14949 + Interview Questions in Maths in Class 11 Page 161 InterviewSolution

8001.	Find the values of theta lying between 0^(@) and 360^(@) when sin theta=sin 21^(@)
Answer» ANSWER :`21^(@),159^(@)`

Discussion

8002.	cos x =- 1/2, x lies in third quadrant.
Answer» Answer :`sin X = - (sqrt3)/(2), cosec x =- (2)/( sqrt3), sec x =-2 , TAN x = sqrt3 ,cot x = (1)/(sqrt3)`

Discussion

8003.	If the equation x^(3)+ax^(2)y+bxy^(2)+y^(3)=0represents three lines two of which are perpendicular then equation of third line is
Answer» `y=ax` `y=bx` `y=X` `y= -x` ANSWER :C

Discussion

8004.	f(x)= 2x^(n) + a. If f(2)= 26 and f(4)= 138 then the value of f(3) is……..
Answer» 56 82 64 122 Answer :C

Discussion

8005.	InDelta ABC, a( b cos C - c cos B) =
Answer» ` B-C` ` b+c` ` b^(2) -c^(2) ` `b^(2)+c^(2)` ANSWER :C

Discussion

8006.	If the line (2+k)x-(2-k)y+(4k+14)=0 passes through the point (-1, 21), find k.
Answer» ANSWER : `k=5/(4)`

Discussion

8007.	The value of cos[cos^(-1)((-1)/7)+sin^(-1)((-1)/7)] isequal to
Answer» `(-1)/3` `0` `1/3` `4/9` ANSWER :B

Discussion

8008.	Write the first five terms of each of the sequenceswhose n^(th)terms are: a_n (n+2)
Answer» ANSWER :3,8,15,24,35

Discussion

8009.	(1+sintheta-costheta)/(1+sintheta+costheta)=
Answer» `"TAN"theta/2` `-"tan"theta/2` `"COT"theta/2` `-"cot"theta/2` ANSWER :C

Discussion

8010.	Standard deviations for first 10 natural numbers is
Answer» 5.5 3.87 2.97 2.87 Answer :D

Discussion

8011.	Translate the following statements into symbolic form: 2,3 and 6 are factors of 12.
Answer» ANSWER :`:.p^^q^^r:2,3` and 6 are FACTORS of 12.

Discussion

8012.	(d)/(dx)sqrt(x^(2)-2x+1)=………
Answer» 0 1 -1 Does not exists Answer :C

Discussion

8013.	The plane which passes through the point (-1, 0, -6) and perpendicular to the line whose d.r.s are (6, 20, -1) also passes through the point
Answer» `(1,1, - 26)` `(0,0,0)` `(2,1,-32)` `(1,1,1)` ANSWER :B

Discussion

8014.	A water tank has the shape of an inverted right circular cone with its axis vertical and vertext lowermost. Its semi-vertical angle is tan^(-1)(0.5). Water is poured into it at a constant rate of 5 cubic metre per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4m.
Answer» ANSWER :`(35)/(88)m//h`

Discussion

8015.	If f(x)=(x)/(sinx)andg(x)=(x)/(tanx), where 0ltxle1 , then in this interval
Answer» both f(x) and G(x) are increasing functions both f(x) and g(x) are decreasing functions f(x) is an increasing function g(x) is an increasing funtion Answer :C

Discussion

8016.	If p - q is small compared to either p or q, then show that sqrt(p/q)=((n+1)p+(n-1)q)/((n-1)p+(n+1)q) Hence find sqrt(15/16).
Answer» ANSWER :0.9916

Discussion

8017.	Prove that the product of any 'k' consecutive integers is divisible by k !.
Answer» ANSWER :`= ""^(n+K)C_(k).k !`.

Discussion

8018.	Evaluate the following limits in lim_(xrarr4)(4x+3)/(x-2)
Answer» ANSWER :`(19)/(2)`

Discussion

8019.	sec h^(-1) (cos theta) =
Answer» `log\|tan((PI)/(6) + (theta)/(2))\|` `log\|tan((pi)/(3) + (theta)/(2))\|` `log\|tan((pi)/(4) + (theta)/(2))\|` `log\|tan ((pi)/(4) - (theta)/(2))\|` ANSWER :C

Discussion

8020.	Find the mean deviation about median for the following data :
Answer» ANSWER :7.35

Discussion

8021.	Find the mean deviation about median for the following data :
Answer» ANSWER :10.34

Discussion

8022.	Number of solution (s) of the equation sinx=[x] {where [.] denotes greatest integer function is
Answer» 1 2 0 infinite Answer :B

Discussion

8023.	If arg(z-1)=arg(z+3i), then find x-1,y,where z=x+iy
Answer» ANSWER :`1:3`

Discussion

8024.	A bag contains 4 red , 6 white and 5 black balls 2 ballsare drawn at random . Findthe probability of getting one red and one white ball .
Answer» ANSWER :`(8)/(35)`

Discussion

8025.	Find the distance between the parallel lines 3x-4y+7=0 and 3x - 4y + 5=0.
Answer» ANSWER :`(2)/(5)`

Discussion

8026.	The roots of the quadratic equation x^(2)+px+8=0 are alphaand beta. Obtain the values of p, if (i) alpha=beta^(2) (ii) alpha-beta=2.
Answer» ANSWER :(i) `p=-6` (II) `p=pm6`.

Discussion

8027.	Which of the following funcitons is not injective ?
Answer» `F(x)=\|x+1\|, x in [-1, 0]` `f(x)= x+1//x , x in (0, OO)` `f(x)=x^(2)+4x-5` `f(x)=e^(-x), x in [0, oo)` ANSWER :B::C

Discussion

8028.	If theta_(1), theta_(2) are solutions of the equation a cos 2theta + bsin 2theta = c, tan theta_(1) != tan theta_(2) and a+c != 0, then find the values of (i) tan theta_(1) + tan theta_(2) (ii) tan theta_(1).tan theta_(2).
Answer» ANSWER :(i) `(2B)/(a+c)`(II) `(c-a)/(c+a)` (III) `b//a`

Discussion

8029.	The owner of a milk store finds that, he can sell 980 litres of milk each week at ₹14/litres and 1220 litres of milk each week at ₹16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sells weekly at ₹17/litres?
Answer» ANSWER :`1340` LITRES.

Discussion

8030.	Let f: R rarr R be a function defined by f(x)=(x^(2)+2x+5)/(x^(2)+x+1) is
Answer» one-one and into one-one and onto many-one and onto many-one and into Answer :D

Discussion

8031.	Iff : R to Rdefined byf(x) = {{:((1+ 3x^(2) - cos 2x)/(x^(2)) , " for " x ne 0),(k , " for " x = 0 ):}
Answer» 5 1 6 0 Answer :A

Discussion

8032.	A plane pases through (1,-2,1) and is perpendicular to two pianes 2x - 2y + z = 0 and x-y + 2z =4. The distance of the plane from the point (1,2,2) is d then (d)/(sqrt2)=
Answer» ANSWER :2

Discussion

8033.	Solve the equation for0 le x le 2pi. 2 + 7 tan ^(2) theta = 3.25 sec ^(2) theta
Answer» ANSWER :`(PI)/(6)`

Discussion

8034.	If (baraxxbarb)xx(barcxxbard)=lamdabarc+μbard then lamda,mu=
Answer» `[barabarbbard],-[BARABARBBARC]` `[barabarbbarc],[barbbarcbard]` `[barabarbbarc],1` 1,0 Answer :A

Discussion

8035.	A vector bar(a) has components 2p and 1 w.r.t a rectangular cartesian system. It is rotated through a certain angle about the origin in the counter clockwise direction. With respect to the new system, if bar(a) has components p +1, 1 then p =
Answer» `(1, (-1)/3)` `(1, 1/3)` `(-1, 1/3)` `(-1, (-1)/3)` ANSWER :A

Discussion

8036.	Determine the conjugate and the reciprocal of each complex number given below: i^(3)
Answer» ANSWER :i,i

Discussion

8037.	Conisider the function f(x) =x cosx-sinx . Then identify the statement which is correct.
Answer» f is NEITHER odd nor even f is MONOTONIC decreasing at x=0 f has a MAXIMA at `x=pi` f has a minima at `x=-pi` Answer :B

Discussion

8038.	The perpendicular distance of point P(x,y,z) from XY plane is (x+y).
Answer» ANSWER :FALSE STATEMENT

Discussion

8039.	If tan(pi cos theta) = cot(pi sin theta) then value of cos(theta - pi/4) among the following is:
Answer» `1/(2sqrt(2))` `1/sqrt(2)` `1/2` `1/4` ANSWER :A

Discussion

8040.	If (1+x^(2))^(2)(1+x)^(n) =a_(0) + a_(1)x + a_(2)x^(2) + …+ x^(n+4) and if a_(0), a_(1), a_(2) are in A.P., then n is:
Answer» 1 5 2 4 Answer :C

Discussion

8041.	If 4 cos 36^(@) + cot(7(1^(@))/(2)) = sqrt(n_(1)) + sqrt(n_(2)) + sqrt(n_(3)) + sqrt(n_(4)) + sqrt(n_(5)) + sqrt(n_(6)) then the product of the digits in sum_(i = 1)^(6) n_(i)^(2) =
Answer» ANSWER :9

Discussion

8042.	The sum of the first fifteen terms of an arithmetical progression is 105 and the sum of the next fifteen terms is 780. Find the first three terms of the arithmetical progression,.
Answer» ANSWER :`-14,-11,-8`

Discussion

8043.	From the data given below state which group is more variable, A or B?
Answer» ANSWER :B

Discussion

8044.	Let f(theta)=(1)/(1+(cottheta)^(x))andS=sum_(theta=1^(o))^(89^(@))f(theta). Then the value of sqrt(2S-8) =
Answer» 8 9 10 12 Answer :B

Discussion

8045.	If f(x) = ax^2+bx+12, f'(2) = 11 and f'(4)=15then possible value of a and b are ............ .
Answer» ANSWER :`a =1 and B = 7`

Discussion

8046.	A tower 51m height has a mark at height of 25m from the ground. At what distance the two parts substend equal angle to an eye at the height of 5m from the ground
Answer» `20M` `30M` `15M` `160M` ANSWER :D

Discussion

8047.	Which of the following sentences are statement? Give reason for your answer: 6 has three prime factors.
Answer» ANSWER :It is a STATEMENT.

Discussion

8048.	Alltrigonometrical functionare
Answer» NONPERIODIC neednot beperiodfunction EVENFUNCTION oddfunction ANSWER :2

Discussion

8049.	Lim_(x to pi/2) (1+cos 2x)/(pi-2x)^(2)
Answer» ANSWER :`1/2`

Discussion

8050.	A sample space 5 consists 1 to 30 positive integers. Event A Ai shows the elementary divisible by i. Write the elements of the events A_(2),A_(3),A_(4),A_(5). Veify the truthless of following statements. (1)A_(2) and A_(3) are mutually exclusive events. (2) A_(4) is a subset of A_(2). (3) A_(3),A_(4) and A_(5) are not mutually exclusive.
Answer» Answer :`A_(2) = {2, 4, 6, ........, 30}` `A_(3)={3,6,9,......,30}` `A_(4)={4,8,12,......28}` `A_(5)={5,10,15,......30}` False(2) TRUE (3)False

Discussion

Explore topic-wise InterviewSolutions in .

Find the values of theta lying between 0^(@) and 360^(@) when sin theta=sin 21^(@)

cos x =- 1/2, x lies in third quadrant.

If the equation x^(3)+ax^(2)y+bxy^(2)+y^(3)=0represents three lines two of which are perpendicular then equation of third line is

f(x)= 2x^(n) + a. If f(2)= 26 and f(4)= 138 then the value of f(3) is……..

InDelta ABC, a( b cos C - c cos B) =

If the line (2+k)x-(2-k)y+(4k+14)=0 passes through the point (-1, 21), find k.

The value of cos[cos^(-1)((-1)/7)+sin^(-1)((-1)/7)] isequal to

Write the first five terms of each of the sequenceswhose n^(th)terms are: a_n (n+2)

(1+sintheta-costheta)/(1+sintheta+costheta)=

Standard deviations for first 10 natural numbers is

Translate the following statements into symbolic form: 2,3 and 6 are factors of 12.

(d)/(dx)sqrt(x^(2)-2x+1)=………

The plane which passes through the point (-1, 0, -6) and perpendicular to the line whose d.r.s are (6, 20, -1) also passes through the point

If f(x)=(x)/(sinx)andg(x)=(x)/(tanx), where 0ltxle1 , then in this interval

If p - q is small compared to either p or q, then show that sqrt(p/q)=((n+1)p+(n-1)q)/((n-1)p+(n+1)q) Hence find sqrt(15/16).

Prove that the product of any 'k' consecutive integers is divisible by k !.

Evaluate the following limits in lim_(xrarr4)(4x+3)/(x-2)

sec h^(-1) (cos theta) =

Find the mean deviation about median for the following data :

Find the mean deviation about median for the following data :

Number of solution (s) of the equation sinx=[x] {where [.] denotes greatest integer function is

If arg(z-1)=arg(z+3i), then find x-1,y,where z=x+iy

A bag contains 4 red , 6 white and 5 black balls 2 ballsare drawn at random . Findthe probability of getting one red and one white ball .

Find the distance between the parallel lines 3x-4y+7=0 and 3x - 4y + 5=0.

The roots of the quadratic equation x^(2)+px+8=0 are alphaand beta. Obtain the values of p, if (i) alpha=beta^(2) (ii) alpha-beta=2.

Which of the following funcitons is not injective ?

If theta_(1), theta_(2) are solutions of the equation a cos 2theta + bsin 2theta = c, tan theta_(1) != tan theta_(2) and a+c != 0, then find the values of (i) tan theta_(1) + tan theta_(2) (ii) tan theta_(1).tan theta_(2).

The owner of a milk store finds that, he can sell 980 litres of milk each week at ₹14/litres and 1220 litres of milk each week at ₹16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sells weekly at ₹17/litres?

Let f: R rarr R be a function defined by f(x)=(x^(2)+2x+5)/(x^(2)+x+1) is

Iff : R to Rdefined byf(x) = {{:((1+ 3x^(2) - cos 2x)/(x^(2)) , " for " x ne 0),(k , " for " x = 0 ):}

A plane pases through (1,-2,1) and is perpendicular to two pianes 2x - 2y + z = 0 and x-y + 2z =4. The distance of the plane from the point (1,2,2) is d then (d)/(sqrt2)=

Solve the equation for0 le x le 2pi. 2 + 7 tan ^(2) theta = 3.25 sec ^(2) theta

If (baraxxbarb)xx(barcxxbard)=lamdabarc+μbard then lamda,mu=

A vector bar(a) has components 2p and 1 w.r.t a rectangular cartesian system. It is rotated through a certain angle about the origin in the counter clockwise direction. With respect to the new system, if bar(a) has components p +1, 1 then p =

Determine the conjugate and the reciprocal of each complex number given below: i^(3)

Conisider the function f(x) =x cosx-sinx . Then identify the statement which is correct.

The perpendicular distance of point P(x,y,z) from XY plane is (x+y).

If tan(pi cos theta) = cot(pi sin theta) then value of cos(theta - pi/4) among the following is:

If (1+x^(2))^(2)(1+x)^(n) =a_(0) + a_(1)x + a_(2)x^(2) + …+ x^(n+4) and if a_(0), a_(1), a_(2) are in A.P., then n is:

If 4 cos 36^(@) + cot(7(1^(@))/(2)) = sqrt(n_(1)) + sqrt(n_(2)) + sqrt(n_(3)) + sqrt(n_(4)) + sqrt(n_(5)) + sqrt(n_(6)) then the product of the digits in sum_(i = 1)^(6) n_(i)^(2) =

The sum of the first fifteen terms of an arithmetical progression is 105 and the sum of the next fifteen terms is 780. Find the first three terms of the arithmetical progression,.

From the data given below state which group is more variable, A or B?

Let f(theta)=(1)/(1+(cottheta)^(x))andS=sum_(theta=1^(o))^(89^(@))f(theta). Then the value of sqrt(2S-8) =

If f(x) = ax^2+bx+12, f'(2) = 11 and f'(4)=15then possible value of a and b are ............ .

A tower 51m height has a mark at height of 25m from the ground. At what distance the two parts substend equal angle to an eye at the height of 5m from the ground

Which of the following sentences are statement? Give reason for your answer: 6 has three prime factors.

Alltrigonometrical functionare

Lim_(x to pi/2) (1+cos 2x)/(pi-2x)^(2)