28278 + Interview Questions in Maths in Class 12 Page 183 InterviewSolution

9101.	A person buys a lottery ticket in 50 lotteries in each of which his chance of winning a prize is 1//100. what is the probability that he will wina prize exactly once
Answer» ANSWER :`(1)/(2)xx ((99)/(100))^(49)`

Discussion

9102.	A person buys a lottery ticket in 50 lotteries in each of which his chance of winning a prize is 1//100. what is the probability that he will wina prize atleast once
Answer» ANSWER :`1-((99)/(100))^(50)`

Discussion

9103.	What is sin^(2)A-sin^(2)B equal to ?
Answer» 0 `1//2` 1 2 Solution :`SIN^(2)A-sin^(2)B=sin^(2)60^(@)-sin^(2)30^(@)=(3)/(4)-(1)/(4)=(1)/(2)`

Discussion

9104.	Using properties of determinants in Exercise 11 to 15 prove that \|{:(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c):}\|=3(a+b+c)(ab+bc+ca)
Answer» ANSWER :`3(a+b+c)(ab+bc+ca)`

Discussion

9105.	If A=[{:(2,-3,5),(3,2,-4),(1,1,-2):}] find A^(-1) . Using A^(-1) solve the system of equations 2x-3y+5z=11 3x+2y-4z=-5 x+y-2z=-3
Answer» ANSWER :x=1,y=-2 and z=3

Discussion

9106.	Which term of the sequence 2005,2000,1995,1990,1985,……. Is the first negative term
Answer» ANSWER :403

Discussion

9107.	If A and B are two events such that P(A) = (5)/(8), P(B) = (3)/(8) and P(A cup B) = (3)/(4)then P(A \| B) = ………..
Answer» `(2)/(5)` `(2)/(3)` `(3)/(5)` `(1)/(4)` Answer :B

Discussion

9108.	Choose the correct answer. The number of arbitrary constants in the perticular solution of a different equation of third order is
Answer» 3 2 1 0 Answer :D

Discussion

9109.	Using elementary transformations, find the inverseof the matrices [(3,1,),(5,2)]
Answer» ANSWER :`[(3,-1,1),(-15,6,-5),(5,-2,2)]`

Discussion

9110.	If 7theta=(2n+1)pi, where n=0,1,2,3,4,5,6, thenanswer the following questions. Thevalue of sec. (pi)/(7)+ sec. (3pi)/(7) + sec. (5pi)/(7)is
Answer» 4 -4 3 -3 Answer :A

Discussion

9111.	Find the sum sum_(r=0)^(5)""^(32)C_(6r).
Answer» Solution :Consider `(1+x)^(32)= .^(32)C_(0) +.^(32)C_(1)x +.^(32)C_(2)x^(2) + "….." +.^(32)C_(32)x^(32)` In `undersetr(r=0)overset(5)sum.^(32)C_(6r)` there is a jump of `'6'` in binomial coefficients, so are will use sixth roots unity. Puttingl `x = cos'(2pir)/(6) + ISIN'(2pir)/(6), r = 0, 1,2,3,4,5` and adding . we GET `6[.^(32)C_(0) + .^(32)C_(6)+.^(32)C_(12)+"....."+.^(32)C_(30)]` `=(1+1)^(32)+(1-1)^(32)+[(3/2+i'(SQRT(3))/(2))^(32)+(3/2-i'(sqrt(3))/(2))^(32)]+[(1/2+i'(sqrt(3))/(2))^(32)+(1/2-i'(sqrt(3))/(2))^(32)]` `=2^(32)+(sqrt(3))^(32)[(cos'(pi)/(6)+isin'(pi)/(6))^(32)+(cos'(pi)/(6)-isin'(pi)/(6))^(32)]+[(cos'(pi)/(3)+isin'(pi)/(3))^(32)+(cos'(pi)/(3)-isin'(pi)/(3))^(32)]` `= 2^(32) + 3^(16)[2COS'(32pi)/(6)]+[2cos'(32pi)/(3)]` `=2^(32)+3^(16)[2cos(5pi+(pi)/(3))]+[2cos(11pi-pi/3)]` ` = 2^(32) + 3^(16)[2(-(1)/(2))]+[2(-(1)/(2))]` `= 2^(32) - 3^(16) - 1`

Discussion

9112.	The locus of z satisfying \|z\|+\|z-1\|= 3 is
Answer» a CIRCLE a pair of straight LINES an ELLIPSE a parabola ANSWER :C

Discussion

9113.	Find the value of the following tan^(-1)"tan"^(7pi)/6
Answer» ANSWER :`(PI)/6`

Discussion

9114.	Solvetheequation x^4 +4x^3 -2x^2 -12x +9=0given thatit haspairsofequalroots
Answer» ANSWER :`-3,1,-3,1`

Discussion

9115.	Integration of some particular functions : int (sin 2x)/(p cos^(2) x+q sin^(2)x) dx=.....+c
Answer» `(q)/(p) log\|p sin2x+q COS2X\|` `(q-p)log\|p COS^(2)X+q sin^(2)x\|` `(1)/(q-p)log\|p cos^(2)x+q sin^(2)x\|` `(1)/(p^(2)+q)log\|p cos^(2)x+q sin^(2)x\|` ANSWER :C

Discussion

9116.	The odds against A solving a problem are 3 to 2 and the odds in favour of B solving the same problem are 5 to 4. Then the probability that the problem will be solved if both of themtry the problem is
Answer» ANSWER :`(33)/(45)`

Discussion

9117.	Let C be a set containing (3n + 1) elements and A is a sub-set of C containing exactly an elements, then the number of ways of choosing sub-set BofC such that: A sube B sube C, B ne A, B ne C, is
Answer» `2^(2n+1)` `2^(2n-1)` `2^(2n+1)-2` `2^(2n+1)-2^(2)` ANSWER :C

Discussion

9118.	int (3x+2)sqrt((x^(2)+2x+c))dx=
Answer» `(x^(2)+2x+5)^((3)/(2))-((x+1))/(2)SQRT(x^(2)+2x+5)+2Sinh^(-1)((x+1)/(2))+c` `(x^(2)+2x+5)^((3)/(2))+((x+1))/(2)sqrt(x^(2)+2x+5)-2Sinh^(-1)((x+1)/(2))+c` `(x^(2)+2x+5)^((3)/(2))-((x+1))/(2)sqrt(x^(2)+2x+5)-2Sinh^(-1)((x+1)/(2))+c` `(x^(2)+2x+5)^((3)/(2))+((x+1))/(2)sqrt(x^(2)+2x+5)+2Sinh^(-1)((x+1)/(2))+c` ANSWER :3

Discussion

9119.	int_(0)^(pi//2) (sin^(100)x-cos^(100)x)dx=
Answer» `(1)/(100)` `(100!)/(100^(100))` `pi/100` 0 Answer :D

Discussion

9120.	If 2x+3y+12=0 and x-y+4lambda=0 are conjugate lines with respect to the parabola y^(2)=8x, then lambda is equal to
Answer» 2 `-2` 3 `-3` ANSWER :D

Discussion

9121.	The negation of pharrq is
Answer» `(~PVVQ)^^(~qvvp)` `(~pvvq)VV(~qvvp)` `(~p^^q)^^(~q^^p)` `(~p^^q)vv(~q^^p)` ANSWER :D

Discussion

9122.	Consider a hyperbola (x^(2))/36-(y^(2))/25=1 A chord QPL meets in asymptote in L and a tangent from L is drawn touching at R. If PM, RE, QN be drawn parallel to the asymptote to meet the other asymptote PM+QN=lamda.RE where
Answer» `lamda` is LESS than 1 `lamda` is less than `5/2` `[lamda]` is 2 `[lamda]` is zero Solution :PROPERTY

Discussion

9123.	Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below have inverses. Find f^(-1) if it exist f={(1,4,),(2,3),(3,2),(4,1)}
Answer» Solution :x={1,2,3,4} f is BIJECTIVE. Hence `f^(-1)` EXISTS. ` f^(-1) ={(4,1),(3,2),(2,3),(1,4)}`

Discussion

9124.	The points A(vec(a)),B(vec(b)) and C(vec( c )) are collinear then ………….
Answer» `VEC(a)+vec(b)+vec( c )=vec(0)` `vec(a)XX vec(b)+vec(b)xx vec( c )+vec( c )xx vec(a)=vec(0)` `vec(a).vec(b)+vec(b).vec( c )+vec( c ).vec(a)=0` None of these ANSWER :B

Discussion

9125.	Find the number of words that can be formed using all the letters of the word 'REGULATIONS' such that E, G always come after R
Answer» ANSWER :`2XX^(11)P_8`

Discussion

9126.	Find the number of words that can be formed using all the letters of the word 'REFULATIONS' such that the vowels must come in a specified order (need not come together)
Answer» ANSWER :`""^(11)P_6`

Discussion

9127.	Find the number of words that can be formed using all the letters of the word “REGULATIONS' such that E always comes after R
Answer» ANSWER :`""^(11)P_9`

Discussion

9128.	Find the number of words that can be formed using all the letters of the word 'REGULATIONS' such that G must come after R,L must come after A, and S must come after N
Answer» ANSWER :`(lfloor11)/8`

Discussion

9129.	Let z be a complex number such that the principal value of argument, argzgt0. Then arg z-arg(-z) is
Answer» `PI/2` `PMPI` `pi` `-pi` ANSWER :C

Discussion

9130.	If I_(n) = int_(0)^(pi//4) Tan^(n) x dx then I_(2)+I_(4), I_(3)+I_(5), I_(4)+I_(6)..... are in
Answer» A.P. G.P. H.P. A.G.P. Answer :C

Discussion

9131.	State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
Answer» ANSWER :(II), (III) and (IV)

Discussion

9132.	Let A=[{:(2,-1),(3,4):}],B=[{:(5,2),(7,4):}],C=[{:(2,5),(3,8):}].Find a matrix D such that CD-AB=O
Answer» ANSWER :`=[{:(-191,-110),(77,44):}]`

Discussion

9133.	For the circles x^(2)+y^(1)=1 and (x-1)^(2)+(y-3)^(2)=4 the line 4x-3y=5 is a
Answer» COMMON chord direct common tangent transverse common tangent common tangent Answer :B

Discussion

9134.	If the angle between the lines whose direction ratios are 2 , -1 , 2 and x , 3 , 5 is pi//4 , then the smallest value of x is
Answer» `52` 4 2 1 Answer :C

Discussion

9135.	If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then the value of k is
Answer» `2^n` `2^(n-1)` `2^(n+1)` 1 Answer :C

Discussion

9136.	A string of length 75 cm is stretched between two fixed supports. It is found that standing waves may be excited at frequencies of 315 Hz and 420Hz, but at no frequencies in between. What is the lowest frequency at which a standing wave may be excited in this string ?
Answer» SOLUTION :0105 `nlambda_(1)=(n+1)lambda_(2)` `(n)/(315)=(n+1)/(420)impliesn=3` fundamental n=1 so `V=(315)/(3)=105H_(2)`

Discussion

9137.	Consider the binary operation ^^ on the set {1,2,3,4,5} defined by a^^b = min {a,b} . Write the operation table of the operation ^^ .
Answer» SOLUTION :N/A

Discussion

9138.	A woman wishes to mix two types of foods in such a way that the vitamin contents of the mixture contain at least 8 units of vitaminA and at least 10 units of vitamin B. Food I contains 2 units/kg of vitaminA and 1 unit /kg of vitamin B. Food II contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin B. The cost of food I is Rs. 50/kg and of food II is Rs. 70/kg. Find the minimum cost of such a mixture.
Answer» SOLUTION :NA

Discussion

9139.	int_(0)^(pi//4)(Sin^(9)x)/(Cos^(11)x)dx=
Answer» `1/9` `1/10` `1/99` `1/90` ANSWER :B

Discussion

9140.	If a=hati-hatk, b=xhati+hatj=(1-x)hatk and c=yhati+xhatj+(1+x-y)hatk. Then, [ab c ] depends on
Answer» Only X Only y Both x and y Neither x nor y Solution :GIVEN vectors are `a = hati - HATK , b = x hati + hatj + (1-x) hatk` and `c = y hati + x hatj + (1+x-y) hatk` Now, `[ABC] = \|{:(1,0,-1),(x,1,1-x),(y,x,1+x-y):}\|` On applying `C_(3) rarr C_(3) + C_(1)`, we get `= \|{:(1,0,0),(x,1,1),(y,x,1+x):}\|` Thus, [a,b,c] dependsupon neither x nor y.

Discussion

9141.	int_(-2)^(2) ( x -\|x\|)dx=
Answer» 0 2 4 -4 Answer :D

Discussion

9142.	(d)/(dx) tan^(-1) [(sqrt( 1 + sin x) - sqrt(1 - sin x))/(sqrt(1 + sin x ) + sqrt(1 - sin x))] is equal to
Answer» 1 `-(1)/(2)` `(1)/(2)` `-1` ANSWER :C

Discussion

9143.	If e is unity vector perpendicular to the planedetermined by the points2hati + hatj + hatk , hati - hatj + hatk - hatj + hatk and- hati + hatj - hatk. Ifa = 2 hati-3 hatj + 6 hatk , then the projection vector of a on e is
Answer» `11/14 ( - 2 hati + hatj + 3 hatk) ` `1/3 (hati - 2hatj+ 2hatk)` `1/7 (2hati - 3hatj + 6hatk)` `(1)/(SQRT14) (2 hati - hatj + 3 hatk)` ANSWER :A

Discussion

9144.	Let A be a square matrix of order 3xx3 then \| kA\| is equal to
Answer» ` k\|A\| ` ` k^(2) \|A\| ` ` k^(3) \|A\| ` ` 3K \|A\| ` Answer :C

Discussion

9145.	If a < -1, which of the following best descirbes a general relationship between a^(3) and a^(2) ?
Answer» `a^(3) gt a^(2)` `a^(3) LT a^(2)` `a^(3) = a^(2)` `a^(3) = -a^(2)` Answer :B

Discussion

9146.	Integrate the following functions : (sin^(-1)x)^(2)
Answer» ANSWER :`X(SIN^(-1)x)^(2)+2sqrt(1-x^(2))sin^(-1)x-2x+c`

Discussion

9147.	For x in R, x != 0, if y(x) is a differentiable function such that x int_(1)^(x) y(t) dt=(x+1)int_(1)^(x)ty (t) dt, then y(x) equals: (where C is a constant.)
Answer» `C a^(3) 1/e^(x)` `(C)/(x^(2))e^(1/x)` `(C)/(x) e^(- 1/x)` `(C)/(x^(3))e^(- 1/x)` ANSWER :D

Discussion

9148.	Let P_(k)(k=1,2,…n) be the nth root of unity. Let z =a +ib and A_(k) = Re(z) Re(P_(k))+i{lm(z)lm(P_(k))} then which of the following is true
Answer» `A_k` LIES on ELLIPSE `A_k` lies on hyperbola If S be the FOCUS of locus of `A_k` then `sum_(k=1)^(n)(A_k)S =na` If S be the focus of locus of `A_k` then `sum_(k=1)^(n) (A_(k) S)^2 = (n)/(2) (3a^2 - b^2)` Answer :A, C, and D

Discussion

9149.	If p, q are odd integers, then the roots of the equation2px^(2) +(2p+q)x+q=0 are
Answer» rational irrational non-real EQUAL ANSWER :a

Discussion

9150.	One side of length 3a of a triangle of area a^(2) square units lies on the line x = a. Then one of the lines on which the third vertex lies, is
Answer» `X= -a^(2)` `x=a^(2)` x = -a `x=(a)/(3)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

A person buys a lottery ticket in 50 lotteries in each of which his chance of winning a prize is 1//100. what is the probability that he will wina prize exactly once

A person buys a lottery ticket in 50 lotteries in each of which his chance of winning a prize is 1//100. what is the probability that he will wina prize atleast once

What is sin^(2)A-sin^(2)B equal to ?

Using properties of determinants in Exercise 11 to 15 prove that |{:(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c):}|=3(a+b+c)(ab+bc+ca)

If A=[{:(2,-3,5),(3,2,-4),(1,1,-2):}] find A^(-1) . Using A^(-1) solve the system of equations 2x-3y+5z=11 3x+2y-4z=-5 x+y-2z=-3

Which term of the sequence 2005,2000,1995,1990,1985,……. Is the first negative term

If A and B are two events such that P(A) = (5)/(8), P(B) = (3)/(8) and P(A cup B) = (3)/(4)then P(A | B) = ………..

Choose the correct answer. The number of arbitrary constants in the perticular solution of a different equation of third order is

Using elementary transformations, find the inverseof the matrices [(3,1,),(5,2)]

If 7theta=(2n+1)pi, where n=0,1,2,3,4,5,6, thenanswer the following questions. Thevalue of sec. (pi)/(7)+ sec. (3pi)/(7) + sec. (5pi)/(7)is

Find the sum sum_(r=0)^(5)""^(32)C_(6r).

The locus of z satisfying |z|+|z-1|= 3 is

Find the value of the following tan^(-1)"tan"^(7pi)/6

Solvetheequation x^4 +4x^3 -2x^2 -12x +9=0given thatit haspairsofequalroots

Integration of some particular functions : int (sin 2x)/(p cos^(2) x+q sin^(2)x) dx=.....+c

The odds against A solving a problem are 3 to 2 and the odds in favour of B solving the same problem are 5 to 4. Then the probability that the problem will be solved if both of themtry the problem is

Let C be a set containing (3n + 1) elements and A is a sub-set of C containing exactly an elements, then the number of ways of choosing sub-set BofC such that: A sube B sube C, B ne A, B ne C, is

int (3x+2)sqrt((x^(2)+2x+c))dx=

int_(0)^(pi//2) (sin^(100)x-cos^(100)x)dx=

If 2x+3y+12=0 and x-y+4lambda=0 are conjugate lines with respect to the parabola y^(2)=8x, then lambda is equal to

The negation of pharrq is

Consider a hyperbola (x^(2))/36-(y^(2))/25=1 A chord QPL meets in asymptote in L and a tangent from L is drawn touching at R. If PM, RE, QN be drawn parallel to the asymptote to meet the other asymptote PM+QN=lamda.RE where

Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below have inverses. Find f^(-1) if it exist f={(1,4,),(2,3),(3,2),(4,1)}

The points A(vec(a)),B(vec(b)) and C(vec( c )) are collinear then ………….

Find the number of words that can be formed using all the letters of the word 'REGULATIONS' such that E, G always come after R

Find the number of words that can be formed using all the letters of the word 'REFULATIONS' such that the vowels must come in a specified order (need not come together)

Find the number of words that can be formed using all the letters of the word “REGULATIONS' such that E always comes after R

Find the number of words that can be formed using all the letters of the word 'REGULATIONS' such that G must come after R,L must come after A, and S must come after N

Let z be a complex number such that the principal value of argument, argzgt0. Then arg z-arg(-z) is

If I_(n) = int_(0)^(pi//4) Tan^(n) x dx then I_(2)+I_(4), I_(3)+I_(5), I_(4)+I_(6)..... are in

State which of the following are not the probability distributions of a random﻿ variable. Give reasons for your answer.﻿

Let A=[{:(2,-1),(3,4):}],B=[{:(5,2),(7,4):}],C=[{:(2,5),(3,8):}].Find a matrix D such that CD-AB=O

For the circles x^(2)+y^(1)=1 and (x-1)^(2)+(y-3)^(2)=4 the line 4x-3y=5 is a

If the angle between the lines whose direction ratios are 2 , -1 , 2 and x , 3 , 5 is pi//4 , then the smallest value of x is

If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then the value of k is

A string of length 75 cm is stretched between two fixed supports. It is found that standing waves may be excited at frequencies of 315 Hz and 420Hz, but at no frequencies in between. What is the lowest frequency at which a standing wave may be excited in this string ?

Consider the binary operation ^^ on the set {1,2,3,4,5} defined by a^^b = min {a,b} . Write the operation table of the operation ^^ .

int_(0)^(pi//4)(Sin^(9)x)/(Cos^(11)x)dx=

If a=hati-hatk, b=xhati+hatj=(1-x)hatk and c=yhati+xhatj+(1+x-y)hatk. Then, [ab c ] depends on

int_(-2)^(2) ( x -|x|)dx=

(d)/(dx) tan^(-1) [(sqrt( 1 + sin x) - sqrt(1 - sin x))/(sqrt(1 + sin x ) + sqrt(1 - sin x))] is equal to

If e is unity vector perpendicular to the planedetermined by the points2hati + hatj + hatk , hati - hatj + hatk - hatj + hatk and- hati + hatj - hatk. Ifa = 2 hati-3 hatj + 6 hatk , then the projection vector of a on e is

Let A be a square matrix of order 3xx3 then | kA| is equal to

If a < -1, which of the following best descirbes a general relationship between a^(3) and a^(2) ?

Integrate the following functions : (sin^(-1)x)^(2)

For x in R, x != 0, if y(x) is a differentiable function such that x int_(1)^(x) y(t) dt=(x+1)int_(1)^(x)ty (t) dt, then y(x) equals: (where C is a constant.)

Let P_(k)(k=1,2,…n) be the nth root of unity. Let z =a +ib and A_(k) = Re(z) Re(P_(k))+i{lm(z)lm(P_(k))} then which of the following is true

If p, q are odd integers, then the roots of the equation2px^(2) +(2p+q)x+q=0 are

One side of length 3a of a triangle of area a^(2) square units lies on the line x = a. Then﻿ one of the lines on which the third vertex﻿ lies, is

State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

One side of length 3a of a triangle of area a^(2) square units lies on the line x = a. Then one of the lines on which the third vertex lies, is