28278 + Interview Questions in Maths in Class 12 Page 86 InterviewSolution

4251.	IFtan( theta/2) = (2)/(3) , thensec theta =
Answer» `(13)/(5)` `(13)/(3)` `(3)/(13)` `(5)/(13)` ANSWER :A

Discussion

4252.	Let A = {-1,0,1,2}, B = {-4,-2,0,2} and f , g : A rarr B be functions defined f(x) = x^(2)-x, x inRand g(x) = 2 \|x-(1)/2\|-1,x inR. Are f and g equal ? Justify your answer. (Hint : One may note that two functions f : A rarr B and g : A rarr Bsuch that f (a) = g(a) A a inA, are called equal functions).
Answer» SOLUTION :N/A

Discussion

4253.	An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express theset of candidates who passed in Mathematics and Chemistry , but not in physics using union , intersection and different symbols.
Answer» <P> Solution :Set of candidates who passed in Mathematics and CHEMISTRY , but not in PHYSICS `(M nn C)-P`

Discussion

4254.	An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who passed in Mathematics only using union , intersection and different symbols.
Answer» SOLUTION :SET of CANDIDATES who PASSED in MATHEMATICS only `M-C-P`.

Discussion

4255.	An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who passed in all the three subjects using union , intersection and different symbols.
Answer» SOLUTION :Set of candidates who passed in all the THREE SUBJECTS `Mn N C nn P`.

Discussion

4256.	An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who passed in at least two subjects using union , intersection and different symbols.
Answer» Solution :SET of CANDIDATES who passed in at least two SUBJECTS.

Discussion

4257.	An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who failed in Mathematics but passed in at least one subject using union , intersection and different symbols.
Answer» SOLUTION :Set of CANDIDATES who FAILED in MATHEMATICS, but passed in at least one SUBJECT `(P uu C) -M`.

Discussion

4258.	An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who failed in one subject only using union , intersection and different symbols.
Answer» <P> SOLUTION :Set of candidates who failed in ONE SUBJECT only.`(P nn C-M) uu(P nn M-C) uu(M nn C -P)`

Discussion

4259.	Let C be incircle of DeltaABC. If the tangents of lengths t_(1),t_(2) and t_(3) are drawn inside the given triangle parallel to side a,b, and c, respectively, then (t_(1))/(a) + (t_(2))/(b) + (t_(3))/(c) is equal to
Answer» 0 1 2 3 Solution : `DeltaAP_(1) P_(2) ~ DeltaABC` `rArr (t_(1))/(a) = (h-2r)/(h) = 1 -(2r)/(h)` `rArr (t_(1))/(a) = 1 -(2Delta)/(h)`(where `Delta ~= ar (DeltaABC)`) `rArr (t_(1))/(a) = 1 -(2(1)/(2) ah)/(SH)` `rArr (t_(1))/(a) = 1 - (a)/(s)` Similarly, `(t_(2))/(b) = 1 - (b)/(s) and, (t_(3))/(c) = 1 -(c)/(s)` `:. (t_(1))/(a) + (t_(2))/(b) + (t_(3))/(c) = 3 - ((a+b+c))/(s) = 3 -2 =1`

Discussion

4260.	Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2)), if x ne 0 and f(0) =0 int _(0)^(1)f(x) is equal to
Answer» `1- SIN (1)` `sin (1)-1` ` sin (1)` `- sin(1)` ANSWER :A

Discussion

4261.	Find the angle between the following pairs of lines :(i) vecr=2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and veck=7hati-6hatk+mu(hati+2hatj+2hatk)(ii) vecr=3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)
Answer» ANSWER :(i) `THEREFORE theta=cos^(-1)((19)/(21))` (ii)`therefore theta=cos^(-1)((8)/(5sqrt3))`

Discussion

4262.	If A and B are independent, then P (exactly one of A, B occurs) = P(A) * P(B') + P(A') * P(B).
Answer» ANSWER :1

Discussion

4263.	A circle S=0 with radius sqrt2 touches the line x+y-2=0 at (1,1). Then the length of the tangent drawn from the point (1,2) to S=0 is
Answer» 1 `SQRT(2)` `sqrt(3)` 2 Answer :C

Discussion

4264.	If 'a' and 'b' are two distinct prime numbers lying between 1 and 10, which of the following can be the sum of 'a' and 'b'-
Answer» 5 6 7 8 Answer :A::C::D

Discussion

4265.	Choose the correct answer: The probability of obtaining an even prime number on each die, when a pair of dice is rolled isa) 0 b)1/3 c)1/12 d)1/36
Answer» 0 1/3 1/12 1/36 Answer :D

Discussion

4266.	Determine P(E\|F) A coinis tossed three times, whereE : headon third toss, F : heads on firsttwo tosses
Answer» ANSWER :`(1)/(2)`

Discussion

4267.	int_(0)^(pi)\|costheta-sintheta\|d""theta
Answer» 2 `SQRT(2)` `2sqrt(2)` 4 Answer :C

Discussion

4268.	If A is any mxn matrix and B is a matrix such that AB and BA are both defined, then B is a matrix of order
Answer» `nxxn` `mxxm` `mxxn` `nxxm` ANSWER :D

Discussion

4269.	Evaluate the following definite integrals as limit of sums. int_(0)^(4)(x+e^(3x))dx
Answer» ANSWER :`(15+e^(8))/2`

Discussion

4270.	\|{:(2,3,4),(4x,6x,8x),(5,7,8):}\|=......
Answer» 18x 0 1 `18 x^3` ANSWER :B

Discussion

4271.	int_(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int_(0)^(cos^(2)x) cos^(-1) sqrt(t) dt=
Answer» `PI/4` `pi/2` `pi` `2PI` ANSWER :A

Discussion

4272.	Write"Set of all natural numbers that are divisible by 5 " set in the form of lists?
Answer» SOLUTION :`{5,10,15,20,………..}`

Discussion

4273.	Three real numbers x, y, z are such that x^(2) + 6y =-17, y^(2) + 4z=1 and z^(2) + 2x=2. What is the value of x^(2) + y^(2) + z^(2).
Answer» ANSWER :14

Discussion

4274.	Two unbaised coins are tossed. If one coinshows head, the probability that the other also shows head is ……..
Answer» `(1)/(4)` `(1)/(2)` `(1)/(8)` 1 Answer :B

Discussion

4275.	Find (dy)/(dx) of y=log_0x
Answer» SOLUTION :`d/dx(log_8x)=1/(xlog8)d/dx(a^x)=a^xlogad/dx(log_ax)=1/(xloga)`

Discussion

4276.	If\|x\| lt (1)/(2),thenthe coefficientofx^rintheexpansionof(1 + 2x ) /((1 - 2x)^2), is
Answer» ` r2 ^r ` ` (2R - 1 ) 2 ^r ` ` r2^( 2r + 1 ) ` ` (2r + 1 ) 2^r ` Solution : `( 1 +2X ) /((1- 2x ) ^ 2 ) ` `( 1 + 2x )(1 -2x) ^ ( -2 ) ` `=(1+2x ) [ 1 +(2 ) /(1! )2x+((2) (3))/(2!)(2x) ^ 2+((2)(3) …(2 +r - 2 ))/((r - 1 ) !)( 2x ) ^( r - 1 )+((2)(3) …(2 + r- 1 )) /(r !)( 2x)^ r+...] ` `therefore` Co- efficientof X. is ` 1.[ ((2)(3)... (r + 1 ))/(r! )2 ^ r] +2 [ ((2) (3)... (r ))/((r - 1 ) !)] 2^(r - 1 )` `= (( r+ 1 ) ! ) /(r ! )2 ^r+(r! ) /((r - 1 ) ! ) 2 ^ r =(r+ 1 +r ) 2 ^ r ` `= (2r + 1 ) 2 ^r`

Discussion

4277.	lim_(x rarr oo) (1-4/(x-1))^(3x-1) =
Answer» `e^(12)` `e^(-12)` `e^(4)` `e^(3)` ANSWER :B

Discussion

4278.	If y=\|(f(x),g(x),h(x)),(1,m,n),(a,b,c)\|, then (dy)/(dx) is equal to
Answer» 1.`\|(F^(1)(x),g^(1)(x),H^(1)(x)),(1,m,n),(a,B,c)\|` 2.`\|(1,m,n),(f^(1)(x),g^(1)(x),h^(1)(x)),(a,b,c)\|` 3.`\|(f^(1)(x),1,a),(g^(1)(x),m,b),(h^(1)(x),n,c)\|` 4.`\|(1,m,n),(a,b,c),(f^(1)(x),g^(1)(x),h^(1)(x))\|` Answer :A::C::D

Discussion

4279.	int cos^(5)x dx=
Answer» ANSWER :`=(cos^(4)xsinx)/(5)+(4)/(15)cos^(2)X sinx +(8)/(15)sinx+c`

Discussion

4280.	Integrate the following: int(dx)/(5-13sinx) (ii) int(dx)/(13+3cosx+4sinx) (iii)int(dx)/(a^(2)-b^(2)cos^(2)x)(a^(2)gtb^(2)) (iv) int(dx)/(a^(2)-b^(2)cos^(2)x)(a^(2)ltb^(2)) (v) int(sin2x+sin4x-sin6x)/(1+cos2x+cos4x+cos6x)dx
Answer» Answer :`(1)/(12)ln\|(5tan""(1)/(2)xx-25)/(5tan""(1)/(2)x-1)\|+c` `(1)/(6)tan^(-1)((5tan""(1)/(2)x+2)/(6))+c` `(1)/(asqrt(a^(2)-B^(2)))tan^(-1)((a)/(SQRT(a^(2)-b^(2)))tanx)+c` `(1)/(2asqrt(a^(2)-b^(2)))LOG[(atanx-sqrt(b^(2)-a^(2)))/(atanx+sqrt(b^(2)-a^(2)))]+c` `(1)/(3)ln\|sec3x\|-(1)/(2)ln\|sec2x\|-ln\|secx\|+c`

Discussion

4281.	If x = a is a root of multiplicity two of a polynomial equation f(x) = 0, then
Answer» `F'(a) = f''(a) = 0` `f''(a) = f(a) = 0` `f'(a) != 0 != f''(a)` `f(a) = f'(a) = 0, f''(a) != 0` ANSWER :D

Discussion

4282.	The solution of the differential equation (dy)/(dx)-ytanx=e^(x)secx is
Answer» `y=e^(X)cosx+C` `ycosx=e^(x)+c` `y=e^(x)sinx+c` `ysinx=e^(x)+c` ANSWER :B

Discussion

4283.	Find the area of the triangularregion bonded by x= 0, y = x and x + 2y =6
Answer» ANSWER :3 SQ. UNIT

Discussion

4284.	The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and coordinates of points B and C are (1, 5) and (7, –2) respectively. If the area of Delta ABC be 2 units, then k equals
Answer» 7, 9 6, 7 7, 31/9 9, 31/9 Answer :C

Discussion

4285.	Bundles of striated muscle fibres called fasciculi are surrounded by a sheath called :-
Answer» Epimysium Perimysium Exomysium Endomysium Answer :A

Discussion

4286.	Find the area of a parallelogram whose adjacent sides are given by the vectors overset(to)(a) = 3 hat(i) + 5 hat(j) - 2 hat(k) and overset(to)( b) = 2 hat(i) + hat(j) + 3 hat(k).
Answer» `(1)/(2) sqrt(507)` `sqrt(387)` `sqrt(507)` `25` Answer :C

Discussion

4287.	If f(x) = 0 has n roots, then f'(x) = 0 has ………..roots
Answer» `N` `n-1` `n+1` `(n-r)` ANSWER :B

Discussion

4288.	Of all the articles in a box, 80% are satisfactory, while 20% are not. The probability of obtaining exactly five good items out of eight randomly selected articles is
Answer» `0.003` `0.013` `0.132` `0.147` SOLUTION : Since the problem doesn't SAY how many ARTICLES are in the box, we must assume that it is an unlimited number. The probability of picking 5 satisfactory items (and THEREFORE 3 unsatisfactory ones) is`(8.0 )^(5) (0.2)^(3)`, and there are `8/5` way of doing this. Therefore, the desired probability is `8/5(8.0)^(5) (0.2)^(3)= 0.147`

Discussion

4289.	Find the polar of (1,-2) with respect of x^(2) + y^(2) - 10 x - 10y + 25 = 0
Answer» ANSWER :` 4X -3Y -10 =0 `

Discussion

4290.	For what values of x: [1" "2" "3][{:(1,2,0),(2,0,1),(1,0,2):}][{:(0),(2),(x):}]=Q?
Answer» ANSWER :`thereforex=-1`

Discussion

4291.	If the letters of the word BRING are permuted in all possible ways and the words thus formed are arranged in the dictionary order, then find the 59th word.
Answer» ANSWER :IGRBN

Discussion

4292.	How many different factors does 2,000 have?
Answer» ANSWER :20

Discussion

4293.	The negation of the proposition "If a quadrilateral is a square, then it is a rhombus" is
Answer» if a quadrilateral is a SQUARE, then it is a rhombus. If a quadrilateral is a square, then it is not a rhombus. A quadrilateral is a square and it is not a rhombus A quadrilateral is ONT a square and it is a rhombus Answer :C

Discussion

4294.	Examine the consistency of the system of equations x+2y =2 2x+ 3y =3
Answer» ANSWER :CONSISTENT

Discussion

4295.	If y = f(x) defined parametrically by x = 2t - \|t - 1\| and y = 2t^(2) + t\|t\|, then
Answer» F(X) is continuous for all `x in R` f(x) is continuous for all `x in R - {2}` f(x) is DIFFERENTIABLE for all `x in R` f(x) is differentiable for all `x in R - {2}` ANSWER :A::D

Discussion

4296.	If (1)/(f(x)) is a anti-derivative of log[f(x)]^(2)+cthen f(x)=...
Answer» X+K `(x^(2))/(2)+k` `(x)/(2)+k` `x^(2)+C` ANSWER :C

Discussion

4297.	Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p, n x 3 and Respectively.The restriction on n , k and p so that PY +WY will be defined are : (A) k=3,p=n (B) k is arbitrary, p=2 (C ) p is arbitrary, k=3 (D) k=2,p=3
Answer» ANSWER :`THEREFORE(A)` is TRUE.

Discussion

4298.	Out of 10000 families with 4 children each, find the frequencies of distribution of number of male children.
Answer» Answer :FREQUENCY of R MALE is `(625) ""^(4)C_(r)`

Discussion

4299.	int_(0)^(pi//2) (16sin x. cos x)/(sin^(4) x + cos^(4)x)dx=
Answer» `PI^(2)/4` `pi^(2)/2` `pi^(2)` `4PI` ANSWER :D

Discussion

4300.	If int (1)/(x^(2) - 13x+ 42) "dx = log " \|(x - a)/(x - b)\| +C then a + b =
Answer» 13 1 `-13` `-1` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

IFtan( theta/2) = (2)/(3) , thensec theta =

An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who passed in Mathematics only using union , intersection and different symbols.

An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who passed in all the three subjects using union , intersection and different symbols.

An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who passed in at least two subjects using union , intersection and different symbols.

An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who failed in one subject only using union , intersection and different symbols.

Let C be incircle of DeltaABC. If the tangents of lengths t_(1),t_(2) and t_(3) are drawn inside the given triangle parallel to side a,b, and c, respectively, then (t_(1))/(a) + (t_(2))/(b) + (t_(3))/(c) is equal to

Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2)), if x ne 0 and f(0) =0 int _(0)^(1)f(x) is equal to

Find the angle between the following pairs of lines :(i) vecr=2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and veck=7hati-6hatk+mu(hati+2hatj+2hatk)(ii) vecr=3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

If A and B are independent, then P (exactly one of A, B occurs) = P(A) * P(B') + P(A') * P(B).

A circle S=0 with radius sqrt2 touches the line x+y-2=0 at (1,1). Then the length of the tangent drawn from the point (1,2) to S=0 is

If 'a' and 'b' are two distinct prime numbers lying between 1 and 10, which of the following can be the sum of 'a' and 'b'-

Choose the correct answer: The probability of obtaining an even prime number on each die, when a pair of dice is rolled isa) 0 b)1/3 c)1/12 d)1/36

Determine P(E|F) A coinis tossed three times, whereE : headon third toss, F : heads on firsttwo tosses

int_(0)^(pi)|costheta-sintheta|d""theta

If A is any mxn matrix and B is a matrix such that AB and BA are both defined, then B is a matrix of order

Evaluate the following definite integrals as limit of sums. int_(0)^(4)(x+e^(3x))dx

|{:(2,3,4),(4x,6x,8x),(5,7,8):}|=......

int_(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int_(0)^(cos^(2)x) cos^(-1) sqrt(t) dt=

Write"Set of all natural numbers that are divisible by 5 " set in the form of lists?

Three real numbers x, y, z are such that x^(2) + 6y =-17, y^(2) + 4z=1 and z^(2) + 2x=2. What is the value of x^(2) + y^(2) + z^(2).

Two unbaised coins are tossed. If one coinshows head, the probability that the other also shows head is ……..

Find (dy)/(dx) of y=log_0x

If|x| lt (1)/(2),thenthe coefficientofx^rintheexpansionof(1 + 2x ) /((1 - 2x)^2), is

lim_(x rarr oo) (1-4/(x-1))^(3x-1) =

If y=|(f(x),g(x),h(x)),(1,m,n),(a,b,c)|, then (dy)/(dx) is equal to

int cos^(5)x dx=

Integrate the following: int(dx)/(5-13sinx) (ii) int(dx)/(13+3cosx+4sinx) (iii)int(dx)/(a^(2)-b^(2)cos^(2)x)(a^(2)gtb^(2)) (iv) int(dx)/(a^(2)-b^(2)cos^(2)x)(a^(2)ltb^(2)) (v) int(sin2x+sin4x-sin6x)/(1+cos2x+cos4x+cos6x)dx

If x = a is a root of multiplicity two of a polynomial equation f(x) = 0, then

The solution of the differential equation (dy)/(dx)-ytanx=e^(x)secx is

Find the area of the triangularregion bonded by x= 0, y = x and x + 2y =6

The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and coordinates of points B and C are (1, 5) and (7, –2) respectively. If the area of Delta ABC be 2 units, then k equals

Bundles of striated muscle fibres called fasciculi are surrounded by a sheath called :-

Find the area of a parallelogram whose adjacent sides are given by the vectors overset(to)(a) = 3 hat(i) + 5 hat(j) - 2 hat(k) and overset(to)( b) = 2 hat(i) + hat(j) + 3 hat(k).

If f(x) = 0 has n roots, then f'(x) = 0 has ………..roots

Of all the articles in a box, 80% are satisfactory, while 20% are not. The probability of obtaining exactly five good items out of eight randomly selected articles is

Find the polar of (1,-2) with respect of x^(2) + y^(2) - 10 x - 10y + 25 = 0

For what values of x: [1" "2" "3][{:(1,2,0),(2,0,1),(1,0,2):}][{:(0),(2),(x):}]=Q?

If the letters of the word BRING are permuted in all possible ways and the words thus formed are arranged in the dictionary order, then find the 59th word.

How many different factors does 2,000 have?

The negation of the proposition "If a quadrilateral is a square, then it is a rhombus" is

Examine the consistency of the system of equations x+2y =2 2x+ 3y =3

If y = f(x) defined parametrically by x = 2t - |t - 1| and y = 2t^(2) + t|t|, then

If (1)/(f(x)) is a anti-derivative of log[f(x)]^(2)+cthen f(x)=...

Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p, n x 3 and Respectively.The restriction on n , k and p so that PY +WY will be defined are : (A) k=3,p=n (B) k is arbitrary, p=2 (C ) p is arbitrary, k=3 (D) k=2,p=3

Out of 10000 families with 4 children each, find the frequencies of distribution of number of male children.

int_(0)^(pi//2) (16sin x. cos x)/(sin^(4) x + cos^(4)x)dx=

If int (1)/(x^(2) - 13x+ 42) "dx = log " |(x - a)/(x - b)| +C then a + b =