14949 + Interview Questions in Maths in Class 11 Page 197 InterviewSolution

9801.	Show that the product of the perpendicular from two points (+-sqrt(a^(2)-b^(2)),0) to the line x/a cos alpha+y/b sin alpha=1 is b^(2).
Answer» ANSWER :`B^(2)`

Discussion

9802.	The point on bar(AB) through which the perpendicular bisector of the segment joining the points A(7,1),B(3,-3) passes is
Answer» `(5,1)` `(5,-1)` `(-5,1)` `(-1,-5)` ANSWER :B

Discussion

9803.	Find sqrt(4+x^(2))-sqrt(4-x^(2)) when x is small.
Answer» ANSWER :`x/8`

Discussion

9804.	A particle velocity v at time is given by v = 2e^(2t) cos(pi t)/(3). The least value of t at which the acceleration becomes zero is
Answer» 0 `(3)/(2)` `(3)/(pi)tan^(-1)(6)/(pi)` `(3)/(pi)cot^(-1)(6)/(pi)` ANSWER :C

Discussion

9805.	The solution set of cos2theta=cos^(2)theta-sin^(2)theta is …………
Answer» R `KPI,k inZ` `PHI` `(2k+1)(PI)/(2),kinZ` Answer :A

Discussion

9806.	If y=x-x^2,then the derivative of y^2 with respect to x^2 is
Answer» `1-2x` `2-4x` `3x-2x^2` `1-3x+2x^2` ANSWER :B

Discussion

9807.	A fair coinwith 1 marked on one face and 6 on the other and a fair die are both tossed Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12
Answer» ANSWER :(i) `1/12` (II) `1/12`

Discussion

9808.	Sin^(-1)(2cos^(2)x-1)+Cos^(-1)(1-2sin^(2)x)=
Answer» 0 1 `-1` `(PI)/2` ANSWER :A

Discussion

9809.	O' is the origin in the cartesian plane. From the origin 'O' take point A is the North East direction such that \|bar(OA)\|=5. B is a pointin the North West direction such that \|bar(OB)\|=5. Then \|bar(OA)-bar(OB)\|=
Answer» 25 `5sqrt(2)` `10sqrt(5)` `SQRT(5)` ANSWER :B

Discussion

9810.	Find the sum of all 4-digit numbers that can be formedusingthe digits 1,2,4,6 and 8.
Answer» ANSWER :21

Discussion

9811.	A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ?
Answer» ANSWER :`= 9`

Discussion

9812.	If:[ -2 ,2 ] toRis defined by f(x) = {: { ((sqrt(1+cx) -sqrt(1-cx))/x , " for"-2 le x lt 0), ((x+3)/(x +1) , " for "0 le x le 2):} continuouson[ -2, 2]then c is equal to
Answer» `(2)/(SQRT(3))` 3 `3/2` `(3)/(sqrt(2))` ANSWER :B

Discussion

9813.	If ysqrt(x^2+1)=log(sqrt(x^2+1)-x),then(x^2+1)dy/dx+xy+1=
Answer» 0 1 2 none of these ANSWER :A

Discussion

9814.	If xgt 0 the minimum value of x^x is
Answer» `E^(-1//e)` `e^(1//e)` `e^(e)` e Answer :A

Discussion

9815.	Out of 100 students,two sections of 40 and 60 are formed.If you and your friend are among the 100 students,what is the probability that (a) you both enter the same section ?( b) you both enter the different section?
Answer» ANSWER :(a) `17/33` (B) `16/33`

Discussion

9816.	Range of the function f: R rarr R, f(x)= x^(2) is………
Answer» R Z `R^(+) uu {0}` `R- {0}` ANSWER :C

Discussion

9817.	Write down all the subsets of the following sets : {5 ,{5} }
Answer» ANSWER :`PHI, {5}, { {5} }, {5, {5} }`

Discussion

9818.	A triangle is formed by the lines whose equations are AB:x+y-5=0, BC:x+7y-7=0, and CA:7x+y+14=0. Find the bisector of the interior angle at B
Answer» ANSWER : `3x+6y-16=0`

Discussion

9819.	A triangle is formed by the lines whose equations are AB:x+y-5=0, BC:x+7y-7=0, and CA:7x+y+14=0. Find the bisector of the exterior angle at C.
Answer» ANSWER : `8x+8y+7=0`

Discussion

9820.	Perpendicular distance from origin to point (3,4,5) is ......... .
Answer» ANSWER :`5sqrt2`

Discussion

9821.	If the lines 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10pi, then the equation of the circle is :
Answer» ANSWER :`X^(2)+y^(2)-2x+2y-23=0`

Discussion

9822.	If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1:2, then find the equation of the line. Thinking Process : Coordinates of the point which divides line segment joining (x_1 , y_1 ) and ( x_2, y_2) in ratio (m_1 : m_2) ((m_1 x_2 + m_2 x_1)/( m_1 + m_2) , ( m_1 y_2 + m_2 y_1)/( m_1 + m_2)).
Answer» ANSWER :`8 X+ 5Y + 60=0`,

Discussion

9823.	A real valued function is given by f (x) = (x^(2)+x+2)/(x^(2)+x +1), find its domain and range .
Answer» ANSWER :`D_(F) = R;R_(f) = [1,7/3] `

Discussion

9824.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ C
Answer» ANSWER :`{11}`

Discussion

9825.	Lt_(xto0)((729)^(x)-(243)^(x)-(81)^(x)+9^(x)+3^(x)-1)/x^(3)
Answer» ANSWER :`6(ln3)^(3)`

Discussion

9826.	If the algebraic sum of the perpendicular distances from the point (3,1),(-1,2) and (1,3) to a variable line is zero, and \|{:(x^2+1,x+1,x+2),(2x+3,3x+2,x+4),(x+4,4x+3,2x+5):}\|=mx^4+nx3+px^2+qx+r, then the variable line always passes through the point
Answer» (-m,R) (-r,m) (r,m) (2R,m) ANSWER :C

Discussion

9827.	A (-3,2), B(2,5) be two points. If the point P(O,K) on y-axis, such that abs(PA-PB) " is greatest, then " (k-1)/5 is equal to
Answer» ANSWER :2

Discussion

9828.	The shortest distance between the skew line (x-3)/(-1) =(y-4)/(2)=(z+2)/(1), (x-1)/(1)=(y+7)/(3)=(z+2)/(2) is
Answer» 6 7 `3SQRT5` `SQRT(35)` ANSWER :D

Discussion

9829.	sin^(2)""(pi)/(18)+sin^(2)""(2pi)/(18)+sin^(2)""(4pi)/(18)+sin^(2)""(8pi)/(18)+sin^(2)""(7pi)/(18)+sin^(2)""(5pi)/(18)=
Answer» 1 2 3 4 Answer :C

Discussion

9830.	cot[Sin^(-1)sqrt(13/17)]-sin[Tan^(-1)""2/3]=
Answer» `-2/sqrt(13)` 0 `2/sqrt(13)` `2/(3sqrt(13))` ANSWER :B

Discussion

9831.	An equilateral triangle is constructed between two parallel line sqrt3x+y-6=0 and sqrt3x+y+9=0 with base on and vertex on the other. Then the area of triangle is
Answer» `(4)/(SQRT3` `(3)/4sqrt3` `4sqrt3/3` `(3)/4sqrt3` ANSWER :B

Discussion

9832.	The most general value of theta satisfies both the equations tan theta = -1 and cos theta = (1)/(sqrt(2)) is
Answer» Answer :`(1)/(2)[(2m-N)pi - (pi)/(4) PM (pi)/(6)]` where m, `n in l`.

Discussion

9833.	The value of Sin^(-1)(sin10) is
Answer» 10 `10-3pi` `3pi-10` -10 Answer :C

Discussion

9834.	How many terms of the A.P. -6, -11/2, -5,… are needed to give the sum -25?
Answer» ANSWER :4

Discussion

9835.	In triangle ABC, triangle A^(1)B^(1)C^(1) are such that B=B^(1),A+A^(1)=180^(0) then b b^(1)+c c^(1)=
Answer» `AA^(1)` `a+a^(1)` `a-a^(1)` `a//a^(3)` ANSWER :A

Discussion

9836.	Differentiate from first principles: 2. (x-1)^(2)
Answer» ANSWER :`2(x-1)`

Discussion

9837.	Find the cartesian equation of the curve whose parametric equations are : x=4"cos"theta, y=4"sin"theta
Answer» ANSWER :`X^(2)+y^(2)=16`

Discussion

9838.	If 1/2sin^(-1)[(3sin2theta)/(5+4cos2theta)]=tan^(-1)x, then x =
Answer» `TAN3THETA` `3tantheta` `(1//3)TANTHETA` `3COT""THETA` ANSWER :C

Discussion

9839.	Of 12 different books a shelf will hold five. how manydifferent arrangements may be made on the shelf?
Answer» ANSWER :` ""^(12)p_5 = 95,040`

Discussion

9840.	If 1^(@)=0.01745 radians. Then the approximate value of tan46^(@) is
Answer» 1.0259 1.0394 1.0349 1.0493 Answer :C

Discussion

9841.	Convert the products into sum or difference. 2 sin 48^(@) cos 12 ^(@)
Answer» ANSWER :`1.4538`

Discussion

9842.	Express (1)/(1-cos theta+2i sin theta) in the form of a+ib.
Answer» ANSWER :`((1-COS theta)/(2-2 cos theta+ 3 SIN^(2) theta))+i((-2 sin theta)/(2-cos theta+3 sin^(2) theta))`

Discussion

9843.	For some constants a and b, find the derivative of (ax^(2)+b)^(2)
Answer» ANSWER :`4AX(AX^(2)+B)`

Discussion

9844.	The principal solution of sintheta=sqrt((1+sqrt(2))/(2sqrt(2))) is
Answer» `22.5 ^(0)` `67.5^(0)` `72^(0)` `9^(0)` ANSWER :B

Discussion

9845.	Find the new coordinates of point (3,-4) if the origin is shifted to (1,2) by a translation.
Answer» ANSWER :`2,-6`

Discussion

9846.	construct truthtable for(p vv q)vv(r ^^ ~q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_027_A01##)`

Discussion

9847.	Differentiate the following functions: 14. (i) (2x-3)^(2) (ii) (2x -3)^(100)
Answer» ANSWER :(i) `8x-12,` (II) `200 (2x -3)^(99)`

Discussion

9848.	Let A={1,2,3,4}. Examine whether the statements given below are true or false. (i) exists x in A" such that "x+3=8. (ii) AA x in A, x+2 lt7. (iii) exists z harr A" such that "x+1lt3. (iv) AA x in A, x+3 ge5.
Answer» Solution :(i) Clearly, no number in A satisfies x+3=8. `therefore` the given STATEMENT is FALSE. (ii) Every number in A satisfies `x+2lt7.` So, the given statement is true. (III) Clearly, `x=1harrA" satisfies "x+1lt3.` `therefore` the given statement is true. (IV) Since `x=1 in A` does not satisfy `x+3ge5`, the given statement is false.

Discussion

9849.	Which of the following sets are finite or infinite {1, 2, 3, . . .99, 100}
Answer» ANSWER :it is a FINITE SET

Discussion

9850.	Find the modulus and the arguments of the following complex numbers : sin 120^(@)-i cos120^(@)
Answer» ANSWER :Modulus =1 Argument `=(pi)/(6)`

Discussion

Explore topic-wise InterviewSolutions in .

Show that the product of the perpendicular from two points (+-sqrt(a^(2)-b^(2)),0) to the line x/a cos alpha+y/b sin alpha=1 is b^(2).

The point on bar(AB) through which the perpendicular bisector of the segment joining the points A(7,1),B(3,-3) passes is

Find sqrt(4+x^(2))-sqrt(4-x^(2)) when x is small.

A particle velocity v at time is given by v = 2e^(2t) cos(pi t)/(3). The least value of t at which the acceleration becomes zero is

The solution set of cos2theta=cos^(2)theta-sin^(2)theta is …………

If y=x-x^2,then the derivative of y^2 with respect to x^2 is

A fair coinwith 1 marked on one face and 6 on the other and a fair die are both tossed Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12

Sin^(-1)(2cos^(2)x-1)+Cos^(-1)(1-2sin^(2)x)=

O' is the origin in the cartesian plane. From the origin 'O' take point A is the North East direction such that |bar(OA)|=5. B is a pointin the North West direction such that |bar(OB)|=5. Then |bar(OA)-bar(OB)|=

Find the sum of all 4-digit numbers that can be formedusingthe digits 1,2,4,6 and 8.

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ?

If:[ -2 ,2 ] toRis defined by f(x) = {: { ((sqrt(1+cx) -sqrt(1-cx))/x , " for"-2 le x lt 0), ((x+3)/(x +1) , " for "0 le x le 2):} continuouson[ -2, 2]then c is equal to

If ysqrt(x^2+1)=log(sqrt(x^2+1)-x),then(x^2+1)dy/dx+xy+1=

If xgt 0 the minimum value of x^x is

Out of 100 students,two sections of 40 and 60 are formed.If you and your friend are among the 100 students,what is the probability that (a) you both enter the same section ?( b) you both enter the different section?

Range of the function f: R rarr R, f(x)= x^(2) is………

Write down all the subsets of the following sets : {5 ,{5} }

A triangle is formed by the lines whose equations are AB:x+y-5=0, BC:x+7y-7=0, and CA:7x+y+14=0. Find the bisector of the interior angle at B

A triangle is formed by the lines whose equations are AB:x+y-5=0, BC:x+7y-7=0, and CA:7x+y+14=0. Find the bisector of the exterior angle at C.

Perpendicular distance from origin to point (3,4,5) is ......... .

If the lines 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10pi, then the equation of the circle is :

A real valued function is given by f (x) = (x^(2)+x+2)/(x^(2)+x +1), find its domain and range .

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ C

Lt_(xto0)((729)^(x)-(243)^(x)-(81)^(x)+9^(x)+3^(x)-1)/x^(3)

If the algebraic sum of the perpendicular distances from the point (3,1),(-1,2) and (1,3) to a variable line is zero, and |{:(x^2+1,x+1,x+2),(2x+3,3x+2,x+4),(x+4,4x+3,2x+5):}|=mx^4+nx3+px^2+qx+r, then the variable line always passes through the point

A (-3,2), B(2,5) be two points. If the point P(O,K) on y-axis, such that abs(PA-PB) " is greatest, then " (k-1)/5 is equal to

The shortest distance between the skew line (x-3)/(-1) =(y-4)/(2)=(z+2)/(1), (x-1)/(1)=(y+7)/(3)=(z+2)/(2) is

sin^(2)""(pi)/(18)+sin^(2)""(2pi)/(18)+sin^(2)""(4pi)/(18)+sin^(2)""(8pi)/(18)+sin^(2)""(7pi)/(18)+sin^(2)""(5pi)/(18)=

cot[Sin^(-1)sqrt(13/17)]-sin[Tan^(-1)""2/3]=

An equilateral triangle is constructed between two parallel line sqrt3x+y-6=0 and sqrt3x+y+9=0 with base on and vertex on the other. Then the area of triangle is

The most general value of theta satisfies both the equations tan theta = -1 and cos theta = (1)/(sqrt(2)) is

The value of Sin^(-1)(sin10) is

How many terms of the A.P. -6, -11/2, -5,… are needed to give the sum -25?

In triangle ABC, triangle A^(1)B^(1)C^(1) are such that B=B^(1),A+A^(1)=180^(0) then b b^(1)+c c^(1)=

Differentiate from first principles: 2. (x-1)^(2)

Find the cartesian equation of the curve whose parametric equations are : x=4"cos"theta, y=4"sin"theta

If 1/2sin^(-1)[(3sin2theta)/(5+4cos2theta)]=tan^(-1)x, then x =

Of 12 different books a shelf will hold five. how manydifferent arrangements may be made on the shelf?

If 1^(@)=0.01745 radians. Then the approximate value of tan46^(@) is

Convert the products into sum or difference. 2 sin 48^(@) cos 12 ^(@)

Express (1)/(1-cos theta+2i sin theta) in the form of a+ib.

For some constants a and b, find the derivative of (ax^(2)+b)^(2)

The principal solution of sintheta=sqrt((1+sqrt(2))/(2sqrt(2))) is

Find the new coordinates of point (3,-4) if the origin is shifted to (1,2) by a translation.

construct truthtable for(p vv q)vv(r ^^ ~q)

Differentiate the following functions: 14. (i) (2x-3)^(2) (ii) (2x -3)^(100)

Let A={1,2,3,4}. Examine whether the statements given below are true or false. (i) exists x in A" such that "x+3=8. (ii) AA x in A, x+2 lt7. (iii) exists z harr A" such that "x+1lt3. (iv) AA x in A, x+3 ge5.

Which of the following sets are finite or infinite {1, 2, 3, . . .99, 100}

Find the modulus and the arguments of the following complex numbers : sin 120^(@)-i cos120^(@)