28278 + Interview Questions in Maths in Class 12 Page 258 InterviewSolution

12851.	For1le rlen,thevalueof""^(n)C_(r) +""^(n-1) C_(r) +""^(n-2)C_(r) + . . .+ ""^(r ) C _(r)is
Answer» `""^(N)C_r+1` `""^(n+1)C_r` `""^(n+1)C_(r+1)` NONE of these ANSWER :C

Discussion

12852.	If x^(2)y^(3)=e^(5), x^(3)y^(4)=e^(7) then y is :
Answer» 1 2 `E^(2)` e Answer :D

Discussion

12853.	Which one of the following releation is true regarding the angles of the quadrilateral shown in the figure?
Answer» `/_A = /_C` `/_B GT /_D` `/_A LT /_C` `/_B = /_D` ANSWER :B

Discussion

12854.	Integrate the functions (2x)/(1+x^(2))
Answer» ANSWER :`LOG(1+x^(2))+C`

Discussion

12855.	{:("Column A" , "The functons f(x,y) is defined for all","ColumnB"),(, "the geometric mean of x and y",),(, "(geometric mean of x and y equals)",),(, sqrt(xy)",and the function g(x,y)",),(,"defined as the least common",),(,"multiple of x and y.a and b are",),(, "two different prime numbers",),( f(a,b), ,f(a,b)):}
Answer» If column A is LARGER If column B is larger If the COLUMNS are equal If there is not ENOUGH information to decide Answer :B

Discussion

12856.	Integrate the functions e^(x)(sinx+cosx)
Answer» ANSWER :`E^(X)sinx+C`

Discussion

12857.	v49_newFlow
Answer» `(1,1,-1)` `(1,-1,1)` `(-1,-1,-1)` `(1,1,1)` ANSWER :C

Discussion

12858.	The side if an equilateral triangle are increasing at the rate of 4 cm/sec. the rate at which its areais increasing, when the side is 14 cm.
Answer» 1)`42cm^(2)//SEC` 2)`10sqrt2 cm^(2)//sec` 3)`14cm^(2)//sec` 4)`28sqrt3cm^(2)//sec`

Discussion

12859.	.......... is the probability of an event that there are 53 sundays in year 2019.
Answer» `(2)/(7)` `(3)/(7)` `(1)/(7)` `(4)/(7)` Answer :C

Discussion

12860.	Prove the inequalities : (a) n! lt ((n+1)/2)^(n) for a natural n gt 1: (b) 1/3 .3/4. 5/6 ......(2n-1)/(2n) lt (1)/sqrt(2n+1)
Answer» ANSWER :`(1)/(2n+1)`

Discussion

12861.	The real value of n for which substitutor transform differential equation 2x^(2)y.Into a homogeneous equation
Answer» `(1)/(2)` 1 `(3)/(2)` 2 Answer :C

Discussion

12862.	Integrate the function in Exercise. e^(x) (sinx+cosx)
Answer» ANSWER :`E^(X)+sinx+c`

Discussion

12863.	Find all values of x, y and k for which the system of equations. sinx cos2y = k^(4)-2k^(2)+2 cosx sin2y=k+1 has a solution.
Answer» SOLUTION :`X = 2NPI +-pi/2, y= (NPI)/2`

Discussion

12864.	\|bar(a)\|=2,\|bar(b)\|=3 and bar(a) and bar(b) are perpendicular to each other. The area of the triangle with vertices bar(0),bar(a)+bar(b) and bar(a)-bar(b) is ……………
Answer» 5 1 6 8 Answer :C

Discussion

12865.	The corner points of the bounded feasible region are (0, 0), (0, 8), (4, 10), (6, 8),(6, 5) and (5, 0). For the objective function z = 3x -4y ………(Maximum value of z + Minimum value of z) is equal to
Answer» 13 1 -13 -17 Answer :D

Discussion

12866.	The sum of variance and mean of a binomial distribution for 10 trials is 7.5. Find thedistribution.
Answer» SOLUTION :N/A

Discussion

12867.	If the operation oplusis defined bya oplus b = a^(2)+b^(2)for allreal numbers'a' and 'b' then (2 oplus 3) oplus 4 = __________
Answer» 185 184 182 181 Answer :A

Discussion

12868.	int (1)/(x^(2)+6x+10))dx=
Answer» ANSWER :`(1)/(2)TAN^(-1)((x+1)/(2))+C`

Discussion

12869.	If a given line is tangent to the circle then perpendicular distance from centre of the circle is equal to radius of the circle solve the following : If 4l^(2)-5m^(2)+6l+1=0 then the director circle of the circle whose tangent is lx + my + 1 = 0 is
Answer» `X^(2)+y^(2)+6x-1=0` `x^(2)+y^(2)-6x-1=0` `x^(2)+y^(2)-6x-10=0` `x^(2)+y^(2)+6x+1=0` ANSWER :B

Discussion

12870.	If a given line is tangent to the circle then perpendicular distance from centre of the circle is equal to radius of the circle solve the following : If 16m^(2)-8l-1=0 the equation fo circle whose tangent is lx + my +n=0 is
Answer» `X^(2)+y^(2)+8x=0` `x^(2)+y^(2)-8x=0` `x^(2)+y^(2)+8y=0` `x^(2)+y^(2)-8y=0` ANSWER :B

Discussion

12871.	If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo then find 3x^(2)+6x.
Answer» 1 2 3 4 Answer :B

Discussion

12872.	C_1is a circle of radius 1 and touching both the axis . C_2 is another circle which touch both the axis and also circleC_1whose radius gt1 then radius of C_2 is
Answer» ` (3-2SQRT2) ` ` 2sqrt2` ` (3+2sqrt2) ` ` (4+ 2sqrt2)` ANSWER :C

Discussion

12873.	Write down negations of Fifteen is greater than five.
Answer» SOLUTION :FIFTEEN is not GREATER than FIVE.

Discussion

12874.	Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2,0),B(4,5)" and "C(6,3).
Answer» ANSWER :7

Discussion

12875.	int_(pi/4)^(pi/2) cot^(9)x dx=
Answer» `(-7)/(42)+1/2 LOG2` `(7)/(24)-1/2 log2` `(25)/(24)+1/2 log 2` `(1)/(24)+2 log 2` Answer :A

Discussion

12876.	If u sin t+v cos t=5 and u cos t-v sin t=7, find the value of uvu v, where u,v denote the first and second derivatives of u with respect to t and v,u have sililar meanings.
Answer» ANSWER :74

Discussion

12877.	An urn contains 6 balls of which two are red and four are black. Two balls are drawn at random. Probability that they are of the different colours is :
Answer» (2/5) (1/15) (8/15) (4/15) ANSWER :C

Discussion

12878.	I= int ( x^(2) + 3x+ 5) cos 2x dx.
Answer» ANSWER :`int ( X^(2) + 3x + 5) cos 2 xdx = ( x)/( 2) + (3)/(4) ) cos 2x + ((1)/(2) x^(2) + (3)/(2) x + (9)/(4) ) sin^(2) x + C`.

Discussion

12879.	Let f(x)=ax^(4)+bx^(3)+x^(2)+x-1. If 9b^(2) lt 24a, then number of real roots of f(x) = 0 are
Answer» 4 `GT 2` 0 can’t say Answer :B

Discussion

12880.	Express the value of sin "cos"^(-1) tan sec^(-1)sqrt2in simplest form.
Answer» Solution :`"SINCOS"^(-1) "tansec"^(-1) sqrt2` `"SIN cos"^(-1)"TAN" pi/4 ` ` "sin cos"^(-1)= "sin" 0=0`

Discussion

12881.	If the expression 1/2(x+c)(x-c), where c is a positive constant, can be rewritten as 1/2x^2-5, what is the value of c?
Answer» `SQRT5` `SQRT10` 5 10 Answer :B

Discussion

12882.	Find the equation of the ellipse whose focus (-1,1) e=1/2 and directrix is x-y+3=0
Answer» ANSWER :`(i) 7X^(2)+2x+7y^(2)+10x-10y+7=0` `(II) 7x^(2)-4xy+7y^(2)-26x+10y+10=0`

Discussion

12883.	Determine a binomial distribution whose mean is 9 and variance is 6.
Answer» ANSWER :`(2/3+1/3)^(27)`

Discussion

12884.	Integrate the following functions: (1-cosx)/(1+cosx)
Answer» SOLUTION :`(1-cosx)/(1+cosx) = (2 sin^2(x/2))/(2 cos^2(x/2))` = `tan^2(x/2) = sec^2(x/2)-1` THEREFORE` int(1-cosx)/(1+cosx) DX = (tanx/2)/(1/2)-x+c` `x+c-=2tan(x/2)`

Discussion

12885.	Which of thefollowingfunctionis non- differentiable ?
Answer» `f(x) =(e^(x)-1)\|e^(2X)-1\|"in" R` `f(x)=(x-1)/(x^(2)+1)i NR ` `f(x) ={{:(\|\|x-3\|-1\|, xlt3),((x)/(3)[x] -2 , x ge 3):}` where [.]representsthegreatestintegerfunction `f(x) =3(x-2)^((3)/(4))+3 i N R` ANSWER :D

Discussion

12886.	The moment about the point M(-2, 4, -6) of the force represented in magnitude and position AB, where the points A and B have the coordinates (1, 2, -3) and (3, -4, 2) respectively, is
Answer» `8hati-9hatj-14hatk` `2hati-6hatj+5hatk` `-3hati+2hatj-3hatk` `-5hati-8hatj-8hatk` SOLUTION :Force`F= A=(3-1) hati +(-4-2)haj +(2+3)hatk` `= 2hati- 6 hatj +5hatk` MOMENT of FORCEF withrespectto M `=MAxxF ` ` :'MA =(1+2)hati+(2-4)hatj+(-3+6)hatk =3hati- 2hatj + 3 hatk` Now `,MA xxF =\|{:(hati,hatj,hatk),(3,-2,3),(2,-6,5):}\|` `=hati (-10+18)-hatj (15-6)+hatk(-18+4)` `=8 hati -9hatj -1hatk`

Discussion

12887.	If int(dx)/(sin x cos x)=log\|f(x)\|+C then
Answer» F(x) = SIN x + cos x f(x) = TAN x f (x) = `sec^(2) x` none of these Answer :B

Discussion

12888.	Six horses take part in a race. In how many ways can these horses come in the first, second and third place, if a particular horse is among the three winners (Assume NO Ties)?
Answer» ANSWER :60

Discussion

12889.	If the equation ax^(2)+bx+c=0, a gt 0, has two distinct real roots alpha" and "beta such that alpha lt -5" and "beta gt 5, then
Answer» `C GT 0` `c =0` `c=(a+b)/(2)` `c lt 0` Answer :D

Discussion

12890.	Let R be a relation defined on the set of natural numbers N as follow : R= {(x,y):x in N,y in N and 2x+y=24} Find the domain and range of the relation R. Also, find R is an equivalence relation or not.
Answer» ANSWER :R is not an EQUIVALENCE RELATION.

Discussion

12891.	Integration using rigonometric identities : int(1+cosx)/(sin xcos x)dx=....+c
Answer» `log\|sinx\|+log\|cosx\|` `log\|tanx*TAN((X)/(2))\|` `log\|1+tan((x)/(2))\|` `log\|sec((x)/(2))+tan((x)/(2))\|` ANSWER :B

Discussion

12892.	Evaluate : (i) int_(-pi//2)^(pi//2)sin^(2)xcos^(2)x(sinx+cosx)dx , (ii) int_(0)^(pi)xsin^(5)xdx (iii) int_(0)^(2)x^(3//2)sqrt(2-x)dx, (iv) int_(0)^(2pi)x(sin^(2)xcos^(2)x)
Answer» SOLUTION :N//A

Discussion

12893.	intcos^-1xdx
Answer» SOLUTION :`intsox^-1x.dx` [Choose cos^-1x=1st and 1=2nd FUNCTION] =`cos^-1x.x-int(-1)/sqrt(1-xx^2) .XDX` =`xcos^-1x+int1/sqrt(1-xx^2) .xdx` [PUT `1-x^2=t^2` Then xdx=-tdt] =`xcos^-1x+int(-tdt)/t` `xcos^-1x-t+C` =`xcos^-1x-sqrt(1-x^2) +C`

Discussion

12894.	The value of k, if (1,2) (k,-1) are conjugate point with respect to the ellipse 2x^(2)+3y^(2)=6 is
Answer» 2 4 6 8 Answer :C

Discussion

12895.	If A= {:((3a,2b),(-a,b)):}and B = {:((-a,b),(2a,2b)):}, then find a matrix X such that XA = B.
Answer» SOLUTION :`1/6{:((4,4,2),(11,8,-5),(10,10,2)):}`

Discussion

12896.	** is a binary operation on the set Q. a""b = (2a+b)/4 then find 2""3.
Answer» SOLUTION :N/A

Discussion

12897.	An arch is in the shape of a parabola whose axis is vertically downwords and measures 24 mts across its boltom on the ground. Its highest point is 24 mts. The measure of the horizontal beam acrossits cross section at a height or 18 mts is
Answer» 50 mt 40 mt 45 mt 55 mt ANSWER :B

Discussion

12898.	If the radius of a sphere is measured as 9m with an error of 0.03m, then find the approximte error in calculating its surface area.
Answer» ANSWER :`9.72 PI CM^(3)`

Discussion

12899.	State True or False .There is no function which is its own derivative.
Answer» ANSWER :F

Discussion

12900.	int_(-pi//2)^(pi//2) Cos x. Sin h x dx=
Answer» 1 -1 0 `1/2` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

For1le rlen,thevalueof""^(n)C_(r) +""^(n-1) C_(r) +""^(n-2)C_(r) + . . .+ ""^(r ) C _(r)is

If x^(2)y^(3)=e^(5), x^(3)y^(4)=e^(7) then y is :

Which one of the following releation is true regarding the angles of the quadrilateral shown in the figure?

Integrate the functions (2x)/(1+x^(2))

Integrate the functions e^(x)(sinx+cosx)

v49_newFlow

The side if an equilateral triangle are increasing at the rate of 4 cm/sec. the rate at which its areais increasing, when the side is 14 cm.

.......... is the probability of an event that there are 53 sundays in year 2019.

Prove the inequalities : (a) n! lt ((n+1)/2)^(n) for a natural n gt 1: (b) 1/3 .3/4. 5/6 ......(2n-1)/(2n) lt (1)/sqrt(2n+1)

The real value of n for which substitutor transform differential equation 2x^(2)y.Into a homogeneous equation

Integrate the function in Exercise. e^(x) (sinx+cosx)

Find all values of x, y and k for which the system of equations. sinx cos2y = k^(4)-2k^(2)+2 cosx sin2y=k+1 has a solution.

|bar(a)|=2,|bar(b)|=3 and bar(a) and bar(b) are perpendicular to each other. The area of the triangle with vertices bar(0),bar(a)+bar(b) and bar(a)-bar(b) is ……………

The corner points of the bounded feasible region are (0, 0), (0, 8), (4, 10), (6, 8),(6, 5) and (5, 0). For the objective function z = 3x -4y ………(Maximum value of z + Minimum value of z) is equal to

The sum of variance and mean of a binomial distribution for 10 trials is 7.5. Find thedistribution.

If the operation oplusis defined bya oplus b = a^(2)+b^(2)for allreal numbers'a' and 'b' then (2 oplus 3) oplus 4 = __________

int (1)/(x^(2)+6x+10))dx=

If a given line is tangent to the circle then perpendicular distance from centre of the circle is equal to radius of the circle solve the following : If 4l^(2)-5m^(2)+6l+1=0 then the director circle of the circle whose tangent is lx + my + 1 = 0 is

If a given line is tangent to the circle then perpendicular distance from centre of the circle is equal to radius of the circle solve the following : If 16m^(2)-8l-1=0 the equation fo circle whose tangent is lx + my +n=0 is

If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo then find 3x^(2)+6x.

C_1is a circle of radius 1 and touching both the axis . C_2 is another circle which touch both the axis and also circleC_1whose radius gt1 then radius of C_2 is

Write down negations of Fifteen is greater than five.

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2,0),B(4,5)" and "C(6,3).

int_(pi/4)^(pi/2) cot^(9)x dx=

If u sin t+v cos t=5 and u cos t-v sin t=7, find the value of uvu v, where u,v denote the first and second derivatives of u with respect to t and v,u have sililar meanings.

An urn contains 6 balls of which two are red and four are black. Two balls are drawn at random. Probability that they are of the different colours is :

I= int ( x^(2) + 3x+ 5) cos 2x dx.

Let f(x)=ax^(4)+bx^(3)+x^(2)+x-1. If 9b^(2) lt 24a, then number of real roots of f(x) = 0 are

Express the value of sin "cos"^(-1) tan sec^(-1)sqrt2in simplest form.

If the expression 1/2(x+c)(x-c), where c is a positive constant, can be rewritten as 1/2x^2-5, what is the value of c?

Find the equation of the ellipse whose focus (-1,1) e=1/2 and directrix is x-y+3=0

Determine a binomial distribution whose mean is 9 and variance is 6.

Integrate the following functions: (1-cosx)/(1+cosx)

Which of thefollowingfunctionis non- differentiable ?

The moment about the point M(-2, 4, -6) of the force represented in magnitude and position AB, where the points A and B have the coordinates (1, 2, -3) and (3, -4, 2) respectively, is

If int(dx)/(sin x cos x)=log|f(x)|+C then

Six horses take part in a race. In how many ways can these horses come in the first, second and third place, if a particular horse is among the three winners (Assume NO Ties)?

If the equation ax^(2)+bx+c=0, a gt 0, has two distinct real roots alpha" and "beta such that alpha lt -5" and "beta gt 5, then

Let R be a relation defined on the set of natural numbers N as follow : R= {(x,y):x in N,y in N and 2x+y=24} Find the domain and range of the relation R. Also, find R is an equivalence relation or not.

Integration using rigonometric identities : int(1+cosx)/(sin xcos x)dx=....+c

Evaluate : (i) int_(-pi//2)^(pi//2)sin^(2)xcos^(2)x(sinx+cosx)dx , (ii) int_(0)^(pi)xsin^(5)xdx (iii) int_(0)^(2)x^(3//2)sqrt(2-x)dx, (iv) int_(0)^(2pi)x(sin^(2)xcos^(2)x)

intcos^-1xdx

The value of k, if (1,2) (k,-1) are conjugate point with respect to the ellipse 2x^(2)+3y^(2)=6 is

If A= {:((3a,2b),(-a,b)):}and B = {:((-a,b),(2a,2b)):}, then find a matrix X such that XA = B.

** is a binary operation on the set Q. a"*"b = (2a+b)/4 then find 2"*"3.

An arch is in the shape of a parabola whose axis is vertically downwords and measures 24 mts across its boltom on the ground. Its highest point is 24 mts. The measure of the horizontal beam acrossits cross section at a height or 18 mts is

If the radius of a sphere is measured as 9m with an error of 0.03m, then find the approximte error in calculating its surface area.

State True or False .There is no function which is its own derivative.

int_(-pi//2)^(pi//2) Cos x. Sin h x dx=

** is a binary operation on the set Q. a""b = (2a+b)/4 then find 2""3.