14949 + Interview Questions in Maths in Class 11 Page 61 InterviewSolution

3001.	If the probabiliy of a horse A winning a race is (1)/(5) and the probability of horse B winning the same race is (1)/(4) , what is the probability that one of the horses will win ?
Answer» ANSWER :`(9)/(20)`

Discussion

3002.	If f(x) and g(x) are two positive and increasing function , then
Answer» `(f(X))^(G(x))` is ALWAYS INCREASING If `(f(x))^(g(x))` is decreasing then `f(x)lt1` If `(f(x))^(g(x))` is increasing then `f(x)gt1` If `f(x)gt1`,then `(f(x))^(g(x))` is increasing Answer :C::D

Discussion

3003.	What is the value of d/(dx) (sec x ) ?
Answer» SOLUTION :SEC X TAN x

Discussion

3004.	Evaluate the following limits : Lt_(xto0)(e^(3+x)-e^(3))/x
Answer» ANSWER :`E^(3)`

Discussion

3005.	Two parallel lines lying in the same quadrant make intercepts a and b on x,y axes respectively between them then the distance between the lines is
Answer» `(AB)/(SQRT(a^2+b^2))` `sqrt(a^2+b^2)` `1/sqrt(a^2+b^2)` `1/a^2+1/b^2` ANSWER :A

Discussion

3006.	A(5, 2), B(2, 3) and C(6, 5) are the verticies of Delta ABC. Find equation of internal bisector of angle BAC.
Answer» ANSWER :`2X + y - 12 = 0`

Discussion

3007.	If theta lies in third Quardrant and Sintheta=(-4)/5. Find the values of " cosec "(theta/2)and Tan(theta/2)
Answer» ANSWER :`(-3)/SQRT13, (-2)/sqrt13`

Discussion

3008.	Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If I will not marry her, then she is not beautiful.
Answer» <P> ANSWER :~p => ~Q

Discussion

3009.	Discuss the continuity of the following functions : f(x)= sin x +cos x
Answer» ANSWER :CONTINOUS

Discussion

3010.	Solve the inequality for x: -14 lt (3(x-2))/( 5) le 0
Answer» ANSWER :`(-23,2]`

Discussion

3011.	Find the domains of the following functionsf(x) = ( 1)/( sqrt( 4-x^(2)))
Answer» ANSWER :`( - 2,2)`

Discussion

3012.	YZ plane divides line segment joining (4,8,10) and (6,10,-8) in ratio -2:3 .
Answer» ANSWER :TRUE STATEMENT

Discussion

3013.	"cosec"h^(-1) ((3)/(2))+"cosec"h^(-1)(-(1)/(2))=
Answer» `log_(E)((2+sqrt(13))/(3))` `log_(e)(sqrt(5)-2)` `log((2+sqrt(13))/(3(sqrt(5)+2)))` `log_(e)2` Answer :C

Discussion

3014.	Find the sum to 20 terms of 2 + 6 + 18 + .....
Answer» ANSWER :`3^(20)-1`

Discussion

3015.	If bara = bari+2barj+3bark, barb = -bari+2barj+bark, barc =3bari +barj and bara+tbarbis perpendicular tobarc,then t =
Answer» 5 4 3 2 Answer :A

Discussion

3016.	A right triangle has perimeter of length 7 and hypotenuse of length 3. iftheta is the larger non-right angle in the triangles, then the value of cos theta equals
Answer» `(SQRT(6)-sqrt(2))/(4)` `(4+sqrt(2))/(6)` `(4-sqrt(2))/(3)` `(4-sqrt(2))/(6)` ANSWER :D

Discussion

3017.	There 12 points in a plane of which 5 are collinear . Find the number of triangles that can be formed with vertices at these points.
Answer» ANSWER :` 210 `

Discussion

3018.	(cos(17^(@))+sin(17^(@)))/(cos(17^(@))-sin(17^(@)))= …………
Answer» `tan62^(@)` `tan56^(@)` `tan54^(@)` `tan73^(@)` ANSWER :A

Discussion

3019.	Find the specified term of the expression in each of the following binomials: (v) Middle term of ((x^2)/( 4) - (4)/( x^2) )^(10)
Answer» ANSWER :`-252`

Discussion

3020.	Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x)where g(x) is continuous . Then f^(1) (x) equals
Answer» `f(x) g(0)` `2f(x) g(0)` `2G(0)` `2f(0)` Answer :B

Discussion

3021.	There are 10 persons named ""P_1,P_2,P_3,....,P_10' Out of 10 persons, 5 persons are to be arrangement P_1 must occur where as P_4 and P_5 do not occur. Find the number of such possible arrangements.
Answer» ANSWER :`= 4,200`

Discussion

3022.	.......... is the equation of line passes from point A(2,-(3)/(2) ) and parallel to X- axis.
Answer» `x=2` `2x-3=0` `2y-3=0` `2y+3=0` ANSWER :D

Discussion

3023.	Which one of the following statement is true?
Answer» A SCALAR quantity is conserved in a process A scalar quantity does not vary from one point to ANOTHER in space A scalar quantity can never TAKE -ve values A scalar quantity has only MAGNITUDE and no direction. Solution :A scalar quantity has only magnitude and no direction.

Discussion

3024.	Determine the sum of first 35 terms of an A.P. if t_(2), = 1 and t_(7) , = -22.
Answer» ANSWER :2387

Discussion

3025.	The probability that in a throw of two dice weget, an even sum or sum less than 5 is
Answer» `(1)/(2)` `(1)/(6)` `(2)/(3)` `(5)/(9)` Answer :D

Discussion

3026.	2tanh^(-1)((1)/(2))=
Answer» ANSWER :A

Discussion

3027.	Show that the equation of the line passing through the origin and making an angle theta with the line y=mx +c is (y)/( x) = ( mpm tan theta)/(1 pm m tan theta ).
Answer» ANSWER :`THEREFORE (y)/(x) = (m pm tan theta)/( 1 pm m tan theta)`, which is the EQUATION of required line.

Discussion

3028.	Find the transformed equation of When the axes of rotated through 90^(0), find the transformed equation of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1
Answer» ANSWER :`(Y^(2))/(a^(2))-(X^(2))/(B^(2))=1`

Discussion

3029.	Simplify:i^(18)
Answer» ANSWER :`-1`

Discussion

3030.	Function f:NrarrR,f(x)=sqrtx= then value off(25)/ ( f(16)+f(1) )= …. .
Answer» ANSWER :1

Discussion

3031.	A and B are fixed points of PA+PB=K constant) and KgtAB then the locus of P is
Answer» Hyperbola an ellipse Parabola a circle Answer :2

Discussion

3032.	Prove that: .^(2)C_(2)+^(3)C_(2)+^(4)C_(2)+â€¦..+^(n+1)C_(2)=1/6n(n+1)(n+2)
Answer» SOLUTION :N/a

Discussion

3033.	Differentiate the following functions w.r.t. x: tan (6x + 11)
Answer» ANSWER :`6 SEC^(2) (6x+11)`

Discussion

3034.	A person standing at the juction (crossing ) of two straight paths represented the equations 2x-3y+4=0 and 3x+4y-5=0 wants to reach the path whose equation is 6x-7y+8=0 in the least time. Find the equation of the path that he should follow.
Answer» ANSWER :`119x+102y-125=0`

Discussion

3035.	If sin^(2) theta lt cos ^(2) thetathen
Answer» `n pi + (pi)/( 2) LT theta lt n pi + (pi)/( 4) , n in Z` `n pi + ( 3 pi)/( 2 ) lt theta lt n pi + (5 pi)/( 4) , n in Z` `n pi + (pi)/(4) lt theta lt n pi + (3 pi)/( 4) , n in Z` `n pi + (3 pi)/( 4) lt theta lt n pi + (5 pi)/( 4) , n in Z` ANSWER :C

Discussion

3036.	If the square ABCD where A(0,0), B(2,0), C(2,2), D(0,2) undergoes the following the transformations successively (i) f_(1)(x,y) to f(y,x) (ii) f_(2) (x,y) to f(x + 3y, y) (iii) f_(3) (x,y) to f((x-y)/(2),(x + y)/(2)) then find nature of the final figure of ABCD
Answer» ANSWER :PARALLELOGRAM

Discussion

3037.	Prove that the ratio of the coeffiecient of x^10 "in" (1-x^2 )^10& the term independent of x in (x-2/x)^10 is 1:32
Answer»

Discussion

3038.	If theta in ((-pi)/(4), (pi)/(4)) and x=log_(e )[cot((pi)/(4)+theta)] then prove that (i) cosh x= sec 2theta"" (ii) sinh x=-tan 2theta
Answer» `TAN(2THETA)` COT`2theta` `-"Tan"2theta` `-"Cot"2theta` ANSWER :C

Discussion

3039.	Solve: 4 cos ^(2) theta = 3 . (theta ^(@) le theta lt 360 ^(@)).
Answer» ANSWER :`330^(@)`

Discussion

3040.	f(x)={{:( a+(Sin[x])/(x)"," , x gt 0),(2",",x=0),(b+[(Sinx-x)/(x^(3))]",", x lt 0):} where [.] denots the greates integer function . If f(x) is continuous at x=0 then b=
Answer» `a-1` `a+1` `a+2` `a-2` ANSWER :A

Discussion

3041.	Consider the lines L _(1) : ( x -1)/(2) = y/1 = (z +3)/(1) , L _(2) : (x-4)/(1) = (y+3)/(1) = (z+3)/(2) and the planes P _(1) : 7 x + y + 2z =3, P _(2) : 3x + 5y - 6z = 4, Let ax + by + cz =d the equation of the plane passing through the point of intersection of lines L _(1) and L _(2) and perpendicular to planes P _(1) and P _(2). Match List -I with List - II and select the correct answer using the code given below the lists
Answer» <P>`{:(P, Q, R, S), (3,2,4,1):}` `{:(P, Q, R, S), (1,3,4,2):}` `{:(P, Q, R, S), (3,2,1,4):}` `{:(P, Q, R, S), (2,4,1,3):}` ANSWER :A

Discussion

3042.	Anurag draws a card from a pack of cards . Whatis the probability that he draws one of following numbers ? 7
Answer» ANSWER :`(1)/(13)`

Discussion

3043.	Anurag draws a card from a pack of cards . Whatis the probability that he draws one of following numbers ? 3
Answer» ANSWER :`(1)/(13)`

Discussion

3044.	Anurag draws a card from a pack of cards . Whatis the probability that he draws one of following numbers ? 3 or 7
Answer» ANSWER :`(2)/(13)`

Discussion

3045.	Find the number of all possible arrangements of the letters of the word "MATHEMATICS" taken four at a time
Answer» ANSWER :` 2454`

Discussion

3046.	Check whether the following statement is true ornot: If x,y in Z are such that x and y are odd, then xy is odd.
Answer» ANSWER :TRUE.

Discussion

3047.	If y = Tan^(-1)(cot(pi/2-x)) then (dy)/(dx) =
Answer» 1 `-1` 0 `1/2` ANSWER :A

Discussion

3048.	Consider the system of equations sin x cos 2 y = (a ^(2) - 1)^(2) + 1, cos x sin 2 y = a = 1 The number of values of a for which the system has a solution is
Answer» 1 2 3 infinite Answer :B

Discussion

3049.	Solve inequality5 (2x -7) -3 (2x+3) le 0, 2x+19 le 6x+47.and represent solution graphically on number line.
Answer» ANSWER :`[-7,11]` `(##NCERT_TEL_MAT_XI_C06_E04_010_A01##)`

Discussion

3050.	Find the number of terms in the following expansions. (2x-3y)^(5)
Answer» ANSWER :`=6`

Discussion

Explore topic-wise InterviewSolutions in .

If the probabiliy of a horse A winning a race is (1)/(5) and the probability of horse B winning the same race is (1)/(4) , what is the probability that one of the horses will win ?

If f(x) and g(x) are two positive and increasing function , then

What is the value of d/(dx) (sec x ) ?

Evaluate the following limits : Lt_(xto0)(e^(3+x)-e^(3))/x

Two parallel lines lying in the same quadrant make intercepts a and b on x,y axes respectively between them then the distance between the lines is

A(5, 2), B(2, 3) and C(6, 5) are the verticies of Delta ABC. Find equation of internal bisector of angle BAC.

If theta lies in third Quardrant and Sintheta=(-4)/5. Find the values of " cosec "(theta/2)and Tan(theta/2)

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If I will not marry her, then she is not beautiful.

Discuss the continuity of the following functions : f(x)= sin x +cos x

Solve the inequality for x: -14 lt (3(x-2))/( 5) le 0

Find the domains of the following functionsf(x) = ( 1)/( sqrt( 4-x^(2)))

YZ plane divides line segment joining (4,8,10) and (6,10,-8) in ratio -2:3 .

"cosec"h^(-1) ((3)/(2))+"cosec"h^(-1)(-(1)/(2))=

Find the sum to 20 terms of 2 + 6 + 18 + .....

If bara = bari+2barj+3bark, barb = -bari+2barj+bark, barc =3bari +barj and bara+tbarbis perpendicular tobarc,then t =

A right triangle has perimeter of length 7 and hypotenuse of length 3. iftheta is the larger non-right angle in the triangles, then the value of cos theta equals

There 12 points in a plane of which 5 are collinear . Find the number of triangles that can be formed with vertices at these points.

(cos(17^(@))+sin(17^(@)))/(cos(17^(@))-sin(17^(@)))= …………

Find the specified term of the expression in each of the following binomials: (v) Middle term of ((x^2)/( 4) - (4)/( x^2) )^(10)

Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x)where g(x) is continuous . Then f^(1) (x) equals

There are 10 persons named ""P_1,P_2,P_3,....,P_10' Out of 10 persons, 5 persons are to be arrangement P_1 must occur where as P_4 and P_5 do not occur. Find the number of such possible arrangements.

.......... is the equation of line passes from point A(2,-(3)/(2) ) and parallel to X- axis.

Which one of the following statement is true?

Determine the sum of first 35 terms of an A.P. if t_(2), = 1 and t_(7) , = -22.

The probability that in a throw of two dice weget, an even sum or sum less than 5 is

2tanh^(-1)((1)/(2))=

Show that the equation of the line passing through the origin and making an angle theta with the line y=mx +c is (y)/( x) = ( mpm tan theta)/(1 pm m tan theta ).

Find the transformed equation of When the axes of rotated through 90^(0), find the transformed equation of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

Simplify:i^(18)

Function f:NrarrR,f(x)=sqrtx= then value off(25)/ ( f(16)+f(1) )= …. .

A and B are fixed points of PA+PB=K constant) and KgtAB then the locus of P is

Prove that: .^(2)C_(2)+^(3)C_(2)+^(4)C_(2)+â€¦..+^(n+1)C_(2)=1/6n(n+1)(n+2)

Differentiate the following functions w.r.t. x: tan (6x + 11)

A person standing at the juction (crossing ) of two straight paths represented the equations 2x-3y+4=0 and 3x+4y-5=0 wants to reach the path whose equation is 6x-7y+8=0 in the least time. Find the equation of the path that he should follow.

If sin^(2) theta lt cos ^(2) thetathen

If the square ABCD where A(0,0), B(2,0), C(2,2), D(0,2) undergoes the following the transformations successively (i) f_(1)(x,y) to f(y,x) (ii) f_(2) (x,y) to f(x + 3y, y) (iii) f_(3) (x,y) to f((x-y)/(2),(x + y)/(2)) then find nature of the final figure of ABCD

Prove that the ratio of the coeffiecient of x^10 "in" (1-x^2 )^10& the term independent of x in (x-2/x)^10 is 1:32

If theta in ((-pi)/(4), (pi)/(4)) and x=log_(e )[cot((pi)/(4)+theta)] then prove that (i) cosh x= sec 2theta"" (ii) sinh x=-tan 2theta

Solve: 4 cos ^(2) theta = 3 . (theta ^(@) le theta lt 360 ^(@)).

f(x)={{:( a+(Sin[x])/(x)"," , x gt 0),(2",",x=0),(b+[(Sinx-x)/(x^(3))]",", x lt 0):} where [.] denots the greates integer function . If f(x) is continuous at x=0 then b=

Anurag draws a card from a pack of cards . Whatis the probability that he draws one of following numbers ? 7

Anurag draws a card from a pack of cards . Whatis the probability that he draws one of following numbers ? 3

Anurag draws a card from a pack of cards . Whatis the probability that he draws one of following numbers ? 3 or 7

Find the number of all possible arrangements of the letters of the word "MATHEMATICS" taken four at a time

Check whether the following statement is true ornot: If x,y in Z are such that x and y are odd, then xy is odd.

If y = Tan^(-1)(cot(pi/2-x)) then (dy)/(dx) =

Consider the system of equations sin x cos 2 y = (a ^(2) - 1)^(2) + 1, cos x sin 2 y = a = 1 The number of values of a for which the system has a solution is

Solve inequality5 (2x -7) -3 (2x+3) le 0, 2x+19 le 6x+47.and represent solution graphically on number line.

Find the number of terms in the following expansions. (2x-3y)^(5)