14949 + Interview Questions in Maths in Class 11 Page 8 InterviewSolution

351.	A mathematical club consists of 18 members.In how many ways can the members select a president, a vice - president, a secretary and a treasurer if a member can hold only one position at a time.
Answer» ANSWER :73440

Discussion

352.	In a certain city, all telephone numbers have six digits , the first two digits always being 41 or 42 or 46 or 60 or 64. How many telephone number have all six digits distinct ?
Answer» ANSWER :8400

Discussion

353.	For P(n):2^n lt n!……….. Is true
Answer» <P>P(1) P(2) Any P(N) , `n in N` P(4) ANSWER :D

Discussion

354.	If the plane (x)/(2) + (y)/(3) + (z)/(6) = 1cuts the axes of coordinates at point A,B and C then find the area of the triangle ABC.
Answer» 18 SQ UNIT 36 sq unit `3sqrt14` unit `2sqrt14` sq unit ANSWER :C

Discussion

355.	If alpha is a root of 25 cos^(2)theta + 5 cos theta - 12 =0, (pi)/(2) lt alpha lt pi, then sin 2alpha is equal to
Answer» `24//25` `-24//25` `13//18` `-13//18` ANSWER :B

Discussion

356.	Compute the following limits : Lt_(t to1/2)(4t^(2)-1)/(8t^(3)-1)
Answer» ANSWER :`2/3`

Discussion

357.	Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n)is true for
Answer» `AA in in N` `n =1` `n GT 1, AA n in N` `n gt 2` ANSWER :C

Discussion

358.	A variable plane through a fixed point (1, 2, 3) then the foot of the perpendicular from the origin to the plane lies on
Answer» a circle a SPHERE an ELLIPSE a PARABOLA Answer :B

Discussion

359.	If bar(a) ne bar(0), then are the vectors 2bar(a) and sqrt(3)/2bar(a) like or unlike vectors ?
Answer» ANSWER :LIKE VECTORS

Discussion

360.	If h, k are the perpendicular distances from (4, 2, 5) to the x-axis, y-axis respectively, then hk =
Answer» `SQRT(29)` `sqrt(13)` `sqrt(29) sqrt(41)` `sqrt(13)sqrt(19)` ANSWER :c

Discussion

361.	If cos alpha=(5)/(13) and alpha lies in the fourth quadrant, find the value of (2-3cot alpha)/(4-9sqrt(sec^(2)alpha-1)).
Answer» ANSWER :`(-65)/(352)`.

Discussion

362.	Then function f(x)=int_(-2)^(x)t(e^(t)-1)(t-2)^(3)(t-3)^(5)dt has a local minima at x=
Answer» 0 2 3 5 Answer :C

Discussion

363.	about to only mathematics
Answer» ANSWER :`(29)/(4)`m

Discussion

364.	Find the union of each of the following pairs of sets. A= {x : x = 2n+1, n in Z}, B= {x : x = 2n, n in Z}
Answer» ANSWER :`A CUP B= {x : x" is integer" }= Z`

Discussion

365.	The radius of nine point circle of the triangle whose vertices are (4, 6), (0, 4) , (6, 2) is
Answer» `(sqrt(7))/(2)` `sqrt(2)` `sqrt((5)/(2))` `(5)/(sqrt(2))` ANSWER :C

Discussion

366.	If f(x) is an even function and g(x) is an odd function and satisfies the relation x^(2)f(x)-2f(1/x) = g(x) then
Answer» `f(x)=0, AA x in R` `f(2009)=0` f is constant FUNCTION `G(x)=0, AA x in R` Answer :A::B::C

Discussion

367.	Count the number of positive integers greater than 7000 and less than 8000 which are divisible by 5, provided that no digits are repeated.
Answer» ANSWER :112

Discussion

368.	If vec(a)= 2vec(i) + 3vec(j)- 5vec(k), vec(b)= m vec(i) + n vec(j) + 12 vec(k) and vec(a) xx vec(b) = vec(0) then (m, n)=
Answer» `((-24)/(5), (-36)/(5))` `((-24)/(5), (36)/(5))` `((24)/(5), (-36)/(5))` `((24)/(5), (36)/(5))` ANSWER :A

Discussion

369.	Find the equation to the pair of lines joining the origin to the points of intersection of the curve 7x^(2)-4xy+8y^(2)+2x-4y-8=0 with the striaht line 3x-y=2 and the angle between them.
Answer» `(PI)/(4)` `(pi)/(3)` `(pi)/(2)` `(pi)/(6)` Answer :C

Discussion

370.	A function f from the set of natural numbers to integers defined by f(n)={{:((n-1)/(2)",","when n is odd"),(- n/2",","when n is even"):} is
Answer» one-one but not ONTO. onto but not one-one. one-oneand onto both. neither one-one nor onto. Answer :C

Discussion

371.	If z=4 + 3i, then verify that \|z\|= \|bar(z)\|
Answer» ANSWER :5

Discussion

372.	The point on the curve y=x^2 which is nearest to (3,0) is
Answer» `(1,-1)` `(-1,1)` `(-1,-1)` `(1,1)` ANSWER :D

Discussion

373.	If f:R rarr R is defined by f(x)= floor(x-3)+\|x+4\| for xepsilonR,then lim_(xrarr3^-)f(x) is equal to:
Answer» `-2` `-1` 0 1 Answer :C

Discussion

374.	1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=
Answer» `N ( n+1) (n+2)` `(n +1) (n+2) (n+3) ` `(n+2) (n+3) (n+4)` `(n-1)n (n+1)` ANSWER :A

Discussion

375.	A die is thrown, find the probability of getting: a prime number
Answer» ANSWER :`=(1)/(2)`.

Discussion

376.	Find the equation locus of a point, the difference of whose distances from (-5,0) and (5,0) is 8
Answer» ANSWER :`x^2/16-y^2/9=1`

Discussion

377.	If A.M.and G.M. of roots of a quadratic equation are 8 and 5 respectively then abtain the quadratic equation.
Answer» ANSWER :`x^2 –16x + 25 = 0`

Discussion

378.	Find the tangent to the y ^(2) = 16x, making of 45 ^(@) with the x-axis.
Answer» ANSWER :`y = X +4`

Discussion

379.	If sin theta + cos theta = (1)/(5) and 0 le theta le pi, then tan theta is
Answer» `-4//3` `-3//4` `3//4` `4//3` ANSWER :A

Discussion

380.	If A, B are acute angles, sin A =4/5 , tan B=5/12 , then sin (A+B)=
Answer» `(36)/(65)` `(65)/(56)` `(65)/(63)` `(63)/(65)` ANSWER :D

Discussion

381.	Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digit are repeated .
Answer» ANSWER :192

Discussion

382.	Two unbiased dice are thrown . Find the probability that the total of the numbers on the dice is 8 ,
Answer» ANSWER :`=(5)/(36)`.

Discussion

383.	Byrotating the axes through an angle of pi the equation x - 2y + 3 = 0 changes as
Answer» `X + 2y - 3 = 0` `x - 2y + 3 = 0` `x - 2y - 3 = 0` `x + 2y + 3 = 0` ANSWER :C

Discussion

384.	Find Cov (X,Y) for the following data :
Answer» ANSWER :`-2`

Discussion

385.	Express each of the following complex number in the form a+ib: (1+i)(1+2i)
Answer» ANSWER :`-1+3i`

Discussion

386.	If {:A=[(1,2,2),(2,3,0),(0,1,2)]and adjA=[(6,-2,-6),(-4,2,x),(y,-1,-1)]:},then x + y =
Answer» 6 -1 3 1 Answer :a

Discussion

387.	To find the condition that the three straight lines A_(1)x+B_(1)y+C_(1)=0, A_(2)x+B_(2)y+C_(2)=0 and A_(3)x+B_(3)y+C_(3)=0 are concurrent.
Answer» ANSWER :`rArrA_(3)(B_(1)C_(2)-B_(2)C_(1))+B_(3)(C_(1)A_(2)-C_(2)A_(1))+C_(3)(A_(1)B_(2)-A_(2)B_(1))=0`

Discussion

388.	If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=2bar(i)+3bar(j), bar(c)=3bar(i)+5bar(j)-2bar(k) and bar(d)=bar(k)-bar(j), then the ratio of moduli of bar(b)-bar(a) and bar(d)-bar(c) is
Answer» `2:3` `1:3` `3:1` `4:1` ANSWER :B

Discussion

389.	Ifa,b,care inA.P.Then cos "" (A-C)/(2) cosec ""(B)/(2) =
Answer» `(1)/(2) ` ` 2` ` ( 1)/(3) ` ` 3` ANSWER :B

Discussion

390.	Match the statements/expressions in Column I with the statements/expressions in Column II
Answer» ANSWER :A-prs

Discussion

391.	The sum of n terms of two A.P are in the ratio (3n+6): (5n-13). Find the ratio of their 11^(th) terms
Answer» ANSWER :`3: 4`

Discussion

392.	Find the value of f(0) so thatf(x) = (e^(x^((1)/(2))) + 1)/(e^(x^((1)/(2))) - 1) (x ne 0)is continuous at x = 0
Answer» ANSWER :1

Discussion

393.	An experiment consists of rolling a die until a 2 appears. (i) How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die ?
Answer» ANSWER :`=5^(k-1)`

Discussion

394.	The period of ( sin(2pix + a) )/( sin (2pix + b) ) is
Answer» `(a)/(B)` 1 2 `PI` ANSWER :B

Discussion

395.	If two sides of a triangle are roots of the equation x^(2)- 7x + 8 = 0 and the angle between these sides is 60^(@) then the product of inradius and circumradius of the triangle is
Answer» `(8)/(7)` `(5)/(3)` `(5 sqrt(2))/(3)` 8 Answer :B

Discussion

396.	If I is the centre of a circle inscribed in a DeltaABC, then abs(bar(BC))bar(IA)+abs(bar(CA))bar(IB)+abs(bar(AB))bar(IC)=
Answer» `bar(0)` `bar(IA)+bar(IB)+bar(IC)` `(bar(IA)+bar(IB)+bar(IC))/3` `2(bar(IA)+bar(IB)+bar(IC))` ANSWER :A

Discussion

397.	Find the rth term of an AP sum of whose first n terms is 2n+ 3n^(2)
Answer» ANSWER :`6r-1`

Discussion

398.	Let N=""^(2000)C_1+2 .""^(2000)C_2+3 .""^(2000)C_(3)+....+2000.""^(2000)C_(2000).Prove that N is divisible by 2^(2003)
Answer»

Discussion

399.	If tan^(2) theta=1- k^(2) then sec theta+ tan^(3) theta "cosec" theta=
Answer» `SQRT(2-k^(2))` `sqrt(2+k^(2))` `(2-k^(3))^(3//2)` `(2+k^(2))^(3//2)` ANSWER :C

Discussion

400.	Let f'(sinx)lt0andf''(sinx)gt0AAx in(0,(pi)/(2))andg(x)=f(sinx)+f(cosx).Which of the following is true ?
Answer» g(X) is decreasing in `((PI)/(4),(pi)/(2))` g(x) INCREASING in `(0,(pi)/(4))` g(x)is monotonically increasing None of these Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

A mathematical club consists of 18 members.In how many ways can the members select a president, a vice - president, a secretary and a treasurer if a member can hold only one position at a time.

In a certain city, all telephone numbers have six digits , the first two digits always being 41 or 42 or 46 or 60 or 64. How many telephone number have all six digits distinct ?

For P(n):2^n lt n!……….. Is true

If the plane (x)/(2) + (y)/(3) + (z)/(6) = 1cuts the axes of coordinates at point A,B and C then find the area of the triangle ABC.

If alpha is a root of 25 cos^(2)theta + 5 cos theta - 12 =0, (pi)/(2) lt alpha lt pi, then sin 2alpha is equal to

Compute the following limits : Lt_(t to1/2)(4t^(2)-1)/(8t^(3)-1)

Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n)is true for

A variable plane through a fixed point (1, 2, 3) then the foot of the perpendicular from the origin to the plane lies on

If bar(a) ne bar(0), then are the vectors 2bar(a) and sqrt(3)/2bar(a) like or unlike vectors ?

If h, k are the perpendicular distances from (4, 2, 5) to the x-axis, y-axis respectively, then hk =

If cos alpha=(5)/(13) and alpha lies in the fourth quadrant, find the value of (2-3cot alpha)/(4-9sqrt(sec^(2)alpha-1)).

Then function f(x)=int_(-2)^(x)t(e^(t)-1)(t-2)^(3)(t-3)^(5)dt has a local minima at x=

about to only mathematics

Find the union of each of the following pairs of sets. A= {x : x = 2n+1, n in Z}, B= {x : x = 2n, n in Z}

The radius of nine point circle of the triangle whose vertices are (4, 6), (0, 4) , (6, 2) is

If f(x) is an even function and g(x) is an odd function and satisfies the relation x^(2)f(x)-2f(1/x) = g(x) then

Count the number of positive integers greater than 7000 and less than 8000 which are divisible by 5, provided that no digits are repeated.

If vec(a)= 2vec(i) + 3vec(j)- 5vec(k), vec(b)= m vec(i) + n vec(j) + 12 vec(k) and vec(a) xx vec(b) = vec(0) then (m, n)=

Find the equation to the pair of lines joining the origin to the points of intersection of the curve 7x^(2)-4xy+8y^(2)+2x-4y-8=0 with the striaht line 3x-y=2 and the angle between them.

A function f from the set of natural numbers to integers defined by f(n)={{:((n-1)/(2)",","when n is odd"),(- n/2",","when n is even"):} is

If z=4 + 3i, then verify that |z|= |bar(z)|

The point on the curve y=x^2 which is nearest to (3,0) is

If f:R rarr R is defined by f(x)= floor(x-3)+|x+4| for xepsilonR,then lim_(xrarr3^-)f(x) is equal to:

1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

A die is thrown, find the probability of getting: a prime number

Find the equation locus of a point, the difference of whose distances from (-5,0) and (5,0) is 8

If A.M.and G.M. of roots of a quadratic equation are 8 and 5 respectively then abtain the quadratic equation.

Find the tangent to the y ^(2) = 16x, making of 45 ^(@) with the x-axis.

If sin theta + cos theta = (1)/(5) and 0 le theta le pi, then tan theta is

If A, B are acute angles, sin A =4/5 , tan B=5/12 , then sin (A+B)=

Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digit are repeated .

Two unbiased dice are thrown . Find the probability that the total of the numbers on the dice is 8 ,

Byrotating the axes through an angle of pi the equation x - 2y + 3 = 0 changes as

Find Cov (X,Y) for the following data :

Express each of the following complex number in the form a+ib: (1+i)(1+2i)

If {:A=[(1,2,2),(2,3,0),(0,1,2)]and adjA=[(6,-2,-6),(-4,2,x),(y,-1,-1)]:},then x + y =

To find the condition that the three straight lines A_(1)x+B_(1)y+C_(1)=0, A_(2)x+B_(2)y+C_(2)=0 and A_(3)x+B_(3)y+C_(3)=0 are concurrent.

If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=2bar(i)+3bar(j), bar(c)=3bar(i)+5bar(j)-2bar(k) and bar(d)=bar(k)-bar(j), then the ratio of moduli of bar(b)-bar(a) and bar(d)-bar(c) is

Ifa,b,care inA.P.Then cos "" (A-C)/(2) cosec ""(B)/(2) =

Match the statements/expressions in Column I with the statements/expressions in Column II

The sum of n terms of two A.P are in the ratio (3n+6): (5n-13). Find the ratio of their 11^(th) terms

Find the value of f(0) so thatf(x) = (e^(x^((1)/(2))) + 1)/(e^(x^((1)/(2))) - 1) (x ne 0)is continuous at x = 0

An experiment consists of rolling a die until a 2 appears. (i) How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die ?

The period of ( sin(2pix + a) )/( sin (2pix + b) ) is

If two sides of a triangle are roots of the equation x^(2)- 7x + 8 = 0 and the angle between these sides is 60^(@) then the product of inradius and circumradius of the triangle is

If I is the centre of a circle inscribed in a DeltaABC, then abs(bar(BC))bar(IA)+abs(bar(CA))bar(IB)+abs(bar(AB))bar(IC)=

Find the rth term of an AP sum of whose first n terms is 2n+ 3n^(2)

Let N=""^(2000)C_1+2 .""^(2000)C_2+3 .""^(2000)C_(3)+....+2000.""^(2000)C_(2000).Prove that N is divisible by 2^(2003)

If tan^(2) theta=1- k^(2) then sec theta+ tan^(3) theta "cosec" theta=

Let f'(sinx)lt0andf''(sinx)gt0AAx in(0,(pi)/(2))andg(x)=f(sinx)+f(cosx).Which of the following is true ?