14949 + Interview Questions in Maths in Class 11 Page 71 InterviewSolution

3501.	Assertion (A) : tan (alpha - beta) + tan (beta - lambda) + tan (lambda - alpha) = tan (alpha - beta) tan (beta - lambda) tan (lambda - alpha) Reason (R ) : InDelta ABC sum tan A = pi tan A
Answer» A is TRUE R is TURE and R is corect 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 :B

Discussion

3502.	Consider the equation -2sqrt(3)pisinx=\|x+pi\|+\|x-2pi\| then the true statements among the following are
Answer» The EQUATION has no REAL root. The equation has exactly four DISTINCT real roots All the roots of the equation are irrational All the roots of the equation lie between `-pi` and `2pi` Answer :B

Discussion

3503.	A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of (i) exactly 3 girls (ii) atleast 3 girls? (iii) atmost 3 girls?
Answer» ANSWER :(i) 504, (II) 588, (III) 1632

Discussion

3504.	Use the formula Lim_(xto 0) (a^(x)-1)/x = log_(e)a " to find " Lim_(xto0) (2^(x)-1)/((1+x)^(1//2)-1)
Answer» ANSWER :` 2 log_(E) 2 `

Discussion

3505.	If x + y = (2pi)/(3) and cos x + cos y = (sqrt(3))/(2)l find x and y.
Answer» ANSWER :`y = (PI)/(2) - 2N pi`

Discussion

3506.	Derive the expression for the co-ordinates of a point that divides the line joining the points A ( x_1,y_1 ,z_1)and B ( x_2,y_2,z_2) internally in the ratio m : n and hence find the co-ordinates of A (1,2,3) and B ( 5,6,7,)
Answer» ANSWER :`(3,4,5)`

Discussion

3507.	If f= {(1, 2), (2, -3), (3, -1)} then find: (i) 2f, (ii) 2+f, (iii) f^(2), (iv) sqrt(f)
Answer» ANSWER :(i) [(1,4),(2,-6),(3,-2)}, (ii) {(1,4),(2,-1),(3,1)}, (III) {(1,4),(2,9),(3,1)},(iv) `{(1,sqrt(2))}`

Discussion

3508.	For any triangle ABC, prove that : acosA+bcosB+c cosC=2asinBsinC
Answer» ANSWER :`2A SINB SINC (because K sinA=a)`

Discussion

3509.	Assertion (A): Let vec(a) = a_(1) vec(i) + a_(2) vec(j) + a_(3) vec(k). Then identity \|vec(a) xx vec(i)\|^(2) + \|vec(a) xx vec(j)\|^(2) + \|vec(a) xx vec(k)\|^(2) =2\|vec(a)\|^(2) holds for vec(a). Reason (R ): vec(a) xx vec(i) = a_(3) vec(j)- a_(2) vec(k), vec(a) xx vec(j) = a_(1) vec(k) - a_(3) vec(i), vec(a) xx vec(k)= a_(2) vec(i)- a_(1) vec(j) Which of the following is correct ?
Answer» Both (A) and (R ) are TRUE and (R ) is the CORRECT EXPLANATION of (A) Both (A) and (R ) are true and (R ) is not the correct explanation of (A) (A) is true, (R ) is FALSE (A) is false, (R ) is true Answer :A

Discussion

3510.	A non-zero function f(x) is symmetrical about the line y=x then the value of lambda (constant) such that f^(2)(x)=(f^(-1)(x))^(2)- lambda x f(x) f^(-1)(x)+3x^(2)f(x) AA x in R^(+) is
Answer» 1 2 3 4 Answer :C

Discussion

3511.	If repetation is allowed then n objects can be arranged in r places is n.r.
Answer» ANSWER :FALSE STATEMENT

Discussion

3512.	If the zx-plane divides the line segmentjoining(1, -1, 5) and (2, 3, 4) in the ratio p:1, then p+1=
Answer» `(1)/(3)` `1:3` `(3)/(4)` `(4)/(3)` ANSWER :d

Discussion

3513.	A(-9, 0) and B(-1, 0) are two points. If P(x, y) is a point such that 3PB = PA, then the locus of P is
Answer» `X^(2)-y^(2)=9` `x^(2)-y^(2)+9=0` `x^(2)+y^(2)=9` `x^(2)+y^(2)=3` ANSWER :3

Discussion

3514.	Two persons are selected from a group of 10 (5 boys and 5 girls) is succession. Find the probability that both are the boys.when(i)The first person selected is replaced(ii)Not replaced
Answer»

Discussion

3515.	Write themultiplicative inverse of (4-3i) ?
Answer» ANSWER :`4/25 + i3/25`

Discussion

3516.	Find Lt_(x to -oo)(5x^3 + 4)/(sqrt(2x^4 + 1))
Answer» ANSWER :`-OO`

Discussion

3517.	If 10^(n) + 3.4^(n) + x is divisible by 9 for alln in N, then least positive value of 'x' is
Answer» 1 5 14 23 Answer :B

Discussion

3518.	Find the middle terms in the expansions of (3 - x^3/6)^7
Answer» ANSWER :`105/8` `x^9,.35/48 x^12`

Discussion

3519.	Find the value of k, so that the equation 2x^(2)+kx-5=0 and x^(2)-4x+4=0 may have one root common.
Answer» ANSWER :`k=3 or (-27)/(4)`

Discussion

3520.	If (x)=(1)/(x^(2)-17x+66) then find the points of discontinuity of f(2)/(x-2)
Answer» ANSWER :` X = 2, (7)/(3) , (24)/(11)`

Discussion

3521.	Two dice are thrown together. What is the probability that sum of the numbers on the two faces is neither divisible by 3 not by 4 ?
Answer» ANSWER :`(4)/(9)`

Discussion

3522.	A straight pole A subtends a right angle at a point B of another pole at a distance of 30 metres from A, the top of A being 60^(@) above the horizontal line joining the point B to the pole A. The length of the pole A is , in metres.
Answer» `20sqrt3` `40sqrt3` `60sqrt3` `40/sqrt3` ANSWER :B

Discussion

3523.	If absbara = 3,absbarb =2 and theta " is angle between " bara and barb , " then what is the value of " abs(bara+barb)^(2)+abs(bara-barb)^(2)?
Answer» ANSWER :26

Discussion

3524.	Solve sin theta + sin 5 theta = sin 3 theta , 0 lt theta lt pi.
Answer» ANSWER :`(PI)/(6),(pi)/(3),(2pi)/(3),(5PI)/(6)`

Discussion

3525.	2(cos^(2) 73^(0) +cos^(2)47^(0)) - cos 154^(0) =
Answer» 1 2 3 0 Answer :B

Discussion

3526.	Find the value oftan 480^(@)
Answer» ANSWER :`-SQRT(3)`

Discussion

3527.	Let us consider the situation when the axes are inclined at an angle omega . If the coordinates of a point P are (x_1,y_1),thenPN = x_1, PM =y_1where PM is parallel to the y-axis and PN is parallel to the Xaxis. The straight line through P that makes an angle thetawith the x-axisis RQ = y-y_1, PQ = x - x_1 " From " DeltaPQR, we have (PQ)/(sin(omega-theta))=(sqrtQR)/(sin theta) or y-y_1 = (sin theta)/(sin(omega-theta))(x-x_1) writen in the form of y-y_1=m(x-x_1) " where " m=(sin theta)/(sin(omega-theta))Therefore, if the slope of the line is m, then the angle of inclination of the line with the x-axis is given by an tan theta=((m sin omega)/(1+m cos omega)) The axes being inclined at an angle of 60^(@), the angle between the twostraight line y=2x+5 and 2y+x+7=0
Answer» `90^(@)` `TAN^(-1)(5//3)` `tan^(-1)(sqrt3//2)` `tan^(-1)(5//sqrt3)` ANSWER :D

Discussion

3528.	Let us consider the situation when the axes are inclined at an angle omega . If the coordinates of a point P are (x_1,y_1),thenPN = x_1, PM =y_1where PM is parallel to the y-axis and PN is parallel to the Xaxis. The straight line through P that makes an angle thetawith the x-axisis RQ = y-y_1, PQ = x - x_1 " From " DeltaPQR, we have (PQ)/(sin(omega-theta))=(sqrtQR)/(sin theta) or y-y_1 = (sin theta)/(sin(omega-theta))(x-x_1) writen in the form of y-y_1=m(x-x_1) " where " m=(sin theta)/(sin(omega-theta))Therefore, if the slope of the line is m, then the angle of inclination of the line with the x-axis is given by an tan theta=((m sin omega)/(1+m cos omega)) The axes being inclined at an angle of 30^(@), the equation of the straight line which makes an angle of 60^(@) with the positive directon of the x-axis and x-intercept 2 is
Answer» `y-sqrt3x=0` `sqrt3y=x` `y+sqrtx=2sqrt3` `y+2x=0` ANSWER :C

Discussion

3529.	Let us consider the situation when the axes are inclined at an angle omega . If the coordinates of a point P are (x_1,y_1),thenPN = x_1, PM =y_1where PM is parallel to the y-axis and PN is parallel to the Xaxis. The straight line through P that makes an angle thetawith the x-axisis RQ = y-y_1, PQ = x - x_1 " From " DeltaPQR, we have (PQ)/(sin(omega theta))=(sqrtQR)/(sin theta) or y-y_1 = (sin theta)/(sin(omega-theta))(x-x_1) writen in the form of y-y_1=m(x-x_1) " where " m=(sin theta)/(sin(omega-theta))Therefore, if the slope of the line is m, then the angle of inclination of the line with the x-axis is given by an tan theta=((m sin omega)/(1+m cos omega)) The axes being inclined at an angle of 60^(@), the inclination of the straight line y=2x+5 with the x-axis is
Answer» `30^(@)` `tan^(-1)(3//2)` `tan^(-1)2` `60^(@)` ANSWER :B

Discussion

3530.	Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.
Answer» Answer :No, A= {1}, B= {{1}, 2}, C= {{1}, 2, 3}

Discussion

3531.	If x ="Sec" theta- "tan" theta, y="cosec" theta+cot theta then xy+1=
Answer» `x-y` `y-x` `x+y` `2x+y` ANSWER :B

Discussion

3532.	cot^(-1)9+cosec^(-1)(sqrt(41))/4=
Answer» `(PI)/4` `(pi)/2` `(pi)/3` `(pi)/6` ANSWER :A

Discussion

3533.	Find the sum to n terms of the series whose nth term is 4n^(3)+6n^(2)+2n
Answer» ANSWER :`N(n+1)^(2)(n+2)`

Discussion

3534.	Two vertices of Delta ABC are A (1,0,0) B (2,0,0). Third vertex C lies on the line (x -1)/(1) = y/2 (z-1)/(2) and the orthocenter of Delta ABC lies on x ^(2) + 2 xy + 2 zx - 3x - 2y -z + K =0 then K equals
Answer» ANSWER :2

Discussion

3535.	Three balls are drawn from a bag contaning 5 red, 4 white and 3 black balls. The number of ways in which this can be done, if atleast 2 are red, is.
Answer» ANSWER :80

Discussion

3536.	Find the derivativeof the function (1 + (1)/(x)) (1 + (2)/( x)) with respect to x .
Answer» ANSWER :`-(3)/(X^(2))-(4)/(x^(3))`

Discussion

3537.	Find the coordinate of the points which trisect the line segment joining the points A(2, 1, -3) and B(5, -8, 3).
Answer» ANSWER :(3, -2, -1) and (4, -5, 1) are POINTS of trisections of `bar(AB)`.

Discussion

3538.	Find which group is more variable:
Answer» SOLUTION :NA

Discussion

3539.	Find which group is more variable:
Answer» SOLUTION :NA

Discussion

3540.	If x^(2)+alpha y^(2)+2betay=a^(2)a represents a pair of perpendicular lines then beta=
Answer» 2a 3a 4a a Answer :D

Discussion

3541.	Solve the following equations tan theta + sec theta = sqrt(3) in [0, 2pi]
Answer» ANSWER :`NPI+(-1)^(N)(PI)/(4)+(pi)/(6)`

Discussion

3542.	Which of the following is the empty set ?
Answer» `{x :x` is a REAL number and `x ^(2)-1=0}` `{x:x` is a real number and `x ^(2) +1=0}` `{x:x` is a real number and `x ^(2) -9=0}` `{x:x` is a real number and `x ^(2) =x+2}` ANSWER :B

Discussion

3543.	If the three points with positionvectors(1, a, b), (a,2,b) and (a,b,3) are collinear in space, thenthe value of a+b is
Answer» 3 4 5 none Answer :B

Discussion

3544.	If f(x)= min (x^(2),x, sgn ( x^(2) +4x + 5) )then the value of f(2)is equal to
Answer» 2 0 1 4 Answer :C

Discussion

3545.	The origin is shifted to (2,3) by the translation of axes. If a point P has changed as (4,-3), find the coordinates of P in the original system.
Answer» ANSWER :(6,0)

Discussion

3546.	Let f_(n)(theta)= tan""(theta)/2(1+sectheta)(1+sec2theta)(1+sec4theta).....(1+sec2^(n) theta) ,then f_(2)(pi/16)+f_(3)((pi)/32)+f_(4)(pi/64)+f_5(pi/128) =
Answer» 0 2 4 8 Answer :C

Discussion

3547.	Find the approximate value of root(3)(63)
Answer» ANSWER :3.9792

Discussion

3548.	The three points A (0,0,0), B (2,-3, 3), C(-2,3,-3) are collinear. Find in what ratio each point divides the segment joining the other two.
Answer» ANSWER :`(AB)/(BC) = (-1)/(2) , (BC)/(CA)= (-2)/(1) (CA)/(AB) = (1)/(1)`

Discussion

3549.	If 4x + i(3x-y) = 3 + i(-6), where x and y are real numbers, then find the values of x and y.
Answer» ANSWER :`X-(3)/(4) and y=(33)/(4)`

Discussion

3550.	If the function f(x) = x^(3)-6x^(2) + ax + b defined on [1,3] satisfies the Rolle's Theorem for C = ( 2 sqrt(3) + 1)/( sqrt(3)) then find the values of a and b.
Answer» a = 11 b` in ` R a = 10 a = 9 Answer :A::B

Discussion

Explore topic-wise InterviewSolutions in .

Assertion (A) : tan (alpha - beta) + tan (beta - lambda) + tan (lambda - alpha) = tan (alpha - beta) tan (beta - lambda) tan (lambda - alpha) Reason (R ) : InDelta ABC sum tan A = pi tan A

Consider the equation -2sqrt(3)pisinx=|x+pi|+|x-2pi| then the true statements among the following are

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of (i) exactly 3 girls (ii) atleast 3 girls? (iii) atmost 3 girls?

Use the formula Lim_(xto 0) (a^(x)-1)/x = log_(e)a " to find " Lim_(xto0) (2^(x)-1)/((1+x)^(1//2)-1)

If x + y = (2pi)/(3) and cos x + cos y = (sqrt(3))/(2)l find x and y.

Derive the expression for the co-ordinates of a point that divides the line joining the points A ( x_1,y_1 ,z_1)and B ( x_2,y_2,z_2) internally in the ratio m : n and hence find the co-ordinates of A (1,2,3) and B ( 5,6,7,)

If f= {(1, 2), (2, -3), (3, -1)} then find: (i) 2f, (ii) 2+f, (iii) f^(2), (iv) sqrt(f)

For any triangle ABC, prove that : acosA+bcosB+c cosC=2asinBsinC

A non-zero function f(x) is symmetrical about the line y=x then the value of lambda (constant) such that f^(2)(x)=(f^(-1)(x))^(2)- lambda x f(x) f^(-1)(x)+3x^(2)f(x) AA x in R^(+) is

If repetation is allowed then n objects can be arranged in r places is n.r.

If the zx-plane divides the line segmentjoining(1, -1, 5) and (2, 3, 4) in the ratio p:1, then p+1=

A(-9, 0) and B(-1, 0) are two points. If P(x, y) is a point such that 3PB = PA, then the locus of P is

Two persons are selected from a group of 10 (5 boys and 5 girls) is succession. Find the probability that both are the boys.when(i)The first person selected is replaced(ii)Not replaced

Write themultiplicative inverse of (4-3i) ?

Find Lt_(x to -oo)(5x^3 + 4)/(sqrt(2x^4 + 1))

If 10^(n) + 3.4^(n) + x is divisible by 9 for alln in N, then least positive value of 'x' is

Find the middle terms in the expansions of (3 - x^3/6)^7

Find the value of k, so that the equation 2x^(2)+kx-5=0 and x^(2)-4x+4=0 may have one root common.

If (x)=(1)/(x^(2)-17x+66) then find the points of discontinuity of f(2)/(x-2)

Two dice are thrown together. What is the probability that sum of the numbers on the two faces is neither divisible by 3 not by 4 ?

A straight pole A subtends a right angle at a point B of another pole at a distance of 30 metres from A, the top of A being 60^(@) above the horizontal line joining the point B to the pole A. The length of the pole A is , in metres.

If absbara = 3,absbarb =2 and theta " is angle between " bara and barb , " then what is the value of " abs(bara+barb)^(2)+abs(bara-barb)^(2)?

Solve sin theta + sin 5 theta = sin 3 theta , 0 lt theta lt pi.

2(cos^(2) 73^(0) +cos^(2)47^(0)) - cos 154^(0) =

Find the value oftan 480^(@)

Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

If x ="Sec" theta- "tan" theta, y="cosec" theta+cot theta then xy+1=

cot^(-1)9+cosec^(-1)(sqrt(41))/4=

Find the sum to n terms of the series whose nth term is 4n^(3)+6n^(2)+2n

Two vertices of Delta ABC are A (1,0,0) B (2,0,0). Third vertex C lies on the line (x -1)/(1) = y/2 (z-1)/(2) and the orthocenter of Delta ABC lies on x ^(2) + 2 xy + 2 zx - 3x - 2y -z + K =0 then K equals

Three balls are drawn from a bag contaning 5 red, 4 white and 3 black balls. The number of ways in which this can be done, if atleast 2 are red, is.

Find the derivativeof the function (1 + (1)/(x)) (1 + (2)/( x)) with respect to x .

Find the coordinate of the points which trisect the line segment joining the points A(2, 1, -3) and B(5, -8, 3).

Find which group is more variable:

Find which group is more variable:

If x^(2)+alpha y^(2)+2betay=a^(2)a represents a pair of perpendicular lines then beta=

Solve the following equations tan theta + sec theta = sqrt(3) in [0, 2pi]

Which of the following is the empty set ?

If the three points with positionvectors(1, a, b), (a,2,b) and (a,b,3) are collinear in space, thenthe value of a+b is

If f(x)= min (x^(2),x, sgn ( x^(2) +4x + 5) )then the value of f(2)is equal to

The origin is shifted to (2,3) by the translation of axes. If a point P has changed as (4,-3), find the coordinates of P in the original system.

Let f_(n)(theta)= tan""(theta)/2(1+sectheta)(1+sec2theta)(1+sec4theta).....(1+sec2^(n) theta) ,then f_(2)(pi/16)+f_(3)((pi)/32)+f_(4)(pi/64)+f_5(pi/128) =

Find the approximate value of root(3)(63)

The three points A (0,0,0), B (2,-3, 3), C(-2,3,-3) are collinear. Find in what ratio each point divides the segment joining the other two.

If 4x + i(3x-y) = 3 + i(-6), where x and y are real numbers, then find the values of x and y.

If the function f(x) = x^(3)-6x^(2) + ax + b defined on [1,3] satisfies the Rolle's Theorem for C = ( 2 sqrt(3) + 1)/( sqrt(3)) then find the values of a and b.