28278 + Interview Questions in Maths in Class 12 Page 58 InterviewSolution

2851.	The value of int_(0)^(pi//2) (cos3x+1)/(2cos x-1)dx is
Answer» 2 1 `(1)/(2)` 0 Solution :Let `I=underset(0)OVERSET(pi//2)INT (cos 3x+1)/(2cos x-1)DX` `=underset(0)overset(pi//2)int (cos 3x-cos""(3pi)/(4))/(2(cosx-cos""(pi)/(3)))dx` `=underset(0)overset(pi//2)int ((4cos^(3)x-3cosx)-(4cos^(3)""(pi)/(4)-3cos""(pi)/(3)))/(2(cos x-cos""(pi)/(3)))dx` `=2underset(0)overset(pi//2)int ((cos^(3)x-cos^(3)""(pi)/(3))/(cos x-cos""(pi)/(3)))dx` `=2underset(0)overset(pi//2)int (cos^(2)x+cos^(2)""(pi)/(3)+cos x cos ""(pi)/(3))dx-(3)/(2)underset(0)overset(pi//2)int 1dx` `=underset(0)overset(pi//2)int (1+cos2x+(1)/(2)+cosx)dx-(3pi)/(4)` `=(3pi)/(4)+1-(3pi)/(4)=1`

Discussion

2852.	int_(0)^(1)x e^(x^(2)) dx
Answer» Solution :`" LET I=" int_(0)^(1) xe^(x^(2))dx` `"Let "x^(2)=trArr 2x=(DT)/(dx) rArr XD x= (dt)/(2)` `x=0rArr t=0 ` `"and " x=1 rArrt=1` ` :, I=(1)/(2) int_(0)^(1) E^(t) dt=(1)/(2)[e^(t)]_(0)^(1)` `=(1)/(2)(e^(1)-e^(0))=(1)/(2)(e-1)`

Discussion

2853.	Determine for which values of x, the following functions are increasing or decreasing : f(x)=x^(3)+(1)/(x^(3)), x ne0
Answer» Answer :`{:("Increasing","DECREASING"),(""(-OO","-1)UU(1","oo),(-1","1)-{0}):}`

Discussion

2854.	If a,b,c are the sides of a triangle then the range of (a^(2)+b^(2)+c^(2))/(ab+bc+ca) is
Answer» [1,2) `(-OO, 1] UU[2, oo)` [2,3] (-1,3) ANSWER :A

Discussion

2855.	(x+(1)/(x))^(x) +x^((1+(1)/(x)))
Answer» SOLUTION :`"Let " y = (x+(1)/(x))^(x) +x^((1+(1)/(x)))` `"Let" u=(x+(1)/(x))^(x) " and "V = x^(1+(1)/(x))` `therefore y=u + v rArr (dy)/(dx) = (DU)/(dx) + (dv)/(dx)"" ...(1)` `"Now", u = (x+(1)/(x))^(x)` `rArr "LOG " u = "log" (x+(1)/(x))^(x) = x" log"(x+(1)/(x))` `rArr (1)/(u) (du)/(dx) = x* (d)/(dx) "log" (x+(1)/(x)) + "log"(x+(1)/(x))(d)/(dx) x` `rArr (du)/(dx) = u [(x)/(x+(1)/(x))(1-(1)/x^(2))+"log" (x+(1)/(x))]` `=(x + (1)/(x))^(x) [(x^(2)-1)/(x^(2)+1) + "log" (x+(1)/(x))]` ` "and "v = x^((1+(1)/(x))` `rArr "log " v = "log" {x^((1+(1)/(x)))} = (1+(1)/(x))"log"x` `rArr (1)/(v) (dv)/(dx) = (1+(1)/(x))(d)/(dx) "log"x + "log"x (d)/(dx) (1+(1)/(x))` `rArr (dv)/(dx) = v[(1+(1)/(x))(1)/(x)+"log"x (-(1)/(x^(2)))]` `rArr (dv)/(dx) = x^((1+(1)/(x)))(1)/(x^(2))[x+1-"log"x]` `therefore "From equation (1)"` `(dy)/(dx) = (x+(1)/(x))^(x)[(x^(2)-1)/(x^(2)+1)+ "log" (x+(1)/(x))] + x^((1+(1)/(x))) * (1)/(x^(2))[x+1-"log"x]`

Discussion

2856.	If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2 and (x-1)/(3k)=(y-1)/1=(z-6)/(-3) are perpendicular, find the value of k.
Answer» ANSWER :`k=-6/7`

Discussion

2857.	If there is an error of 1/(10)% in the measurement of the radius of a sphere, then the percentage erro in the calculation of the volume of the sphere is
Answer» `3//10` `1//8` `1//7` `3//2` ANSWER :A

Discussion

2858.	Reflexion of the point (alpha, beta, gamma) in XY plane is
Answer» 1.`(alpha, beta, 0)` 2.`(0,0,GAMMA)` 3.`(-alpha, -beta, gamma)` 4.`(alpha, beta, -gamma)` ANSWER :D

Discussion

2859.	Thevalue(S) of alpha in [0,2pi] forwhichvectorvec(a)= hat(i) + 3hat(j) + (sin 2 alpha) hat(k)makes an obtuse angle with the z-axis and thevectors vec(b) = (tan alpha)hat(i) - hat(j) + 2 sqrt(sin(alpha)/(2))hat(k) andvec(c) = (tan alpha)hat(i) (tan alpha)hat(j)- 3 sqrt(cosec(alpha)/(2))hat(k) are
Answer» `TAN^(-1) 3` `PI - tan^(-1) 2` `pi + tan^(-1)3` `2PI - tan^(-1) 2` ANSWER :B::D

Discussion

2860.	A coin is tossed successively three times. The probability of getting exactly one head or 2 heads, is
Answer» `1/4` `1/2` `3/4` `1/3` ANSWER :C

Discussion

2861.	Find the area enclosed by y=log_(e)(x+e) and x=log_(e)((1)/(y)) and the x-axis.
Answer» ANSWER :2

Discussion

2862.	For a group of 50 male workers, the mean and S.D. of their daily wages are Rs. 630 and Rs. 90 respectively. For a group of 40 female workers, these are Rs. 540 and Rs. 60 respectively. The S.D. of these 90 workers is
Answer» 60 70 80 90 Answer :D

Discussion

2863.	If p rarr (q vv r) is false, then the truth values of p, q, r are respectively
Answer» T,F,F F,F,F F,T,T T,T,F Answer :A

Discussion

2864.	Total number of species which use d -orbital in their bonding SO_(2),SO_(3),SO_(4)^(-2),CIO_(4)^(oplus),XeO_(2)F_(2),XeO_(3)
Answer» ANSWER :`6.00`

Discussion

2865.	If y = sin ^(3) x + cos^(6) x find (dy)/(dx).
Answer» ANSWER :`3 SIN x COS x(sin x-2 cos^(4)x)`

Discussion

2866.	If (dy)/(dx)+(y)/(sqrt(x^(2)+a^(2)))=3x,y(0)=a^(2) then the value of (y(sqrt(3a)))/(a^(2)).(8-3sqrt3)/(2-sqrt3) is equal to 19k, then find k.
Answer» ANSWER :B

Discussion

2867.	Let f: Rto R be by f(x)=(x-1)(x-2)(x-5). Define F(x)=int_(0)^(x)f(t)dt,xgt0 Then which of the following options is/are correct ?
Answer» `F(x) ne 0` for all `x in (0,5)` F has a local maximum at `x=2` F has two local MAXIMA and ONE local minimum is `(0,oo)` F has a local minimum at `x=1` Solution :Given , `f:R toR and f(x)=(x-1)(x-2)(x-5)` Since , `F(x)-int_(0)^(x) f(t)dt,x gt 0` So, `F'(x)=(x-2)(x-5)` Accroding to wavy curve method `(-""+""-""+)/(1"2"5)` F'(x) chages , it's sign form negative to positive at `x =1` and 5, So, F(x) has minima at ` x=1` and 5 and as F'(x) changes, it's sign from positive to negative at` x=2` so F(x) has maxima at ` x=2` ` because F(2)=int_(0)^(2) f(t)dt= int_(0)^(2)(t^2-8t^2+17t-10)dt` ` =[(t^4)/(4)-8(t^3)/(3)+17(t^2)/(2)-10T]_(0)^(2)` ` =4-(64)/(3)+34-20=38-(124)/(3)=-(10)/(3)` `because` At the point of maxima `x=2`, the functional value `F(2)=-(10)/(3)`, negative for the internal `x in (0,5)`, so `F(x)ne 0` for any value of `x in (0,5)`, Hence , OPTIONS (a),(b) and (d) are correct.

Discussion

2868.	Evaluate P (AnnB)if 2P(A)=P(B)=5/13and P(A/B)=2/5.
Answer» <P> SOLUTION :P(A/B)=2/5`rArr (P(ANNB))/(P(B))=2/5`rArr(P(AnnB))=2/5xxP(B)` 2/5xx5/13=2/13 P(A)=5/26 THUS,`P(AnnB)` `=`P(A)+P(B)-P(AnnB)` =5/26+5/13-2/13=11/26

Discussion

2869.	Integrate the following functions x/(9-4x^2)
Answer» Solution :Let t = `9-4x^2`. Then `dt = -8X DX GT x dx = -1/8 dt` THEREFORE`int x/(9-4x^2) dx = int 1/t xx -1/8 dt` =`-1/8 log\|t\|+C` =-`1/8 log\|9-4x^2\| +c`

Discussion

2870.	Find the area enclosed by y^2=x^3,x=0,y=1
Answer» SOLUTION :Given CURVE is `y^2=x^3` `impliesx=y^(2//3)` It PASS through the origin So the REQUIRED AREA `=int_0^1xdy= int_0^1 y^(2/3)dy=[y^(2/3)/(5//3)]_0^1=3/5`

Discussion

2871.	Evalute the following integrals int (1)/(x^(2)) tan^(-1) xdx
Answer» Answer :`- (1)/(x) tan^(-1) x + LOG x - (1)/(2) log (1 +x^(2)) + C `

Discussion

2872.	The value of int_(0)^(4) 3^(sqrt(2x+1) )dx is
Answer» `(6)/(LOG 3) (13- (4)/(log 3) )` `(66)/(log 3)` `(6)/(log 3) (13- (5)/(log 3) )` NONE of these Answer :D

Discussion

2873.	The value of sum_(r = 1)^15 r^2 ((""^15C_r)/(""^15C_(r - 1)) ) of is equal to
Answer» 1240 560 1085 680 Answer :D

Discussion

2874.	Let the circle (x - 1)^(2) + (y - 1)^(2) = 25 cuts a rectangular with transverse axis along y = x at four points A, B, C and D having co-ordinates (x_(1) , y_(1)) : i = 1,2,3,4 respectively O being the centre of the hyperbola, Now match the entries from the following two columns
Answer» SOLUTION :N/A

Discussion

2875.	Integrate the following functions 1/sqrt(7-6x-x^2)
Answer» SOLUTION :`7-6x-x^2 = 7-(x^2+6x)` =`7-(x^2+6x+9-9)` `16-(x+3)^2` therefore` INT 1/sqrt(7-6x-x^2) dx` =`int 1/sqrt(16-(x+3)^2) dx` =`sin^-1((x+3)/4)+C`

Discussion

2876.	The sum of the series 1/1.2 - 1/2.3 + 1/3.4 … upto infty is equal to
Answer» `log_(e) 2 - 1` `log_(e) 2` `log_(e) (4/e)` `2log_(e) 2 ` Answer :C

Discussion

2877.	The numbers of terms of the A.P 3, 7, 11, 15, …… to be taken so that the sum is 406 is
Answer» 5 10 12 14 Answer :D

Discussion

2878.	The area bounded by the curves y=\|x\|-1 and y= -\|x\|+1 is
Answer» I, II II, II only III All ANSWER :D

Discussion

2879.	One compartment of a purse contains three 25 paise coins and 2 one rupee coins and the other compartment contains two 25 ps. Coins and 3 one rupee coins. The probability of drawing a rupee from the purse is
Answer» `1//5` `2//5` `3//5` `1//2` ANSWER :D

Discussion

2880.	Let S denotes the set consisting of four functions and S = { [x], sin^(-1) x, \|x\|,{x}} where , {x} denotes fractional part and[x] denotes greatest integer function , Let A, B , C aresubsets of S. Suppose A : consists of odd functions (s) B : consists of discontinuous function (s) and C: consists of non-decreasing function(s) or increasing function (s). If f(x) in A nn C, g(x) in B nnC, h (x) in B" but notC and" l(x) inneither A nor B nor C . Then, answer thefollowing. The range ofg(f(x)) i
Answer» `{-1,0,1}` `{-1,0}` `{0,1}` `{-2,-1,0,1}` ANSWER :D

Discussion

2881.	Let S denotes the set consisting of four functions and S = { [x], sin^(-1) x, \|x\|,{x}} where , {x} denotes fractional part and[x] denotes greatest integer function , Let A, B , C aresubsets of S. Suppose A : consists of odd functions (s) B : consists of discontinuous function (s) and C: consists of non-decreasing function(s) or increasing function (s). If f(x) in A nn C, g(x) in B nnC, h (x) in B" but notC and" l(x) inneither A nor B nor C . Then, answer thefollowing. The range of f(h(x)) is
Answer» `(0, pi/2)` `[0, pi/2)` `(0, pi/2]` `[0, pi/2]` ANSWER :B

Discussion

2882.	Let S denotes the set consisting of four functions and S = { [x], sin^(-1) x, \|x\|,{x}} where , {x} denotes fractional part and[x] denotes greatest integer function , Let A, B , C aresubsets of S. Suppose A : consists of odd functions (s) B : consists of discontinuous function (s) and C: consists of non-decreasing function(s) or increasing function (s). If f(x) in A nn C, g(x) in B nnC, h (x) in B" but notC and" l(x) inneither A nor B nor C . Then, answer thefollowing. The function l (x) is
Answer» periodic EVEN ODD neither odd nor even ANSWER :B

Discussion

2883.	If x+y+z=180^(@) then (sinx+siny+sinz)/("cos"x/2."cos"y/2."cos"z/2)=
Answer» 0 3 2 4 Answer :D

Discussion

2884.	Integrate the following intcos(2-7x)dx
Answer» SOLUTION :`INT(COS(2-7x)dx=intcosthetacdot(-1/7d theta)` put 2-7x=`theta` then `-7x=d"theta`or `dx=(-1/7)d"theta` `(-1/7)sintheta+C=(-1/7sin(2-7x)+C`

Discussion

2885.	Evaluate int(1-cos2x)/(1+cos2x)dx.
Answer» SOLUTION :`INT(1-cos2x)/(1+cos2x)=int(2sin^2x)/(2cos^2x)dx=inttan^2xdx=int(sec^2x-1)dx=tanx-x+C`

Discussion

2886.	(1+i)^(6)+(1-i)^(6)=
Answer» `15I` `-15i` `15` 0 Answer :D

Discussion

2887.	' lim_ (x to 0) (a^(x)-b^(x))/(e^(x)-1) is equal to
Answer» `"LOG"(a)/(B)` `"log"(b)/(a)` log ab loga+b Answer :A

Discussion

2888.	int_(0)^((pi)/(2))(f(sinx))/(f(cosx)+f(sinx))dx is :
Answer» `pi` `(pi)/(2)` `(pi)/(4)` `(pi)/(8)`. ANSWER :C

Discussion

2889.	If P(A)=(6)/(11), P(B)=(5)/(11) amd P(A cup B)=(7)/(11), find (i) P(A cup B) (ii) P(A\|B) (iii) P(B\|A)
Answer» ANSWER :(i) `(4)/(11)`, (II) `(4)/(5)`, (III) `(2)/(3)`

Discussion

2890.	Statement :1 If A nad B are two fixed points and P is any point such that PA + PB =k then locus of P is an ellipse. Because Statemet :2 In any ellipse with foci at A and B is PA + PB =k.
Answer» Stateme-1 is True, Statement-2 is True, Statemetn-2 is correct explanation for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is FALSE Statement-1 is False, Statement-2 is TURE Answer :D

Discussion

2891.	A particle is thrown with 12 m/s in positive X direction while acceleration is 2 m//s^2 in negative X direction then distance travelled by particle between t=5 to t=7 sec is
Answer» 0 m 1 m 2 m 3 m

Discussion

2892.	Solve the following equations, using inverse of a matrix : {:(2x+y+z=1),(2x-4y-2x=3),(3y-5z=9):}
Answer» ANSWER :`x=1`, `y=(1)/(2)`, `Z=-(3)/(2)`

Discussion

2893.	Evaluate the integral underset(0)overset(pi//2)int tan^(5)x cos^(8)x dx
Answer» ANSWER :`(1)/(24)`

Discussion

2894.	Obtain the general solution of the following differential equations.dy/dz=sqrt(1-y^2)/sqrt(1-z^2)
Answer» SOLUTION :`dy/dz=SQRT(1-y^2)/sqrt(1-z^2)` `RARR dy/sqrt(1-y^2)=dz/sqrt(1-z^2)` `rArr intdy/sqrt(1-y^2)=intdz/sqrt(1-z^2)`rArr SIN^(-1)y=sin^(-1)z+C`

Discussion

2895.	Integrationof certainirrational expressions I=int(dx)/(x(2+3sqrt((x-1)/(x)))).
Answer» ANSWER :`-(1)/(SQRT(3))arc tan"" (2t + 1)/(sqrt(3))+In\|root(3)((t+2)^(4))/(root(3)(t-1).sqrt(t^(2)+t+1))\|+C,`

Discussion

2896.	State whether the points A(3, 2), B(-4,-3) lie on the same side or opposite sides of the line 2x - 3y +4 = 0.
Answer» SOLUTION :NA

Discussion

2897.	Integrate the following functions : e^(x)((2+sin2x)/(1+cos2x))
Answer» ANSWER :`E^(X)tanx+c`

Discussion

2898.	Let O be a point inside DeltaABC such that angleOAB = angleOBC = angle OCA = theta Area of DeltaABC is equal to
Answer» `((a^(2) + b^(2) + c^(2))/(4)) tan theta` `((a^(2) + b^(2) + c^(2))/(4)) cot theta` `((a^(2) + b^(2) + c^(2))/(2)) tan theta` `((a^(2) + b^(2) + c^(2))/(2)) cot theta` Solution : Applying sine rule in `DeltaAOB`, we have `(OA)/(sin angleABO) = (AB)/(sin angle AOB)` or `OA = (c sin angleABO)/(sin angleAOB) = (c sin (B - theta))/(sin B)`...(i) `[ :' angle ABO = B - theta, angle AOB = 180^(@) - theta - angleABO = 180^(@) -B]` Again in `DeltaAOC`, we have `(OA)/(sin angleACO) = (AC)/(sin angleAOC)` `rArr OA = (b sin angleACO)/(sin angleAOC) = (b sin theta)/(sin A)` `[ :' angleOAC = A - theta, angleAOC = 180^(@) - theta - angleOAC = 180^(@)]` From Eqs. (i) and (ii), we have `(c sin (B - theta))/(sin B) = (b sin theta)/(sin A)` or `c sin A (B - theta) = b sin theta sin B` `= b sin theta sin (A +C)` or `2R sin C sin A (sin B cos theta - cos B sin theta)` `= 2R sin B sin theta (sin A cos C + cos A sin C)` Dividing both SIDES by `2R sin theta sin A sin B sin C`, we get `cot theta - cot B = cot C + cot A` or `cot theta = cot A + cot B + cot C` Squaring both sides, we have `cot^(2) theta = cot^(2) A + cot^(2) B + cot^(2)C + 2(cotA cot B + cot B cot C + cot C cot A)` or `cosec^(2) theta - 1 = (cosec^(2) A -1) + (cosec^(2) B -1) + (cosec^(2) C -1) + 2` [SINCE in `DeltaABC, cot A cot B + cot B cot C + cot C cot A = 1`] or `cosec^(2) theta = cosec^(2) A + cosec^(2) B + cosec^(2)C` Area of triangle ABC, `Delta = Delta_(1) + Delta_(2) + Delta_(3)` `=(1)/(2) [a OB + b OC + c OA] sin theta` `=(1)/(4) tan theta [2 a OB cos theta + 2B OC cos theta+ 2c OA cos theta]` `=(1)/(4) tan theta [(a^(2) + x^(2) -y^(2)) + (b^(2) + y^(2) - z^(2)) + (c^(2) + z^(2) - x^(2)]` `= (1)/(4) tan theta [a^(2) + b^(2) + c^(2)]`

Discussion

2899.	If n(A)=n then n{(x,y,z),x,y,z in A ,x ne y, y ne z ,zne x}=
Answer» `n^(3)` `n(n-1)^(2)` `n^(2)(n-2)` `n^(3)-3N^(2)+2N` ANSWER :D

Discussion

2900.	The vector equation of the line of intersection of the planes vecr=vecb+lamda_1 (vecb-veca) + mu_1 (veca-vecc) and vecr=vecc+lamda_2(vecb-vecc)+mu_2(veca+vecb) veca,vecb,vecc being non - coplanar vectors, is
Answer» `VECR = vecb+mu_1 (veca+vecc)` `vecr = vecb+lamda_1 (veca-vecc)` `vecr = 2vecb+lamda_2 (veca-vecc)` NONE of these Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The value of int_(0)^(pi//2) (cos3x+1)/(2cos x-1)dx is

int_(0)^(1)x e^(x^(2)) dx

Determine for which values of x, the following functions are increasing or decreasing : f(x)=x^(3)+(1)/(x^(3)), x ne0

If a,b,c are the sides of a triangle then the range of (a^(2)+b^(2)+c^(2))/(ab+bc+ca) is

(x+(1)/(x))^(x) +x^((1+(1)/(x)))

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2 and (x-1)/(3k)=(y-1)/1=(z-6)/(-3) are perpendicular, find the value of k.

If there is an error of 1/(10)% in the measurement of the radius of a sphere, then the percentage erro in the calculation of the volume of the sphere is

Reflexion of the point (alpha, beta, gamma) in XY plane is

Thevalue(S) of alpha in [0,2pi] forwhichvectorvec(a)= hat(i) + 3hat(j) + (sin 2 alpha) hat(k)makes an obtuse angle with the z-axis and thevectors vec(b) = (tan alpha)hat(i) - hat(j) + 2 sqrt(sin(alpha)/(2))hat(k) andvec(c) = (tan alpha)hat(i) (tan alpha)hat(j)- 3 sqrt(cosec(alpha)/(2))hat(k) are

A coin is tossed successively three times. The probability of getting exactly one head or 2 heads, is

Find the area enclosed by y=log_(e)(x+e) and x=log_(e)((1)/(y)) and the x-axis.

For a group of 50 male workers, the mean and S.D. of their daily wages are Rs. 630 and Rs. 90 respectively. For a group of 40 female workers, these are Rs. 540 and Rs. 60 respectively. The S.D. of these 90 workers is

If p rarr (q vv r) is false, then the truth values of p, q, r are respectively

Total number of species which use d -orbital in their bonding SO_(2),SO_(3),SO_(4)^(-2),CIO_(4)^(oplus),XeO_(2)F_(2),XeO_(3)

If y = sin ^(3) x + cos^(6) x find (dy)/(dx).

If (dy)/(dx)+(y)/(sqrt(x^(2)+a^(2)))=3x,y(0)=a^(2) then the value of (y(sqrt(3a)))/(a^(2)).(8-3sqrt3)/(2-sqrt3) is equal to 19k, then find k.

Let f: Rto R be by f(x)=(x-1)(x-2)(x-5). Define F(x)=int_(0)^(x)f(t)dt,xgt0 Then which of the following options is/are correct ?

Evaluate P (AnnB)if 2P(A)=P(B)=5/13and P(A/B)=2/5.

Integrate the following functions x/(9-4x^2)

Find the area enclosed by y^2=x^3,x=0,y=1

Evalute the following integrals int (1)/(x^(2)) tan^(-1) xdx

The value of int_(0)^(4) 3^(sqrt(2x+1) )dx is

The value of sum_(r = 1)^15 r^2 ((""^15C_r)/(""^15C_(r - 1)) ) of is equal to

Let the circle (x - 1)^(2) + (y - 1)^(2) = 25 cuts a rectangular with transverse axis along y = x at four points A, B, C and D having co-ordinates (x_(1) , y_(1)) : i = 1,2,3,4 respectively O being the centre of the hyperbola, Now match the entries from the following two columns

Integrate the following functions 1/sqrt(7-6x-x^2)

The sum of the series 1/1.2 - 1/2.3 + 1/3.4 … upto infty is equal to

The numbers of terms of the A.P 3, 7, 11, 15, …… to be taken so that the sum is 406 is

The area bounded by the curves y=|x|-1 and y= -|x|+1 is

One compartment of a purse contains three 25 paise coins and 2 one rupee coins and the other compartment contains two 25 ps. Coins and 3 one rupee coins. The probability of drawing a rupee from the purse is

If x+y+z=180^(@) then (sinx+siny+sinz)/("cos"x/2."cos"y/2."cos"z/2)=

Integrate the following intcos(2-7x)dx

Evaluate int(1-cos2x)/(1+cos2x)dx.

(1+i)^(6)+(1-i)^(6)=

' lim_ (x to 0) (a^(x)-b^(x))/(e^(x)-1) is equal to

int_(0)^((pi)/(2))(f(sinx))/(f(cosx)+f(sinx))dx is :

If P(A)=(6)/(11), P(B)=(5)/(11) amd P(A cup B)=(7)/(11), find (i) P(A cup B) (ii) P(A|B) (iii) P(B|A)

Statement :1 If A nad B are two fixed points and P is any point such that PA + PB =k then locus of P is an ellipse. Because Statemet :2 In any ellipse with foci at A and B is PA + PB =k.

A particle is thrown with 12 m/s in positive X direction while acceleration is 2 m//s^2 in negative X direction then distance travelled by particle between t=5 to t=7 sec is

Solve the following equations, using inverse of a matrix : {:(2x+y+z=1),(2x-4y-2x=3),(3y-5z=9):}

Evaluate the integral underset(0)overset(pi//2)int tan^(5)x cos^(8)x dx

Obtain the general solution of the following differential equations.dy/dz=sqrt(1-y^2)/sqrt(1-z^2)

Integrationof certainirrational expressions I=int(dx)/(x(2+3sqrt((x-1)/(x)))).

State whether the points A(3, 2), B(-4,-3) lie on the same side or opposite sides of the line 2x - 3y +4 = 0.

Integrate the following functions : e^(x)((2+sin2x)/(1+cos2x))

Let O be a point inside DeltaABC such that angleOAB = angleOBC = angle OCA = theta Area of DeltaABC is equal to

If n(A)=n then n{(x,y,z),x,y,z in A ,x ne y, y ne z ,zne x}=

The vector equation of the line of intersection of the planes vecr=vecb+lamda_1 (vecb-veca) + mu_1 (veca-vecc) and vecr=vecc+lamda_2(vecb-vecc)+mu_2(veca+vecb) veca,vecb,vecc being non - coplanar vectors, is