

2839.	A plane which passes through the point (3,2,0) andthe line (x-4)/(1) = (y-7)/(5) = (z-4)/(4) is
Answer» `X - y + z =1` `x + y + z=5` `x + 2y - 2=1` `2x - y + z=5` ANSWER :A

Discussion

2840.	If a_(1)Cos theta+b_(1) Sin theta+c_(1)=0 and a_(2) cos theta+ b_(2) sin theta +c_(2)= 0 then (b_(1)c_(2)-b_(2)c_(1))^(2)+(c_(1)a_(2)-c_(2)a_(1))^(2)=
Answer» `(a_(1)b_(2)-a_(2)b_(1))^(2)` `(a_(2)b_(2)-a_(2)b_(1))^(2)` `(c_(1)-c_(2))^(2)` `(b_(2)c_(2)-b_(1)c_(1))^(2)` ANSWER :A

Discussion

2841.	y=sin""(x)/(2),x in[0,2pi]. The function y is ………. In (0,pi).
Answer» DECREASING Increasing Constant Can not SAY anything Answer :B

Discussion

2842.	The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The percentage error in volume is
Answer» 1 0.01 0.001 `-1` ANSWER :A

Discussion

2843.	Evaluate lim_(x rarr 1) ((x + x^2 + .........+ x^n)-n)/(x - 1)
Answer» SOLUTION :`(N(n+1))/2`

Discussion

2844.	In a DeltaOAB The P.V.'s of A, B are bar(a), bar(b) respectively. The P.V. of 'C' is (3bar(a))/4+bar(b)/2 then 'C' lies
Answer» ANSWER :B

Discussion

2845.	How many different words can be formed by using all the letters of the word MATHEMATICS ? In how many of them, vowels are always together ?
Answer» ANSWER :49,89,600, 1,20,960

Discussion

2846.	The sum of coefficients of the two middle terms in the expansion of (1+x)^(2n-1) is equalto (2n-1)C_(n)
Answer» ANSWER :FALSE

Discussion

2847.	The sum of the solutions of the equation 2sin^(-1)sqrt(x^(2)+x+1)+cos^(-1)sqrt(x^(2)+x)=(3pi)/2 is
Answer» 0 -1 3 2 Answer :D

Discussion

2848.	For any two complex numbers z_(1) and z_(2), prove that Re (z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)
Answer» ANSWER :`Re(z_(1))Re(z_(2))-IM(z_(1))Im(z_(2))`

Discussion

2849.	Write down the slopes of the following lines: 7x-5y+8=0
Answer» ANSWER : `7/(5)`

Discussion

2850.	Theperiodof \|sin x\| .\| cosx \| is
Answer» `(pi)/(2) ` `pi` `4PI` `2PI` ANSWER :1

Discussion

Explore topic-wise InterviewSolutions in .

Simplify the following (20)/(sqrt(-5))

Find the slope of the time passing through the points (3,-2) and ( -1,4)

If the ratio of the sums of m terms and n terms of an A.P. be m^(2) : n^(2), prove that the ratio of its m^(th) and n^(th) terms is (2m-1) : (2n-1).

Evaluate the following limits : Lim_(x to a) (xsqrt(x)-asqrt(a))/(x-a)

If.^(n)C_(12) =^(n)C_(8)then n = . . . . .

If bara,barb,barc " are three mutually perpendicular vectors such that " absbara = absbarb = absbarc, " then " (bara+barb+barc,bara)=

If bar(a), bar(b)&bar(c) are non-coplanar vectors and if bar(d) is such that bar(d)=1/x(bar(a)+bar(b)+bar(c)) and bar(d)=1/y(bar(b)+bar(c)+bar(d)) where x and y are non-zero real numbers, then 1/(xy)(bar(a)+bar(b)+bar(c)+bar(d))=

3sinx+4cosx-6=0 then the general solution of x =

Find (x + 1)^6 + (x-)^6. Hence or otherwise evaluate (sqrt2 + 1)^6 + (sqrt2 - 1)^6.

A coin is tossed twice, what is the probability that at least one tail occurs?

What is the number of terms in the expansion of the following? (6x- (1)/(x^3) )^(17)

Solve: |x-1|le5,|x|ge2

If the real part of (barz+2)/(barz-1) is 4 then show that the locus of the point representing z in the complex plane is circle.

Express (3-i)^2/(2+i) in the form x+iy

If one angle of a triangle is 30^(@) and the lengths of the sides adjacent to it are 40 and 40sqrt(3), then the triangle is

The set of all x for which sin x lex is

If the 4^(th) and 7^(th) term of a G.P. are 27 and 729 respectively, then find the G.P.

If f: R rarr R is a function such that f(x +y) =f(x) +f(y) forall x,y in R then f is continuous on R if it is continuous at a single point in R.

Find the area of the triangle formed by the lines y-x =0, x+y=0 and x-k=0.

Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and (x+3)/(-3)=(y+7)/(2)=(z-6)/(4)

Find the derivative of the following functions: 5sin x-6 cosx+7

Statement- I The soluton of the system of equations 2x-y+3z=9,x+y+z=6,x-y+z=2 is x=1,y=2,z=3 Statement- II : The solution of the system of equations x+2y-z=3,3x=y+2z=1, 2x-2y+3z=2 is x=-1,y=4,z=4 Which of the above Statement(s) is true ?

A straight line through the point (3,4) in the first quadrant meets the axes at A and B . The minimum area of the triangle OAB is

A plane which passes through the point (3,2,0) and the line (x-4)/(1) = (y-7)/(5) = (z-4)/(4) is

(2n+7) lt (n+3)^(2)

Differentiate from first principles: 4. (1)/( sqrtx)

Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) prove that(1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

d/(dx)[tanh^(-1)((2x)/(1+x^2))]=

A window is in the shap of a rectangle surmounted by a semicircle. If the perimeter of the window is 20 ft, find the maximum area.

The plane which passes through the point (3,2,0) and the line (x-3)/(1) = (y-6)/(5) = (z-4)/(4) is

Find the direction in which a straight line must be drawn through the point (-1,2) so that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.

Assertion (A): tan40^(@) + tan 80^(@) - sqrt(3)tan 40^(@) tan80^(@)=-sqrt(3) Reason( R): tan( A + B) =tan A + tan B + tan(A + B) tan A tan B

Find the valueof r , if the coefficients of (2r+4)th and (r-2) th terms in the expansion of (1+x)^(18) are equal .

if a_(n) = sqrt(7+sqrt(7+sqrt(7 +n….))) times, then which one of the following is true ?

If the pair of lines x^2+2xy+ay^2=0 and ax^2+2xy+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by.

If f(x) satisfies Rolle's theorem for f(x) in [a,b] then int_(a)^(b) f'(x) dx =

A plane which passes through the point (3,2,0) andthe line (x-4)/(1) = (y-7)/(5) = (z-4)/(4) is

If a_(1)Cos theta+b_(1) Sin theta+c_(1)=0 and a_(2) cos theta+ b_(2) sin theta +c_(2)= 0 then (b_(1)c_(2)-b_(2)c_(1))^(2)+(c_(1)a_(2)-c_(2)a_(1))^(2)=

y=sin""(x)/(2),x in[0,2pi]. The function y is ………. In (0,pi).

The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The percentage error in volume is

Evaluate lim_(x rarr 1) ((x + x^2 + .........+ x^n)-n)/(x - 1)

In a DeltaOAB The P.V.'s of A, B are bar(a), bar(b) respectively. The P.V. of 'C' is (3bar(a))/4+bar(b)/2 then 'C' lies

How many different words can be formed by using all the letters of the word MATHEMATICS ? In how many of them, vowels are always together ?

The sum of coefficients of the two middle terms in the expansion of (1+x)^(2n-1) is equalto (2n-1)C_(n)

The sum of the solutions of the equation 2sin^(-1)sqrt(x^(2)+x+1)+cos^(-1)sqrt(x^(2)+x)=(3pi)/2 is

For any two complex numbers z_(1) and z_(2), prove that Re (z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)

Write down the slopes of the following lines: 7x-5y+8=0

Theperiodof |sin x| .| cosx | is