14949 + Interview Questions in Maths in Class 11 Page 151 InterviewSolution

7501.	3x + 2y le 150, x + 4y le 80, x le 15, y ge 0, x ge 0
Answer» Solution :First inequation : ` 3x + 2y LE 150 ` CORRESPONDING equation : ` 3x + 2y = 150 ` This LINE passes through the points A(50, 0)and B((0, 75). AB. At point (0, 0), from the inequation, `0le 150` (True) `:.` The solution of this inequation is that region of XY- plane in which (0, 0) lies. This line passes thrugh the point C(80, 0) and D(0, 20). Join CD. At point (0, 0), from the inequation, `0 le 10(True)` `:.` The solution of this inequation is that region of XY-plane divided by line CD in which (0, 0) lies. The solution of ` x ge 0, y ge 0 is in first quadrant. The solution of x`ge` 15 is x = 15 and its left SIDE `:.` The common solution of given inequations is shown by the shaded region.

Discussion

7502.	If n in N, sum_(k=1)^(n)cos^(-1)(x_(k))=npi then the value of sum_(k=1)^(n)sin^(-1)(x_(k))=
Answer» 1)0 2)`(npi)/2` 3)`-(npi)/2` 4)`-N pi ` ANSWER :C

Discussion

7503.	If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0)then show thata, b, c and d are in G.P.
Answer» ANSWER :a,B,C,d are in G.P

Discussion

7504.	A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve x^(2)+y^(2)=4 with x+y=a. The set containing the value of 'a' is
Answer» x+y=a {-3,3} {-4,4} {-5,5} ANSWER :A

Discussion

7505.	Derive Meyer's relation.
Answer» Solution :Consider are mole of an ideal gas enclosed in a cylinder provided with a frictionless piston of area A . P-pressure of gas V- volume of gas T - absolute temperature gas dQ- quantity of heat supplied To keep the volume of the gas constant a small `w_t` is placed over the piston. The pressure and temperature increase to p + dp and T + dt. dQ is used to increase the internal ENERGY du of the gas. But the gas does not do any work [dw= 0] `therefore dQ = dU = 1 xx c_v xx dT`. Now the w, is removed. The piston now moves upwards thus'a dist. DX, the pres. of the enclosed gas equal to atmosphere pressure P. Due to expansion, temperature decreases. Now a quantity of heat dQ’ is supplied till its temperature become `T+DeltaT.` This heat energy is not only used to increase the internal energy dU of the gas but also to do exists work dW in moving the piston upwards. ` therefore dQ^1 =dU + dW` At constant pressure ` dQ^1 = c_p = dT` ` therefore c_p dT = c_v = c_vdT + dW` work done dW = Force x dist. `P xx A xx dx` ` dW = P.dv` [A. dx = dv change in volume] ` therefore c_p dT = c_v dT + Pdv`...(1) The EQN of state of an ideal gas is ` PV = RT` Difference both the sides pdv = Rdt...(2) Subtract (2) in (1) `c_p dT = c_v dT + RdT ,` `c_p = c_v + R ""therefore c_p - c_v + R` This equation is known as Meyer's electron.

Discussion

7506.	Differentiate the following functions w.r.t. x: sin 2x
Answer» ANSWER :`2 COS 2X`

Discussion

7507.	If tan^(-1)(sin^(2)theta-2sintheta+3)+cot^(-1)(5^(sec^(2)beta)+1)=pi/2, then the value of cos^(2)theta-sintheta is
Answer» 0 `-1` `1` `2` ANSWER :C

Discussion

7508.	A coin is tossed twice.What is the probability that atleast one tail occurs?
Answer» ANSWER :`3/4`

Discussion

7509.	Sameer throws , an ordinary die . What is the probability that he throws 5
Answer» ANSWER :`(1)/(6)`

Discussion

7510.	Match the following
Answer» ANSWER :d

Discussion

7511.	Write each of the statement in the form if p, then q: q: There is traffic jam whenever it rains.
Answer» ANSWER :If it RAINS then there is TRAFFIC JAM.

Discussion

7512.	Let y=x^(2/3) + 2x^2.Find the instantaneous rate of change of y with respect to x at x = 1.
Answer» ANSWER :`=(2)/(3) x^((-1)/(3) ) + 4x`

Discussion

7513.	Evaluate the following limits. Lt_(xto1)(x^(2)+2x+3)
Answer» ANSWER :6

Discussion

7514.	Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt((1+x^(2))))/x
Answer» ANSWER :`1/2`

Discussion

7515.	The value of a for which ax^(2)+sin^(-1)(x^(2)-2x+2)+cos^(-1)(x^(2)-2x+2)=0 has a real solution is
Answer» `(PI)/2` `-(pi)/2` `2/(pi)` `-2/(pi)` ANSWER :B

Discussion

7516.	The period of function f(x) = {x} + tan^(2) pi x+ \| sin 3pix\| is
Answer» `(1)/(3)` 1 does not EXIST `(2PI)/(3)` ANSWER :B

Discussion

7517.	If f(x) = sinx, g(x) =2x and h(x)= cos x then show that fog = go(fh).
Answer» ANSWER :`THEREFORE` FOG = GO(FH)

Discussion

7518.	Fill in the blanks of the following If z_(1) and z_(2) are complex numbers such that z_(1)+z_(2) is a real number, then z_(1)=
Answer» ANSWER :`z_(1)=x_(2)`

Discussion

7519.	z_(1) and z_(2) are two complex number such that \|z_(1)\|=\|z_(2)\| and arg (z_(1))+arg(z_(2))=pi, then show that z_(1)=-barz_(2)
Answer» Answer :`:. z_(1)=-barz_(2) "" [ :. barz_(2)=r_(2)(cos theta_(2)- SIN theta_(2))]`

Discussion

7520.	If the greatest and least values of the funciton f(x)=x^(3)-6x^(2)+9x+1 on [0,2] are lambdaandmu then lambda+mu^(6)=
Answer» ANSWER :6

Discussion

7521.	If a:b: c = 7: 8: 9 find cos A : cos B : cos C
Answer» ANSWER :` 14: 11 : 6`

Discussion

7522.	If thefunctionf(x ) = (sin n x)/(sin ((x )/(n ))) n E Z hasperiod pithen showthatn is 2.
Answer» ANSWER :`PI`

Discussion

7523.	Which of the following sentences are statement? Give reason for your answer: Open the door.
Answer» ANSWER :Not a STATEMENT

Discussion

7524.	A(5,3) B (3,-2) are two points . If a point P forms a triangle of area 9 square units with A,B then find the locus of P.
Answer» ANSWER :`(5x-2y-37)(5x-2y-1)=0`

Discussion

7525.	The minimum value of f(x)=2^((log_(8)^(3))cos^(2)x)+3^((log_(8)^(2))sin^(2))xis
Answer» `2^(1-log_(8)SQRT(3))` `2^(log_(8)sqrt(3))` `3^(log_(8)sqrt(2))` `2^(1+log_(8)sqrt(3))` Answer :D

Discussion

7526.	-14 lt (3(x-2))/( 5) le 0
Answer» ANSWER :`(-23,2]`

Discussion

7527.	Consider the sets A = {1,2,3,4} and B = {3,4,5,6} Match the following
Answer» SOLUTION :`A CUP B RARR{1,2,3,,5,6}` `A CAP B rarr {3,4} ` A - B rarr {1,2}` `B -A rarr {5,6}`

Discussion

7528.	A straight line is inclined to the axes of x and y at angles of 60^(@) and 45^(@) respectively. Find the its inclination to the z-axis.
Answer» ANSWER :`60^(@) or 120^(@)`

Discussion

7529.	If tantheta = ntan phithen the maximum value of tan^(2)(theta - phi)is equal to
Answer» `(n+1)^(2)/(4N)` `(n-1)^(2)/(4n)` `(n+1)^(2)/(2N)` `(n-1)^(2)/(2n)` ANSWER :B

Discussion

7530.	A = sum of first 10 natural numbers, B = sum of squares of first 10 natural numbers, C = sum of cubes of first 10 natural numbers, D = sum of first 10 even natural numbers, then increasing order of A,B,C,D
Answer» A, B, C, D A, C, D, B A, B, D, C A, D, B, C Answer :D

Discussion

7531.	For the frequency distribution: Find the standard distribution .
Answer» ANSWER :1.38

Discussion

7532.	If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of cos(90^(@)+theta)
Answer» ANSWER :`-3/5`

Discussion

7533.	In [-1,1], Lagrange's Mean Value theorem is applicable to
Answer» `f(x) = \|x\|` `f(x) = {:{(cotx,"," x cancel(=)0),(0,"," x=0):}` `f(x)= {:{((1)/(x),","x cancel(=)0),(0,"," x =0):}` `f(x) = x^(2)` ANSWER :D

Discussion

7534.	Which of the following sentences are statements? Give reasons for your answer: Mathematics is difficult.
Answer» Answer :This is not a STATEMENT because for some people MATHEMATICS can be EASY and for some others it can be difficult.

Discussion

7535.	Two sides of a rhombus OABC (lying entirely in the first of third quadrant ) of ara equal to2 sq. units are y=x//sqrt3,y=sqrt3x. The the possible coordinates of B is//are(O being the origin)
Answer» `(1+sqrt3,1+sqrt3)` `(-1-sqrt3,-1-sqrt3)` `(3+sqrt3,3+sqrt3)` `(sqrt3-1,sqrt3-1)` ANSWER :A::B

Discussion

7536.	Find the component statements of the following and check whether they are true or not: A square is a quadrilateral and its four sides equal.
Answer» ANSWER :Both SENTENCES are TRUE.

Discussion

7537.	A die is thrown, find the probability of following events : A number less than or equal to one will appear,
Answer» ANSWER :`(1)/(6)`

Discussion

7538.	The point diametrically opposite to the point P(1, 0) on the circle x^(2)+y^(2) + 2x+4y- 3 = 0 is
Answer» (3 ,-4 ) (-3,4) (-3 ,-4 ) (3,4). ANSWER :C

Discussion

7539.	underset(r=1)overset(n)Sigma (underset(m=1)overset(r )Sigma m)=……
Answer» `(N(n+1) (2n+1))/(6)` `(n(n+1)(n+2))/(6)` `(n^(2) (n+1)^(2))/(4)` `(n(n+1)(2n+1))/(12)` Answer :B

Discussion

7540.	(cos h x)/(1-tan h x) + (sin h x)/(1-cot h x) =
Answer» 2 COSEC h x sin h x + cos h x sec h x tan h x Answer :B

Discussion

7541.	Given vec(a) = vec(i) + vec(j)-vec(k), vec(b)= - vec(i) + 2vec(j) + vec(k) and vec(c )= -vec(i) + 2vec(j) -vec(k). A unit vector perpendicular to both vec(a) + vec(b) and vec(b) + vec(c ) is
Answer» `VEC(i)` `vec(J)` `vec(i) + vec(j)` `vec(K)` ANSWER :D

Discussion

7542.	If theta_(1) and theta_2 are two values lying in [0,2pi] for which tan theta = lamda , then tan""(theta_1)/2 tan""(theta_2)/2 is equal to
Answer» 0 `-1` 2 1 Answer :B

Discussion

7543.	Solve the following equations and write general solutions6 tan^(2) theta - 2 cos^(2) theta = cos 2 theta
Answer» ANSWER :`NPI PM (PI)/(6)`

Discussion

7544.	Find the triangle of the greatest area among the right triangles of a given perimeter p.
Answer» <P> ANSWER :`(p^(2))/(2(2+sqrt(2))^(2))`

Discussion

7545.	If the lines 2x-py+1=0, 3x-qy+1=0 and 4x-ry+1=0 are concurrent show that p,q,r are in A.P.
Answer» ANSWER :AP

Discussion

7546.	If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is ____ .
Answer» `2SQRT3` `3sqrt2` `SQRT2` `SQRT3` ANSWER :A

Discussion

7547.	For each given angle, find a coterminal angle with measure of theta" such that "0^(@) le theta lt 360^(@) (i) 395^(@)(ii) 525^(@) (iii) 1150^(@) (iv) -270^(@) (v) -450^(@)
Answer» ANSWER :(i) `35^(@)` (II) `165^(@)` (III) `70^(@)` (IV) `360^(@)` (v) `270^(@)`

Discussion

7548.	Express cos40^@ cos80^@ insum form
Answer» SOLUTION :`1/2(cos120^@+cos40^@)`

Discussion

7549.	Find the distance of the line 4x+7y+5=0 from the point (1,2) along the line 2x-y=0.
Answer» ANSWER :`= ( 23 SQRT5)/( 18)` UNIT

Discussion

7550.	Evaluate : (n!)/(n - r!), when (i) n = 6, r = 2 (ii) n = 9, r = 5,
Answer» ANSWER :15120

Discussion

Explore topic-wise InterviewSolutions in .

3x + 2y le 150, x + 4y le 80, x le 15, y ge 0, x ge 0

If n in N, sum_(k=1)^(n)cos^(-1)(x_(k))=npi then the value of sum_(k=1)^(n)sin^(-1)(x_(k))=

If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0)then show thata, b, c and d are in G.P.

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve x^(2)+y^(2)=4 with x+y=a. The set containing the value of 'a' is

Derive Meyer's relation.

Differentiate the following functions w.r.t. x: sin 2x

If tan^(-1)(sin^(2)theta-2sintheta+3)+cot^(-1)(5^(sec^(2)beta)+1)=pi/2, then the value of cos^(2)theta-sintheta is

A coin is tossed twice.What is the probability that atleast one tail occurs?

Sameer throws , an ordinary die . What is the probability that he throws 5

Match the following

Write each of the statement in the form if p, then q: q: There is traffic jam whenever it rains.

Let y=x^(2/3) + 2x^2.Find the instantaneous rate of change of y with respect to x at x = 1.

Evaluate the following limits. Lt_(xto1)(x^(2)+2x+3)

Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt((1+x^(2))))/x

The value of a for which ax^(2)+sin^(-1)(x^(2)-2x+2)+cos^(-1)(x^(2)-2x+2)=0 has a real solution is

The period of function f(x) = {x} + tan^(2) pi x+ | sin 3pix| is

If f(x) = sinx, g(x) =2x and h(x)= cos x then show that fog = go(fh).

Fill in the blanks of the following If z_(1) and z_(2) are complex numbers such that z_(1)+z_(2) is a real number, then z_(1)=

z_(1) and z_(2) are two complex number such that |z_(1)|=|z_(2)| and arg (z_(1))+arg(z_(2))=pi, then show that z_(1)=-barz_(2)

If the greatest and least values of the funciton f(x)=x^(3)-6x^(2)+9x+1 on [0,2] are lambdaandmu then lambda+mu^(6)=

If a:b: c = 7: 8: 9 find cos A : cos B : cos C

If thefunctionf(x ) = (sin n x)/(sin ((x )/(n ))) n E Z hasperiod pithen showthatn is 2.

Which of the following sentences are statement? Give reason for your answer: Open the door.

A(5,3) B (3,-2) are two points . If a point P forms a triangle of area 9 square units with A,B then find the locus of P.

The minimum value of f(x)=2^((log_(8)^(3))cos^(2)x)+3^((log_(8)^(2))sin^(2))xis

-14 lt (3(x-2))/( 5) le 0

Consider the sets A = {1,2,3,4} and B = {3,4,5,6} Match the following

A straight line is inclined to the axes of x and y at angles of 60^(@) and 45^(@) respectively. Find the its inclination to the z-axis.

If tantheta = ntan phithen the maximum value of tan^(2)(theta - phi)is equal to

A = sum of first 10 natural numbers, B = sum of squares of first 10 natural numbers, C = sum of cubes of first 10 natural numbers, D = sum of first 10 even natural numbers, then increasing order of A,B,C,D

For the frequency distribution: Find the standard distribution .

If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of cos(90^(@)+theta)

In [-1,1], Lagrange's Mean Value theorem is applicable to

Which of the following sentences are statements? Give reasons for your answer: Mathematics is difficult.

Two sides of a rhombus OABC (lying entirely in the first of third quadrant ) of ara equal to2 sq. units are y=x//sqrt3,y=sqrt3x. The the possible coordinates of B is//are(O being the origin)

Find the component statements of the following and check whether they are true or not: A square is a quadrilateral and its four sides equal.

A die is thrown, find the probability of following events : A number less than or equal to one will appear,

The point diametrically opposite to the point P(1, 0) on the circle x^(2)+y^(2) + 2x+4y- 3 = 0 is

underset(r=1)overset(n)Sigma (underset(m=1)overset(r )Sigma m)=……

(cos h x)/(1-tan h x) + (sin h x)/(1-cot h x) =

Given vec(a) = vec(i) + vec(j)-vec(k), vec(b)= - vec(i) + 2vec(j) + vec(k) and vec(c )= -vec(i) + 2vec(j) -vec(k). A unit vector perpendicular to both vec(a) + vec(b) and vec(b) + vec(c ) is

If theta_(1) and theta_2 are two values lying in [0,2pi] for which tan theta = lamda , then tan""(theta_1)/2 tan""(theta_2)/2 is equal to

Solve the following equations and write general solutions6 tan^(2) theta - 2 cos^(2) theta = cos 2 theta

Find the triangle of the greatest area among the right triangles of a given perimeter p.

If the lines 2x-py+1=0, 3x-qy+1=0 and 4x-ry+1=0 are concurrent show that p,q,r are in A.P.

If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is ____ .

For each given angle, find a coterminal angle with measure of theta" such that "0^(@) le theta lt 360^(@) (i) 395^(@)(ii) 525^(@) (iii) 1150^(@) (iv) -270^(@) (v) -450^(@)

Express cos40^@ cos80^@ insum form

Find the distance of the line 4x+7y+5=0 from the point (1,2) along the line 2x-y=0.

Evaluate : (n!)/(n - r!), when (i) n = 6, r = 2 (ii) n = 9, r = 5,