14949 + Interview Questions in Maths in Class 11 Page 295 InterviewSolution

14701.	Let the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2) lie in the plane x+3y-alphaz+beta=0 . Then (alpha,beta)equals
Answer» `(6,-7)` `(-6,7)` `(5,-15)` `(-5,5)` ANSWER :B

Discussion

14702.	sum _(r=1) ^(10) cos ^(3) "" (r pi)/(3) =
Answer» `-1/8` `-7/8` `-9/8` `1/8` ANSWER :C

Discussion

14703.	5y^(2)-9x^(2)=36
Answer» Solution :GIVEN equation is`(y^(2))/((36//5))-(x^(2))/(4)=1.` `thereforea^(2)=(36)/(5),b^(2)=4 and c^(2)=(a^(2)+b^(2))=((36)/(5)+4)=(56)/(5).` Also `, e=( c)/(a)=((sqrt(56))/(sqrt(5))xx(sqrt(5))/(6))=(2sqrt(14))/(6)=(sqrt(14))/(3).`

Discussion

14704.	Find the solution of sin x =- (sqrt3)/(2).
Answer» Answer :`X = n pi + (-1)^(n) (4pi)/(3),` where `n in Z`

Discussion

14705.	Period of sin x sin(120^(@) - x) sin(120^(@) +x) is
Answer» `(PI)/(2)` `(2PI)/(3)` `pi` `(pi)/(2)` Answer :B

Discussion

14706.	AB isvertical pole with B at ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^(@). He movesaway from the pole along the line BC to a point D such that CD =7 m. From D the angle of elevation of the point A is 45^(@) then the hight of the pole is
Answer» ` ( 7sqrt3)/(2) ( SQRT3- 1) ` ` ( 7sqrt3)/(2) ( sqrt3+ 1) ` ` 7sqrt3` ` ( 7sqrt3)/(2) ` ANSWER :B

Discussion

14707.	Differentiate the following w.r.t. x or t or u as the case may be: 2. (x^(100) + 2x^(50) - 3) (7x^(8) + 20x + 5)
Answer» Answer :`(x^(100) + 2X^(50)…3) (56X^(7) + 20) + (7X^(8) + 20x ) (100x^(99) + 100x^(49) )`

Discussion

14708.	sin A + sin B = sqrt(3) ( cos B- cos A )implies sin 3A + sin 3B=
Answer» 0 2 1 -1 Answer :A

Discussion

14709.	By using binomial theorem prove that (i) (2^(3n)-7n-1) is divisible by 49 where n is a positive integer. (ii)(3^(3n)-26n-1) is divisible by 26^(2) Where n is a positive integer. (iii) (6^(n)-5n) when divided by 25 leaves a remainder 1. (iv) (x^(2n)-y^(2n)) is divisible (x-y) , n in N
Answer» SOLUTION :N/a

Discussion

14710.	sec["tan"^(-1)5+"tan"^(-1)1/5-"tan"^(-1)3/4]=
Answer» `3//5` `5//3` `4//5` `SQRT(2)` ANSWER :B

Discussion

14711.	Iflog _((-x^(2) - 6 x)//10)(sin 3 x + sin x) = log_((x^(2) - 6x)//10)(sin 2 x)then x =
Answer» `-(PI)/(3)` `(5 pi)/(3)` `-(5 pi)/(3)` `(pi)/(3)` ANSWER :C

Discussion

14712.	Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . ~q
Answer» ANSWER :I do not LIKE MR. SAXENA.

Discussion

14713.	Find the modeof the followingdata 17, 32,35,33,15,21,41,32,11,18,20,22,11,15,35,23,38,12
Answer» ANSWER :MODE is ILL - DEFINED

Discussion

14714.	Find the derivatives from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1? f(x)=sqrt(1-x^(2))
Answer» Answer : ` = lim_(x to 1^(+)) - sqrt((1 + x)/(1- x) ) = 0 ` From (1) and (2), f' ` (1^(-)) " and " f'(1^(+)) ` are not EQUAL . `therefore f '(x) ` is not DIFFERENTIABLE at x = 1 .

Discussion

14715.	After striking a floor a certain ball rebounds ((4)/(5))^(th) of the height from which it has fallen. Find the total distance that it travels before coming to rest, if it is gently dropped from a height of 120 meters
Answer» ANSWER :1080m.

Discussion

14716.	If A is a non singular square matrix, then the false statement among the following is
Answer» `"ADJ A"=\|A\|A^(-1)` `("Adj A")^(-1)=(A)/(\|A\|)` `"DET "(A^(-1))=("det A")^(-1)` `"Adj A = O if A = I"` ANSWER :D

Discussion

14717.	Assertion (A) : The equation of a circle is x^(2) + y^(2) = 9 on rotation of axes through an angle tan^(-1) 2 then the transformed equation is x^(2) + y^(2) = 9 Reason (R) : On rotation of axes area of the circle does not change. Choose the correct answer.
Answer» Both A and R are TRUE and R is the correct explanation of A BothA and R are trueand R is not the correct explanation of A A is true but R is FALSE A is false BUTIS R is false Answer :B

Discussion

14718.	Find lim_(x rarr 0) f(x),if f(x) =sqrtx,xge0.
Answer» ANSWER :Does not EXIST

Discussion

14719.	Find the product of the following pairs 3a^(2)b,6ab^(3)c^(2)
Answer» ANSWER :`119 X + 102y = 125`

Discussion

14720.	Evaluate: int(sin x)/(1 + cos x) dx.
Answer» ANSWER :`- log \|1 + cos X\| + C`

Discussion

14721.	A vertical pole more than 100 ft high consists of two portions the lower being 1//3 of the whole. If the upper portion subtends an angle tan^(-1)(1/2) at a point distant 40 ft. From the foot of the pole. The hight of the pole is
Answer» 105 120 135 150 Answer :B

Discussion

14722.	A manufacturer has 460 litres of a 9%acid solution. How many litres of a 3% acid solution must be added to it so that the acid content in the resulting mixture be more than 5% but less than 7%?
Answer» Solution :Let x LITRES of a 3% acid solution be added to 460 litres of 9% acid solution. Then, total quantity of mixture`=(460+x)` litres. Total acid content in (460 + x) litres of mixture `={(460xx(9)/(100))+(x xx (3)/(100))}"litres"=((207)/(5)+(3x)/(100))`litres. Now, the acid content in the resulting mixture must be more than 5% and less than 7%. `therefore5%of(460+x)lt((207)/(5)+(3x)/(100))lt7% "of"(460+x)` `rArr(5)/(100)xx(460+x)lt(4140+x)/(100)lt(7)/(100)xx(460+x)` `rArr5(460+x)lt4140+3xlt7(460+x)` `rArr 2300+5xlt4140+3xand 4140+3xlt3220+7x` `rArr 5x=3xlt4140-2300 and 4140+3x lt3220 +7x` `rArr2xlt1840and 920 lt4x` `rArr xlt920and 230ltx` `rArr 230ltxlt920` Hence, the REQUIRED quantity of 3% acid solution to be added must be more than 230 litres and less than 920 litres.

Discussion

14723.	Find the sum of all natural numbers lying between 100 and 1000 , which are multiples of 5.
Answer» ANSWER :98450

Discussion

14724.	Evaluate the following limits : Lim_(x to1/2)((8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1))
Answer» ANSWER :`7/2`

Discussion

14725.	2cos""(5pi)/(24).cos""(pi)/(24) = ……….
Answer» `(SQRT(2)+sqrt(3))/(4)` `(sqrt(3)-sqrt(2))/(2)` `(sqrt(2)+sqrt(3))/(2)` `(sqrt(2)-sqrt(3))/(4)` ANSWER :C

Discussion

14726.	Solve the following: x^(2) + 3=0
Answer» ANSWER :`+- SQRT(3)i`

Discussion

14727.	Find the value of k, if the straight lines y-3kx+4=0 and (2k-1)x-(8k-1)y-6=0 are perpendicular.
Answer» ANSWER :`k=1/6,-1`

Discussion

14728.	Rewrite each of the following statements in the form "p if and only if q"(i) p: if you watch television, then your mind is free and if your mind if free, then you watch television.(ii) q: for you to get an a grade, it is necessary and sufficinet that you do all the homework regularly.(iii) r: if a quardrilateral is equiangular, then it is a rectangular and if a quadrilateral is a rectangle, then it is eqiangular.
Answer» Solution :(i) You WATCH TELEVISION if and only if your mind in free. (ii) You get an A grade if and only if you do all the HOME WORK regularly. (iii) a QUADRILATERAL is equiangular if and only if it is a rectangle.

Discussion

14729.	If (2z_(1))/(3z_(2)) is pure imaginarny then \|(z_(1)-z_(2))/(z_(1)+z_(2))\|=.....
Answer» `(3)/(2)` 1 `(2)/(3)` `(4)/(9)` ANSWER :B

Discussion

14730.	The midpoints of the sides of a trianlge are (3,2, (3)/(2)), (1, (3)/(2) , 3) and (2, (5)/(2) , (5)/(2)) Find its vertices.
Answer» ANSWER :`Z _(1) = 4, z_(2) = 1, z _(3) = 2`

Discussion

14731.	Choose the correctoption for the following lim_(thetararr0)sqrt[(1-cos9theta)/(1-cos16theta)] is :
Answer» `3/4` `9/16` `16/9` `4/3` ANSWER :A

Discussion

14732.	Two coins (a one rupee coin and a two rupee coin) are tossed once. Find a sample space.
Answer» ANSWER :S = {HH. HT, TH, TT}

Discussion

14733.	Evaluate the following limits : Lim_(x to 0) (log(1-x/2))/x
Answer» ANSWER :`-1/2`

Discussion

14734.	Convert the complex number z=(1-i)/(cos pi/3 + I sin pi/3) in the polar form.
Answer» ANSWER :polar FORM is `sqrt(2) (COS (5pi)/12 + I sin (5pi)/12)`

Discussion

14735.	If tan p theta = cot q theta and p ne -q show that the solution are in A.P with common difference (pi)/(p+q)
Answer» ANSWER :`(2PI)/(ppmq)`

Discussion

14736.	If Lt_(xto0)(1-cosxcos2xcos3x.......cosnx)/x^(2) has the value equal to 325 find the value of n.
Answer» ANSWER :12

Discussion

14737.	The value of 'a' so that the volume of parallelopiped formed by bari +abarj +bark, barj +abark, and abari + bark becomes minimum is
Answer» `-3` 3 `1/(SQRT3)` `sqrt3` ANSWER :C

Discussion

14738.	Match the following
Answer» Answer :`(i) RARR (C ), (ii) rarr (a), (III) rarr (b), (iv) rarr (d)`

Discussion

14739.	Match the following
Answer» Answer :`(i) rarr (C ), (II) rarr (B), (III) rarr (a)`

Discussion

14740.	If the sum of n terms of an A . P is 3n^(2)+5n and its m^(th) term is 164 , find the valueofm.
Answer» ANSWER :27

Discussion

14741.	If sin A + cos B = a and sin B + cos A = b, then sin (A + B) is equal to
Answer» `(a^(2)+B^(2))/2` `(a^(2)-b^(2)+2)/2` `(a^(2)+b^(2)-2)/2` `(a^(2)-b^(2)-2)/2` ANSWER :C

Discussion

14742.	Find the 7^(th) term in the expansion of (x+3y)^(8)
Answer» ANSWER :`20412 X^(2)y^(6)`

Discussion

14743.	If x^(m) y^(n)=(x+y)^(m+n) , then dy/dxis equal to
Answer» `y/x` `(x+y)/(XY)` `xy ` `x/y` ANSWER :A

Discussion

14744.	Find the conjugate of ((3-2i)(2+3i))/((1-2i)(2-i))
Answer» ANSWER :`63/25 + 16/25`I

Discussion

14745.	solve x+y=4, y(x^(2)+4)=8
Answer» ANSWER :`TAN^(-1)((1)/(3))`

Discussion

14746.	If \|x - 2\| lt 3 then -1 lt x lt 5.
Answer» ANSWER :TRUE STATEMENT

Discussion

14747.	Image of (2,3) w.r.t (0,0) is
Answer» (0,0) (2,3) (-2,-3) (3,2) ANSWER :C

Discussion

14748.	An experiment consists of recording boy-girl composition of families with 2 childern. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?
Answer» Answer :(i){BB, BG, GB, GG} (ii) {0, 1, 2}

Discussion

14749.	If alpha and beta are different complex numbers with \|beta\|=1, then find \|(beta -alpha)/(1-baralphabeta)\|
Answer» ANSWER :1

Discussion

14750.	A cricket club has 15 members, of whom only 5 can bowl . What is the probability that in a team of 11 members at least 3 bowlers are selected?
Answer» ANSWER :`(12)/(13)`

Discussion

Explore topic-wise InterviewSolutions in .

Let the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2) lie in the plane x+3y-alphaz+beta=0 . Then (alpha,beta)equals

sum _(r=1) ^(10) cos ^(3) "" (r pi)/(3) =

5y^(2)-9x^(2)=36

Find the solution of sin x =- (sqrt3)/(2).

Period of sin x sin(120^(@) - x) sin(120^(@) +x) is

Differentiate the following w.r.t. x or t or u as the case may be: 2. (x^(100) + 2x^(50) - 3) (7x^(8) + 20x + 5)

sin A + sin B = sqrt(3) ( cos B- cos A )implies sin 3A + sin 3B=

By using binomial theorem prove that (i) (2^(3n)-7n-1) is divisible by 49 where n is a positive integer. (ii)(3^(3n)-26n-1) is divisible by 26^(2) Where n is a positive integer. (iii) (6^(n)-5n) when divided by 25 leaves a remainder 1. (iv) (x^(2n)-y^(2n)) is divisible (x-y) , n in N

sec["tan"^(-1)5+"tan"^(-1)1/5-"tan"^(-1)3/4]=

Iflog _((-x^(2) - 6 x)//10)(sin 3 x + sin x) = log_((x^(2) - 6x)//10)(sin 2 x)then x =

Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . ~q

Find the modeof the followingdata 17, 32,35,33,15,21,41,32,11,18,20,22,11,15,35,23,38,12

Find the derivatives from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1? f(x)=sqrt(1-x^(2))

After striking a floor a certain ball rebounds ((4)/(5))^(th) of the height from which it has fallen. Find the total distance that it travels before coming to rest, if it is gently dropped from a height of 120 meters

If A is a non singular square matrix, then the false statement among the following is

Assertion (A) : The equation of a circle is x^(2) + y^(2) = 9 on rotation of axes through an angle tan^(-1) 2 then the transformed equation is x^(2) + y^(2) = 9 Reason (R) : On rotation of axes area of the circle does not change. Choose the correct answer.

Find lim_(x rarr 0) f(x),if f(x) =sqrtx,xge0.

Find the product of the following pairs 3a^(2)b,6ab^(3)c^(2)

Evaluate: int(sin x)/(1 + cos x) dx.

A vertical pole more than 100 ft high consists of two portions the lower being 1//3 of the whole. If the upper portion subtends an angle tan^(-1)(1/2) at a point distant 40 ft. From the foot of the pole. The hight of the pole is

A manufacturer has 460 litres of a 9%acid solution. How many litres of a 3% acid solution must be added to it so that the acid content in the resulting mixture be more than 5% but less than 7%?

Find the sum of all natural numbers lying between 100 and 1000 , which are multiples of 5.

Evaluate the following limits : Lim_(x to1/2)((8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1))

2cos""(5pi)/(24).cos""(pi)/(24) = ……….

Solve the following: x^(2) + 3=0

Find the value of k, if the straight lines y-3kx+4=0 and (2k-1)x-(8k-1)y-6=0 are perpendicular.

If (2z_(1))/(3z_(2)) is pure imaginarny then |(z_(1)-z_(2))/(z_(1)+z_(2))|=.....

The midpoints of the sides of a trianlge are (3,2, (3)/(2)), (1, (3)/(2) , 3) and (2, (5)/(2) , (5)/(2)) Find its vertices.

Choose the correctoption for the following lim_(thetararr0)sqrt[(1-cos9theta)/(1-cos16theta)] is :

Two coins (a one rupee coin and a two rupee coin) are tossed once. Find a sample space.

Evaluate the following limits : Lim_(x to 0) (log(1-x/2))/x

Convert the complex number z=(1-i)/(cos pi/3 + I sin pi/3) in the polar form.

If tan p theta = cot q theta and p ne -q show that the solution are in A.P with common difference (pi)/(p+q)

If Lt_(xto0)(1-cosxcos2xcos3x.......cosnx)/x^(2) has the value equal to 325 find the value of n.

The value of 'a' so that the volume of parallelopiped formed by bari +abarj +bark, barj +abark, and abari + bark becomes minimum is

Match the following

Match the following

If the sum of n terms of an A . P is 3n^(2)+5n and its m^(th) term is 164 , find the valueofm.

If sin A + cos B = a and sin B + cos A = b, then sin (A + B) is equal to

Find the 7^(th) term in the expansion of (x+3y)^(8)

If x^(m) y^(n)=(x+y)^(m+n) , then dy/dxis equal to

Find the conjugate of ((3-2i)(2+3i))/((1-2i)(2-i))

solve x+y=4, y(x^(2)+4)=8

If |x - 2| lt 3 then -1 lt x lt 5.

Image of (2,3) w.r.t (0,0) is

An experiment consists of recording boy-girl composition of families with 2 childern. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

If alpha and beta are different complex numbers with |beta|=1, then find |(beta -alpha)/(1-baralphabeta)|

A cricket club has 15 members, of whom only 5 can bowl . What is the probability that in a team of 11 members at least 3 bowlers are selected?