28278 + Interview Questions in Maths in Class 12 Page 254 InterviewSolution

12651.	If l'(x) means log log log .... (x), the 'log' being repeated 'r' times, then int (1)/(x l (x )l^(2) (x )l^(3) (x)- - - l^(x) (x))dx =
Answer» `L^(R)` ( x) + c `l^(r + 1)`(x ) + c `(l^(r + 1)(x))/(r + 1)` `(l^(r)(x))/(r) + c` Answer :B

Discussion

12652.	a ne 0, b ne 0.The number of real number pair (a, b) which satisfy the equation a^(4) + b^(4) = (a+b)^(4) is:
Answer» ANSWER :no REAL VALUE

Discussion

12653.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(3)xsqrt(1+x)dx=........
Answer» `(112)/(5)` `(106)/(5)` `(116)/(15)` `(15)/(116)` ANSWER :C

Discussion

12654.	underset(x to pi//2)lim (sec x-tan x)/(pi//2-x)=
Answer» 0 1 2 `1//2` ANSWER :B

Discussion

12655.	Find the sum (sumsum)_(0leiltjlen) ""^(n)C_(i).
Answer» Solution :`UNDERSET(0leiltjlen)(sumsum).^(N)C_(i) = ((underset(i=0)overset(n)sumunderset(j=0)overset(n)sum.^(n)C_(i))-underset(i=0)overset(n)sum.^(n)C_(i))/(2)` `= ((underset(i=0)overset(n)sum(n+1)^(n)C_(i))-underset(i=0)overset(n)sum.^(n)C_(i))/(2)` ` = ((n+1)2^(n)-2^(n))/(2)` `= n xx 2^(n-1)`

Discussion

12656.	If A and B are finite setsandA sub B then
Answer» `N(A UU B)=n(A)` `n(A nn B)= n(B)` `n(A uu B)=n(B)` `n(A nn B)=phi` Answer :C

Discussion

12657.	Examine the following functions for continuity : f(x) = x - 5
Answer» ANSWER :CONTINUOUS

Discussion

12658.	CF is the internal bisector of angle C of Delta ABCthen CF is equal to : (i) (2ab)/(a+b) cos.(C )/(2) (ii) (a+b)/(2ab) cos.(C)/(2) (iii) (b sin A)/(sin(B+(C )/(2))) (iv) (a+c)/(2ab) cos.(C )/(2)
Answer» (i), (II) (i), (III) (ii), (IV) (iii), (iv) ANSWER :B

Discussion

12659.	If (x-4)/(x^(2)-5x-2k)=2/(x-2)-1/(x+k), " then "k=
Answer» -3 -2 2 3 Answer :A

Discussion

12660.	Method of integration by parts : intx^(n)logxdx=....
Answer» `(x^(n+1))/(n+1) {LOGX+(1)/(n+1)}+C` `(x^(n+1))/(n+1) {logx+(2)/(n+1)}+c` `(x^(n+1))/(n+1) {2logx-(1)/(n+1)}+c` `(x^(n+1))/(n+1) {logx-(1)/(n+1)}+c` ANSWER :D

Discussion

12661.	Consider the G.P. 3,3/2,3/4,… (i) Find the common ratio of the G.P. (ii) How many terms of the above G.P. are needed to give the sum 3069/512?.
Answer» ANSWER :(i) `1/2` (II) `N = 10`

Discussion

12662.	Statement-1 : If tan A, tan B are the roots of the equation x^(2)-px-1=0, then : sin^(2)(A+B)=(p^(2))/(1+p^(2)) Statement-2 : sin^(2)(A+B)=(tan^(2)(A+B))/(1+tan^(2)(A+B))
Answer» Statement-1 is TRUE, statement-2 is true, statement-2 is a CORRECT EXPLANATION for statement-7 Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-7 Statement-1 is true, statement-2 is FALSE Statement-1 is false, statement-2 is true Answer :D

Discussion

12663.	Let M be a square matix of order 3 whose elements are real number and adj(adj M) = [(36,0,-4),(0,6,0),(0,3,6)], then the absolute value of Tr(M) is [Here, adj P denotes adjoint matrix of P and T_(r) (P) denotes trace of matrix P i.e., sum of all principaldiagonal elements of matrix P]
Answer» ANSWER :8

Discussion

12664.	Q.The table shows the minimum age requirement for obtaining a driver's license. In what percent of the states can a person obtain a driver's license before the age of 16?
Answer» `94%` `47%` `38%` `19%` Answer :C

Discussion

12665.	Find the number of ways of arranging 5 men and 3 women around a round table so that all the three women sit together.
Answer» ANSWER :1440

Discussion

12666.	The solution of (dy)/(dx) = tan^(2)(x+y) is
Answer» `tan(x+y)= x+c` `2(x+y)+sin (2x+2y) = 4x+c` `2(x+y) - sin(2x+2y) = 4x+c` `tan(x+y) - SEC (x+y) = x+c` ANSWER :B

Discussion

12667.	For a gas select the correct potion / options.
Answer» The excluded volume fo a GAS will be higher if `(T_(C))/(P_(C)` is high Higher the critical temperature of a gas higher will be extent of ADSORPTION for the gas Most PROBABLE speed of the gas increases with increase in T At night temperature and low pressure a real gas behaves as an ideal gas Solution :`(A) (T_(C))/(P_(C))=((8a)/(27Rb))/(a/(27b^(2)))=(8B)/(R)` `If ""(T_(C))/(P_(C))"is high then be will be high."` (B) If `T_(C)` is high then `P_(C)` will also be high and extent of adsorption `alpha` pressure of gas. (C ) `U_(mps)=sqrt((2RT)/(M))` (D) Theory BASED

Discussion

12668.	int e^(x" cosecx") [ (sin x - x cos x )/(sin^(2) x) ]dx =
Answer» `e^(X)`.COSECX +C `e^(x " cosecx") + ` C `e^(x " cosecx")+ C` `e^(x" sin x")` + C Answer :B

Discussion

12669.	Find the actute angle between y=x^(2) and y= (x-3)^(2).
Answer» ANSWER :HENCE, `theta=tan^(-1) ((3)/(4))`

Discussion

12670.	Obtain the following integrals : int (sqrt(1+x^(2)))/(x^(4))dx
Answer» Answer :`-(1)/(3)(1+(1)/(X^(2)))^((3)/(2))+C`

Discussion

12671.	The number of values of a for which cubic equation x^(3)+3x^(2)+3-a=0 has all the roots as integers is __________
Answer» ANSWER :2

Discussion

12672.	Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that [adjA]^(-1)=adj(A^(-1))
Answer» ANSWER :`[adjA]^(-1)=ADJ(A^(-1))`

Discussion

12673.	match the items of List-I with those of List-II.
Answer» `{:(A,B,C,D),(III, v, iv,II):}` `{:(A,B,C,D),(iv, v, ii,iii):}` `{:(A,B,C,D),(i, iii, iv,v):}` `{:(A,B,C,D),(iii, iv, i,ii):}` ANSWER :A

Discussion

12674.	Maximizez= x_ 1+x_ 2,subjecttox_ 1+x _ 2le10,3x _ 2-2x_ 1le15x_ 1le6,x_ 1 ,x _ 2ge0 . Showthatthemaximumvalueofzoccursat morethantwopoints. Whatisyourconclusion ?
Answer» Solution :First wedrawthelinesAB, CD andEF whoseequationsare`x_ 1+ x_ 2=10 ,3x _ 2-2x _ 1=15andx _ 1=6`respectively. ThefeasibleregionisOEPQDOwhichisshadedinthe figure. Theverticesofthefeasible regionare`O( 0 , 0 ), E (6, 0) , P , Q and D ( 0,5 ) `. Pisthepointofintersectionof the LINES`x _ 1+x _ 2=10andx _ 1=6`. SUBSTITUTING` x _ 1=6` in` x _ 1+x _ 2=10`,weget `6+x_ 2= 10 ` `thereforex_2=4` `thereforeP=( 6,4 ) ` Qisthepointofintersection OFTHE lines `3x_ 2- 2x_ 1=15 ""`...(1) and`x _ 1+x_ 2=10"" `... (2 ) Multipyingequation(2)by2, weget `2x _ 1+2 x _ 2=20 ` Addingthisequationwith(1) , we get, `5x _ 2=35` `thereforex _ 2=7 ` `therefore `from(2) ,`x_ 1+ 7 =10` `thereforex _ 1=3` `thereforeQ =( 3, 7) ` Thevaluesoftheobjectivefunction`z =x_ 1+x _ 2`at theseverticesare `z(O)=0 +0= 0` `z (E) =6 + 0=6 ` `z (P)=6+4= 10` `z( Q)=3 + 7= 10 ` `z ( D)=0+5 =5` `therefore z`has maximumvalues10attwoconsecutiveverticesPandQ ofthefeasibleregion. Hence , z hasmaximumvalue10 at everypointofthesegmentjoiningthe POINTS `P ( 6, 4 ) and Q (3, 7 ) `, i.e.,maximumvalueofz occursat morethantwopoints. This LPP has infinitesolutions.

Discussion

12675.	Fill int the blanks choosing correct answer from the bracket. In Delta ABC, b is _____
Answer» b COSB + C cosC a COSA + c cosC c cosA + a cosC Answer :A

Discussion

12676.	Evaluate int(1)/(5+4cos2theta)d theta
Answer» ANSWER :`(1)/(3)tan^(-1)((1)/(3)TANTHETA)+c`

Discussion

12677.	If the polar of a point P w.r.t the circle x^(2)+y^(2)=a^(2) touches the parabola y^(2)=4ax then the locus ofP is
Answer» `X^(2)-y^(2)=4A^(2)` `x^(2)-y^(2)=2A^(2)` `x^(2)-y^(2)=a^(2)` none Answer :A

Discussion

12678.	The sum of all real roots of the equation \|x-2\|^(2)+\|x-2\|-2=0 is
Answer» 7 4 1 5 Answer :B

Discussion

12679.	XY-plane divides the line joining the points A(2,3,-5) and B(-1,-2,-3) in the ratio
Answer» 5:3 internally 2:1 internally 5:3 externally 3:2 externally Answer :C

Discussion

12680.	(1.03)^19=
Answer» `1.2529` `1.7250` `1.7215` `1.75 35` ANSWER :D

Discussion

12681.	Integrate the function is exercise. sqrt(x^(2)+4x-5)
Answer» ANSWER :`(X+2)/(2)sqrt(x^(2)+4x-5)-(9)/(2) log\|(x+2)+sqrt(x^(2)+4x-5)\|+C`

Discussion

12682.	The value (2^(2011) I_1) /( 1005I_2) , where I_(1) = int_(0)^(1) x^(1004) (1- x)^(1004) dx and I_(2) = int_(0)^(1) x^(1004) (1-x^(2010) )^(1004) dx is
Answer» ANSWER :8

Discussion

12683.	The value of int_(-pi//2)^(pi//2) cos t sin (2t- pi//4) dt is
Answer» `-1//3` `1//3` `SQRT(2) //3` `- sqrt(2)//3` ANSWER :D

Discussion

12684.	Let p and q be two statements, then q harr ( ~ p vee ~ q )is logically equivalent to
Answer» <P>p Q `p RARR q ` `~ p ^^ q ` ANSWER :D

Discussion

12685.	"Prove that "(""^(4n)C_(2n))/(""^(2n)C_(n))=(1.3,5......(4n-1))/({1.3.5....(2n-1)}^(2))
Answer» `[ 1.3.5. . . (4n-1)][1.3.5 . . .(2n-1)]` `[1.3.5. . .(4n-1)]:[1.3.5. . . (2n-1)]^2` `[1.3.5. . . (4n-1)]^2 :][1.3.5. . . (2n-1)]` `[1.3.5. . .(4n-1)]^2"[1.3.5. . . (2n-1)]^2` ANSWER :B

Discussion

12686.	How many non-negative integral values of x satisfy the equation [x/5]=[x/7](Here [x] denotes the greatest integer less than or equal to x. (For example (3.4) = 3 and [-2.3] = - 3).
Answer» ANSWER :9

Discussion

12687.	A small town has one fire engine and one ambulance available for emergencies. The probability that the fire engine is available when needed is 0.98 and the probability that the ambulance is available when called is 0.92. In the event of injury resulting from a building on fire, the probability that both the ambulance and the fire engine will be available is .........
Answer» 0.0016 0.0784 0.0184 0.9016 Answer :D

Discussion

12688.	The mean ago of 25 teachers in a schools is 40 years. A teacher retiresat the age of 60 years and a new teacher is appointed in his place . If now the mean age of the teachers in thisschools is 39 years, then the age (in years) of the newly appointed teacher is
Answer» 35 30 40 25 Answer :A

Discussion

12689.	The radius of a cyclinder is increasing 2 cm/ sec and its altitude is decreasing at the rate of 3 cm/ sec Find the rate of change of volume when radius is 3 cm and altitude is 5cm.
Answer» ANSWER :` 33 PI CM^(3)//s`

Discussion

12690.	Find the number of (i) 6 (ii) 7 letter palindromes that can be formed using the letters of the word EQUATION.
Answer» ANSWER :`8^(3)` (II) `8^(4)`

Discussion

12691.	If x is real, then the value of (x^(2)-3x+4)/(x^(2)+3x+4) lies in the interval
Answer» `[1/3, 3]` `[1/5, 5]` `[1/6, 6]` `[1/7, 7]` ANSWER :D

Discussion

12692.	A test has 4 parts. The first 3 parts carry 10 marks each and the 4th part carries 20 marks. Assuming that marks are not given in fractions, the number of ways in which a candidate can get 30 marks out of 50 are _________________.
Answer» ANSWER :1111

Discussion

12693.	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

12694.	Integrate the following functions sqrt(ax+b)
Answer» Solution :`int SQRT(ax+b) DX = int (ax+b)^(1/2) dx` =`(ax+b)^(1/2+1)/(a(1/2+1)) +C` = `2/(3a) (ax+b)^(1/2) +c`

Discussion

12695.	The ratio in which yz - plane dividesthe line segment joining (-3,4,-2) and (2,1,3) is
Answer» `-4:1` `3:2` `-2:3` `1:4` ANSWER :B

Discussion

12696.	If A=[{:(2,-1),(2,1):}],B=[{:(a,1),(b,-1):}]and(A+B)^(2)=A^(2)+B^(2)+2ABthen ………….
Answer» `a=2,b=-2` `a=2,b=2` `a=-2,b=2` `a=-2,b=-2` ANSWER :D

Discussion

12697.	Let f: W to W be defined by: f(n)={{:(n-1",","if n is odd"),(n+1",","if n is even"):}. Show that'f' is invertible. Find the inverse of 'f'. (Here 'W' is the set of whole numbers.)
Answer» ANSWER :`F^(-1)=f`

Discussion

12698.	If P(A) = 0.5, P(A nn B) = 0.3 then find the max possible value of P(B).
Answer» ANSWER :0.6

Discussion

12699.	Let A and B be two 3xx3 real matrices such that AB ne BA AB-B^(2)A^(2)=I_(3) A^(3)+B^(3)=O_(3) . then det (BA-A^(2)B^(2)). Then \|12a +5i\|= _______
Answer» ANSWER :17

Discussion

12700.	int (tanx - cot x )^(2) dx =
Answer» TAN X + x + C tan x - x C tan x - cot x + c tan x - cot x - 4x+ C ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

If l'(x) means log log log .... (x), the 'log' being repeated 'r' times, then int (1)/(x l (x )l^(2) (x )l^(3) (x)- - - l^(x) (x))dx =

a ne 0, b ne 0.The number of real number pair (a, b) which satisfy the equation a^(4) + b^(4) = (a+b)^(4) is:

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(3)xsqrt(1+x)dx=........

underset(x to pi//2)lim (sec x-tan x)/(pi//2-x)=

Find the sum (sumsum)_(0leiltjlen) ""^(n)C_(i).

If A and B are finite setsandA sub B then

Examine the following functions for continuity : f(x) = x - 5

CF is the internal bisector of angle C of Delta ABCthen CF is equal to : (i) (2ab)/(a+b) cos.(C )/(2) (ii) (a+b)/(2ab) cos.(C)/(2) (iii) (b sin A)/(sin(B+(C )/(2))) (iv) (a+c)/(2ab) cos.(C )/(2)

If (x-4)/(x^(2)-5x-2k)=2/(x-2)-1/(x+k), " then "k=

Method of integration by parts : intx^(n)logxdx=....

Consider the G.P. 3,3/2,3/4,… (i) Find the common ratio of the G.P. (ii) How many terms of the above G.P. are needed to give the sum 3069/512?.

Statement-1 : If tan A, tan B are the roots of the equation x^(2)-px-1=0, then : sin^(2)(A+B)=(p^(2))/(1+p^(2)) Statement-2 : sin^(2)(A+B)=(tan^(2)(A+B))/(1+tan^(2)(A+B))

Let M be a square matix of order 3 whose elements are real number and adj(adj M) = [(36,0,-4),(0,6,0),(0,3,6)], then the absolute value of Tr(M) is [Here, adj P denotes adjoint matrix of P and T_(r) (P) denotes trace of matrix P i.e., sum of all principaldiagonal elements of matrix P]

Q.The table shows the minimum age requirement for obtaining a driver's license. In what percent of the states can a person obtain a driver's license before the age of 16?

Find the number of ways of arranging 5 men and 3 women around a round table so that all the three women sit together.

The solution of (dy)/(dx) = tan^(2)(x+y) is

For a gas select the correct potion / options.

int e^(x" cosecx") [ (sin x - x cos x )/(sin^(2) x) ]dx =

Find the actute angle between y=x^(2) and y= (x-3)^(2).

Obtain the following integrals : int (sqrt(1+x^(2)))/(x^(4))dx

The number of values of a for which cubic equation x^(3)+3x^(2)+3-a=0 has all the roots as integers is __________

Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that [adjA]^(-1)=adj(A^(-1))

match the items of List-I with those of List-II.

Maximizez= x_ 1+x_ 2,subjecttox_ 1+x _ 2le10,3x _ 2-2x_ 1le15x_ 1le6,x_ 1 ,x _ 2ge0 . Showthatthemaximumvalueofzoccursat morethantwopoints. Whatisyourconclusion ?

Fill int the blanks choosing correct answer from the bracket. In Delta ABC, b is _____

Evaluate int(1)/(5+4cos2theta)d theta

If the polar of a point P w.r.t the circle x^(2)+y^(2)=a^(2) touches the parabola y^(2)=4ax then the locus ofP is

The sum of all real roots of the equation |x-2|^(2)+|x-2|-2=0 is

XY-plane divides the line joining the points A(2,3,-5) and B(-1,-2,-3) in the ratio

(1.03)^19=

Integrate the function is exercise. sqrt(x^(2)+4x-5)

The value (2^(2011) I_1) /( 1005I_2) , where I_(1) = int_(0)^(1) x^(1004) (1- x)^(1004) dx and I_(2) = int_(0)^(1) x^(1004) (1-x^(2010) )^(1004) dx is

The value of int_(-pi//2)^(pi//2) cos t sin (2t- pi//4) dt is

Let p and q be two statements, then q harr ( ~ p vee ~ q )is logically equivalent to

"Prove that "(""^(4n)C_(2n))/(""^(2n)C_(n))=(1.3,5......(4n-1))/({1.3.5....(2n-1)}^(2))

How many non-negative integral values of x satisfy the equation [x/5]=[x/7](Here [x] denotes the greatest integer less than or equal to x. (For example (3.4) = 3 and [-2.3] = - 3).

The mean ago of 25 teachers in a schools is 40 years. A teacher retiresat the age of 60 years and a new teacher is appointed in his place . If now the mean age of the teachers in thisschools is 39 years, then the age (in years) of the newly appointed teacher is

The radius of a cyclinder is increasing 2 cm/ sec and its altitude is decreasing at the rate of 3 cm/ sec Find the rate of change of volume when radius is 3 cm and altitude is 5cm.

Find the number of (i) 6 (ii) 7 letter palindromes that can be formed using the letters of the word EQUATION.

If x is real, then the value of (x^(2)-3x+4)/(x^(2)+3x+4) lies in the interval

A test has 4 parts. The first 3 parts carry 10 marks each and the 4th part carries 20 marks. Assuming that marks are not given in fractions, the number of ways in which a candidate can get 30 marks out of 50 are _________________.

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

Integrate the following functions sqrt(ax+b)

The ratio in which yz - plane dividesthe line segment joining (-3,4,-2) and (2,1,3) is

If A=[{:(2,-1),(2,1):}],B=[{:(a,1),(b,-1):}]and(A+B)^(2)=A^(2)+B^(2)+2ABthen ………….

Let f: W to W be defined by: f(n)={{:(n-1",","if n is odd"),(n+1",","if n is even"):}. Show that'f' is invertible. Find the inverse of 'f'. (Here 'W' is the set of whole numbers.)

If P(A) = 0.5, P(A nn B) = 0.3 then find the max possible value of P(B).

Let A and B be two 3xx3 real matrices such that AB ne BA AB-B^(2)A^(2)=I_(3) A^(3)+B^(3)=O_(3) . then det (BA-A^(2)B^(2)). Then |12a +5i|= _______

int (tanx - cot x )^(2) dx =