28278 + Interview Questions in Maths in Class 12 Page 182 InterviewSolution

9051.	The standard deviation of a,a + d,a + 2d……,a + 2nd is
Answer» nd `N^(2) d` `sqrt((n(n + 1))/(3))d` `sqrt((n(n + 3))/(3)) d` ANSWER :c

Discussion

9052.	Which of thefollowing statements is correct with respect to colloidal state and surface phenomenon.
Answer» GOLD sol can be COAGULATED by SO `._(4)^(2-)ion`. `Sb_(2)S_(3)` sol can be coagulatedby adding `FE(OH)_(3)` sol. Adsorption processes are ENTROPY DRIVEN process always. At very high pressures, adsorption increases with pressure. Solution :`Sb_(2)S_(3)` is the negatively charged sol.

Discussion

9053.	x= f(t), y= phi (t) then (d^(2)y)/(dx^(2))= ……..
Answer» `(f_(1) (t) phi_(2) (t)- phi_(1) (t) f_(2) (t))/((f_(1) (t))^(2))` `(f_(1) (t) phi_(2) (t)- phi_(1) (t) f_(2) (t))/((f_(1) (t))^(3))` `(phi_(1) (t) f_(2) (t) - f_(1) (t) phi_(2) (t))/((f_(1) (t))^(3))` None of these Answer :B

Discussion

9054.	Integration using rigonometric identities : int cos^(-(3)/(7))x sin^(-(11)/(7))x dx=....
Answer» `log\|sin^((4)/(7))x\|+c` `(4)/(7)tan^((4)/(7))x+c` `-(7)/(4) tan^((4)/(7))x+c` `log\|cos^((3)/(7))x\|+c` Answer :C

Discussion

9055.	Six boys and six girls sit at a round table. The probability that the boys and girls sit alternatively is
Answer» `(1)/(462)` `(2)/(462)` `(1)/(460)` `(3)/(460)` Answer :A

Discussion

9056.	Find the angle between the lines barr=3bari-2barj+6bark+lambda(2bari+barj+2bark) and barr=(2barj-5bark)+mu(6bari+3barj+2bark).Hint for solution : Angle between line barr=a_1+lambda barb_1 and r=bara_2+mubarb_2 then angle between them is obtained from cos theta=(\|b_1.b_2\|)/(\|b_1\|.\|b_2\|).
Answer» ANSWER :`=COS^(-1)((19)/(21))`

Discussion

9057.	Find the value of log (- theta) and hence the value of log (- 10 theta).
Answer» `PI i` `1 +pi i` `1 - pi i` `-1 - pi i` ANSWER :B

Discussion

9058.	If A=[(1,2,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)] and C=[(4,1,2),(0,3,2),(1,-2,3)], then compute (A+B) and (B-C). Also, verify that A+(B-C)=(A+B)-C.
Answer» ANSWER :`A+B=[(4,1,-1),(9,2,7),(3,-1,4)],B-C=[(-1,-2,0),(4,-1,3),(1,2,0)]`

Discussion

9059.	Find the number of ways of arranging the letters of the word 'SHIPPING' SUCH' that 2P's do not come together
Answer» ANSWER :7560

Discussion

9060.	Find the area of the region lying in the first quadrant and bounded by y=4x^2, x=0,y=1 and y=4.
Answer» Solution :The REQUIRED AREA `=overset5underset1intxdy` `=overset4underset1intsqrty/2 DY(y=4x^2rArrx^2=y/4rArrx=sqrty/2)` `1/2[y^(3//2)/(3//2)]_1^4=1/3[4^(3//2)-1^(3//2)]` `=1/3[2^3-1]=7/3`sq.units

Discussion

9061.	If vec(a) = xhat(i) + yhat(j) + zhat(k), vec(b) = yhat(i) + zhat(j) + xhat(k) and vec(c) = zhat(i) + xhat(j) + yhat(k), then vec(a) xx (vec(b) xx vec(c)) is
Answer» PARALLEL to`(y -Z )HAT(i)+ (z - X)hat(j) + (x-y)hat(k)` orthogonal to `hat(i) + hat(j) + hat(k)` orthogonal to `(y + z) hat(i) + (z+x)hat(j) + (x + y )hat(k)` orthogoanl to `xhat(i) + yhat(j) + zhat(k)` Answer :A::B::C::D

Discussion

9062.	Evaluate the following integrals int x cos x dx
Answer» ANSWER :`X SIN x + COSX + C`

Discussion

9063.	If int(e^(4x)-1)/(e^(2x))log((e^(2x)+1)/(e^(2x-1)))dx=(t^(2))/(2)logt-(t^(2))/(4)-(u^(2))/(2)logu+(u^(2))/(4)+C, then
Answer» `u=e^(x)+e^(-x)` `u=e^(x)-e^(-x)` `t=e^(x)+e^(-x)` `t=e^(x)-e^(-x)` SOLUTION :`I=INT{(e^(2x)-e^(-2x))ln(e^(x)+e^(-x))-(e^(2x)-e^(-2x))ln(e^(x)-e^(-x))}DX` `=int tln t DT- int u ln u du ("where t"=e^(x)+e^(-x) and u=e^(x)-e^(-x))` `=(t^(2))/(2)ln t-(t^(2))/(4)-(u^(2))/(2)ln u+(u^(2))/(4)+C`

Discussion

9064.	B and C are two points on the circle x^2+y^2=a^2point A (b,c)lies on that circle such that AB = AC = d, then the equation of the line harr(BC) is
Answer» `bx+ay=a^2-d^2` `bx+ay=d^2-a^2` `2(bx+cy)=2a^2-d^2` `2(bx+ay)=2a^2-d^2` ANSWER :C

Discussion

9065.	Let T be the line passing the points P(–2, 7) and Q(2,–5). Let F_(1) be the set of all pairs of circles (S_(1), S_(2)) such that T is tangent to S_(1) at P and tangent to S_(2) at Q, and also such that S_(1) and S_(2) touch each other at a point, say M. Let E_(1) be the set representing the locus of M as the pair (S_(1), S_(2)) varies in F_(1). Let the set of all straight line segments joining a pair of distinct points of E_(1) and passing through the point R(1,1,) be F_(2). Let E_(2) be the set of the mid-points of the line segments in the set F_(2). Then, which of the following statment(s) is (are) TRUE ?
Answer» The point (–2,7) LIES in `E_(1)` The point `((4)/(5), (7)/(5))` does NOTlie in `E_(2)` The point `((1)/(2), 1)` lies in `E_(2)` The point `(0, (3)/(2))` does NOTlie in `E_(1)` Answer :D

Discussion

9066.	lim_(theta rarr 0) ("cosec" theta - cot theta)/(theta) is :
Answer» `(-1)/(2)` `OO` `(1)/(2)` 0 Answer :C

Discussion

9067.	If A= [[-1,2,3],[5,7,9],[-2,1,1]] and B=[[-4,1,-5],[1,2,0],[-1,3,1]] then verify that (A+B)^T=A^T +B^T
Answer» SOLUTION :`A-B=[[3,1,8], [4,5,9], [-1,-2,0]]` `(A-B)^T=[[3,4,-1], [1,5,-2], [8,9,0]]` `A^T-B^T=[[3,4,-1], [1,5,-2], [8,9,0]]` THEREFORE `(A-B)^T=A^T-B^T`

Discussion

9068.	If A^T=[[3,4],[-1,2],[0,1]] and B=[[-1,2,1],[1,2,3]] then verify that (A-B)^T=A^T-B^T
Answer» SOLUTION :`A-B=[[4,-3,-1],[3,0,-2]]` `(A-B)^T =[[4,3],[-3,0],[-1,-2]]` `A^T-B^T =[[4,3],[-3,0],[-1,-2]]` THEREFORE `(A-B)^T=A^T-B^T`

Discussion

9069.	If p and q are chosen randomly from the set {1, 2, 3, 4, 5} with replacement. Find the probability that the roots of the equation x^(2) + px + q = 0 are equal.
Answer» ANSWER :`(2)/(25)`

Discussion

9070.	If a = (1,1,1) c = (0,1, -1) are given vectors then a vector b satisfying the equntions a xx b = c and a.b= 3 is
Answer» 5I + 2J + 2k `(5)/(2)I + j + k` `(5)/(3)I (2)/(3)j + (2)/(3)K` `I + (2)/(5)j + (2)/(5) k` Answer :C

Discussion

9071.	Integrate the following functions sin(ax+b) cos(ax+b).
Answer» Solution :SIN(ax+b) cos(ax+b) =1/2 sin(2(ax+b)) = 1/2 sin(2ax+2b) THEREFORE `int sin (ax+b) cos (ax+b) dx` =`1/2 xx - (cos(2ax+2b))/(2a) +c` = `-1/(4a) cos(2ax+2b)+c` `sin THETA cos theta = 1/2 SIN2THETA`

Discussion

9072.	Find the sum if Ist n terms of the series 3,6,15,42,123……
Answer» ANSWER :`((6n+3)(3^(N)-1))/4`

Discussion

9073.	Let B_(1),C_(1) and D_(1) are points on AB, AC and AD of the parallelogram ABCD, such that bar(AB_(1))=k_(1)bar(AB),bar(AC_(1))=k_(2) bar(AC) and bar(AD_(1))=k_(3) bar(AD), where k_(1),k_(2) and k_(3) are scalar. Statement 1: k_(1),2k_(2) and k_(3) are in harmonic progression. If B_(1),C_(1) and D_(1) are collinear. because Statement 2: (bar(AB_(1)))/(k_(1))+(bar(AD_(1)))/(k_(3))=(bar(AC_(1)))/(k_(2)).
Answer» STATEMENT - 1 is True, Statement -2 is True, Statement-2 is a 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 True ANSWER :A

Discussion

9074.	Obtain following definite integrals : overset(pi) underset(0) int x sin x cos^(2)x dx
Answer» ANSWER :`:. I=(PI)/(3)`

Discussion

9075.	If (e^(x) -1)^(2) =a_0 +a_(1)x +a_(2) x^2 + ......oothen a_4 =
Answer» `5/12` `7/12` `9/7` 0 Answer :B

Discussion

9076.	Using differentials, find the approximate value of : root5(33).
Answer» ANSWER :2.0125

Discussion

9077.	Let f(x)={(e^({x^(2)})-1,xgt1),((sinx-tanx+cosx-1)/(2x^(2)+In(2+x)+tanx),xlt0),(0,x=0):} where { } represents fractional part function. Suppose lines L_(1) andL_(2) represent tangent and normal to curve y=f(x) at x=0. Consider the family of circles touching both the lines L_(1) and L_(2) A circle having radius unity is inscribed in the triangle formed by L_(1) and L_(2) and a tangent to it. Then the minimum area of the triangle possible is
Answer» `3+sqrt(2)` `2+sqrt(3)` `3+2sqrt(2)` `3-2sqrt(2)` ANSWER :B::C

Discussion

9078.	Let f(x)={(e^({x^(2)})-1,xgt1),((sinx-tanx+cosx-1)/(2x^(2)+In(2+x)+tanx),xlt0),(0,x=0):} where { } represents fractional part function. Suppose lines L_(1) andL_(2) represent tangent and normasl to curve y=f(x) at x=0. Consider the family of circles touching both the lines L_(1) and L_(2) If centres of circles belonging to family having equal radii r joined, the area of figure formed is
Answer» `2r^(2)` `4R^(2)` `8r^(2)` `R^(2)` Answer :A::B::D

Discussion

9079.	Let f(x)={(e^({x^(2)})-1,xgt1),((sinx-tanx+cosx-1)/(2x^(2)+In(2+x)+tanx),xlt0),(0,x=0):} where { } represents fractional part function. Suppose lines L_(1) andL_(2) represent tangent and normal to curve y=f(x) at x=0. Consider the family of circles touching both the lines L_(1) and L_(2) Ratio of radii of two circles belonging to his family cutting each other orthogonally is
Answer» `2+SQRT(3)` `sqrt(3)` `2+sqrt(2)` `2-sqrt(2)` ANSWER :B::C

Discussion

9080.	A furniture manufacturing company plans to make two prodcuts cvhairs and tables form its availabelresourcesof 400 boardfeet of mahogany lumber and 450 man hours A chairrequires 5 boardfeet of lumber and 10 man hours and yields a profitof Rs 45 while eachtabel uses 20 board feet of lumberadn 15man hours and a profit of Rs 80 formulate the problem as an LPPto maximize profit [1 board feet =1/12 cubic feet ]
Answer» ANSWER :A::B::C::D

Discussion

9081.	Let f:D rarr R, D sube R , c in Dand r be a non zero real number. Consider the following statements : I. c is an extreme point of f rArr cis an extremepoint of rf II. cis anextreme point of f rArrcis an extreme point of r+f Which of the following is correct ?
Answer» Only (i) is true Only (II) is true Both (i) and (ii) are true Neither (i) nor (ii) is true Answer :C

Discussion

9082.	Amongst the several applications of maxima and minima oneof the application find the largest term of a sequence . Let {a_(n)} be a sequence . Considerf(x) obtained on replacing x by n,e.g let a_(n)=(n)/(n+1). Consider f(x) =(x)/(x+1) on [1,oo),f'(x)=(1)/((x+1)^(2))gt0 For all x. Hence max f(x)=underset(xtooo)limf(x)=1The largest term of a_(n)=(n^(2))/(n^(3)+200)is -
Answer» `(29)/(453)` `(49)/(543)` `(43)/(543)` `(41)/(451)` ANSWER :B

Discussion

9083.	Amongst the several applications of maxima and minima oneof the application find the largest term of a sequence . Let {a_(n)} be a sequence . Considerf(x) obtained on replacing x by n,e.g let a_(n)=(n)/(n+1). Consider f(x) =(x)/(x+1) on [1,oo),f'(x)=(1)/((x+1)^(2))gt0 For all x. Hence max f(x)=underset(xtooo)limf(x)=1The largest term of sequence a_(n)=(n)/((n^(2)+10)) is -
Answer» `(3)/(19)` `(2)/(13)` 1 `(1)/(7)` ANSWER :A

Discussion

9084.	If f(x) =int_(1//x^(2) ) ^(x^2) cos sqrt(t) dt, then f'(1) is equal to
Answer» `COS 1` `2 cos 1` `4 cos 1` none of these Answer :C

Discussion

9085.	Amongst the several applications of maxima and minima oneof the application find the largest term of a sequence . Let {a_(n)} be a sequence . Considerf(x) obtained on replacing x by n,e.g let a_(n)=(n)/(n+1). Consider f(x) =(x)/(x+1) on [1,oo),f'(x)=(1)/((x+1)^(2))gt0 For all x. Hence max f(x)=underset(xtooo)limf(x)=1If f(x) is the function required to find largset term in ques . (i) then -
Answer» F INCREASES for all x f decreases for all x f has a maximum at `x=root(3)(400)` f increases on [0,9] ANSWER :C

Discussion

9086.	Functional Equations: A functional equation is an equation, which relates the values assumed by a function at two or more points, which are themselves related in a particular manner. For example, we define an odd function by the relation f(-x)=-f(x) for all x. This definition can be paraphrased to say that it is a function f(x), which satisfies the functional relation f(x)+f(y)=0, whenever x+y=0. Of course, this does not identify the function uniquely, sometimes with someadditional information, a function satisfying a given functional can be identified uniquely. Suppose a functional equation has a relation between f(x) and f((1)/(x)), then due to the reason that reciprocal of a reciprocal gives back the original number, we can substitute 1/x for x. This will result into another equation and solving these two, we can find (x) uniquely. Similarly, we can solve an equation, which contains f(x) and f(-x). Such equations are of repetitive nature. If for every x in R, the function f(x) satisfies the relation af(x)+bf(-x)=g(x), then
Answer» f(x) can be uniquely determined if `ag(x)-BG(-x)ne0 and a=pm b` f(x) can have infinitely MANY values if `ag(x)-bg(-x)=0 and a pm b` f(x) cannot be determined if `a NE pm b` all of these Answer :B

Discussion

9087.	Prove that (i) sin^(2)0lt 0sin(sin)) for 0lt0ltpi/2 (ii) cos(sinx)gt sin(cosx),0ltxltpi/2.(iii) (a+b)^(p) lea^(p), a, bgt0,0ltplt1.
Answer»

Discussion

9088.	Let f (x) =1+ int _(0) ^(1) (xe ^(y) + ye ^(x)) f (y) dy where x and y are independent vartiables. If complete solution set of 'x' for which function h (x) = f(x) +3x is strictly increasing is (-oo, k) then [(4) e ^(k/3) ] equals to: (where [.] denotes greatest integer function):
Answer» 1 2 3 4 Answer :C

Discussion

9089.	The value of int_((-pi)/(2))^((pi)/(2))(x^(3)+xcosx+tan^(5)x+1)dx is
Answer» 0 2 `PI` 1 Answer :C

Discussion

9090.	Functional Equations: A functional equation is an equation, which relates the values assumed by a function at two or more points, which are themselves related in a particular manner. For example, we define an odd function by the relation f(-x)=-f(x) for all x. This definition can be paraphrased to say that it is a function f(x), which satisfies the functional relation f(x)+f(y)=0, whenever x+y=0. Of course, this does not identify the function uniquely, sometimes with someadditional information, a function satisfying a given functional can be identified uniquely. Suppose a functional equation has a relation between f(x) and f((1)/(x)), then due to the reason that reciprocal of a reciprocal gives back the original number, we can substitute 1/x for x. This will result into another equation and solving these two, we can find (x) uniquely. Similarly, we can solve an equation, which contains f(x) and f(-x). Such equations are of repetitive nature. Suppose that for every x ne 0," af"(x)+bf((1)/(x))=(1)/(x)-5, where abe b then the value of the integral int_(1)^(2)f(x)dx is
Answer» `(2a LN 2-10a+7b)/(2(a^(2)-B^(2)))` `(pi)/(2sqrt2)` `(7a+10b2aln2)/(2(a^(2)-b^(2)))` NONE of these Answer :A

Discussion

9091.	Functional Equations: A functional equation is an equation, which relates the values assumed by a function at two or more points, which are themselves related in a particular manner. For example, we define an odd function by the relation f(-x)=-f(x) for all x. This definition can be paraphrased to say that it is a function f(x), which satisfies the functional relation f(x)+f(y)=0, whenever x+y=0. Of course, this does not identify the function uniquely, sometimes with someadditional information, a function satisfying a given functional can be identified uniquely. Suppose a functional equation has a relation between f(x) and f((1)/(x)), then due to the reason that reciprocal of a reciprocal gives back the original number, we can substitute 1/x for x. This will result into another equation and solving these two, we can find (x) uniquely. Similarly, we can solve an equation, which contains f(x) and f(-x). Such equations are of repetitive nature. In the functional equation given in previous question, if a+b=0, then f(x) is equal to
Answer» 0 `(X-(1)/(x))/(2A)` `(x+(1)/(x))/(2a)` not possible Answer :D

Discussion

9092.	If -1 +iis arootofx^4 + 4x^3 + 5x^2 + k=0 thenits realrootsare
Answer» `-1,-1` `-1/2,-3/2` `-1 +- SQRT(2)` `1+- sqrt(2)` ANSWER :C

Discussion

9093.	A college student has to appear for two examinations A and B. The probabilities that the student passes in A and B are (2)/(3) and (3)/(4) respectively. If it is known that the student passes at least one among the two examinations, then the probability that the student will pass both the examination is
Answer» `(1)/(6)` `(1)/(2)` `(1)/(3)` `(6)/(11)` Answer :D

Discussion

9094.	Find the value of k if f(x)= {(kx^(2),if x le 2),(3, if x gt2):} is continuous at x=2
Answer» ANSWER :`K= (3)/(4)`

Discussion

9095.	Evaluate{:\|(1,x,y),( 1,x+y,y),( 1,x,x+y)\|:}
Answer» ANSWER :XY

Discussion

9096.	Prove that the line of intersection of x + 2y + 3z=0 and 3x + zy+ z=0 is equally inclined to the X and Z axes and that it makes an angletheta with the Y-axis where sec 2 theta=3.
Answer» ANSWER :7

Discussion

9097.	The locus of foot of perpendicular from the focus upon any tangent to the parabola y^(2) = 4ax is
Answer» `l_(1),l_(2),l_(3) ` are in G.P `l_(2),l_(1),l_(3)` are in G.P `l_(3),l_(1),l_(2)` are in A.P `l_(3),l_(2),l_(1)` are in A.P Answer :B

Discussion

9098.	Solve (x^(3)+3xy^(2))dx+3x^(2)y)dy=0
Answer» ANSWER :C

Discussion

9099.	Does there exist an integer such that its cube is equal to 3n^(2) + 3n + 7, n in I ?
Answer» ANSWER :No

Discussion

9100.	If the line y=4x-5 touches to the curve y^2=ax^3+b at the point (2,3) then 7a+2b=
Answer» 0 1 -1 2 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The standard deviation of a,a + d,a + 2d……,a + 2nd is

Which of thefollowing statements is correct with respect to colloidal state and surface phenomenon.

x= f(t), y= phi (t) then (d^(2)y)/(dx^(2))= ……..

Integration using rigonometric identities : int cos^(-(3)/(7))x sin^(-(11)/(7))x dx=....

Six boys and six girls sit at a round table. The probability that the boys and girls sit alternatively is

Find the angle between the lines barr=3bari-2barj+6bark+lambda(2bari+barj+2bark) and barr=(2barj-5bark)+mu(6bari+3barj+2bark).Hint for solution : Angle between line barr=a_1+lambda barb_1 and r=bara_2+mubarb_2 then angle between them is obtained from cos theta=(|b_1.b_2|)/(|b_1|.|b_2|).

Find the value of log (- theta) and hence the value of log (- 10 theta).

If A=[(1,2,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)] and C=[(4,1,2),(0,3,2),(1,-2,3)], then compute (A+B) and (B-C). Also, verify that A+(B-C)=(A+B)-C.

Find the number of ways of arranging the letters of the word 'SHIPPING' SUCH' that 2P's do not come together

Find the area of the region lying in the first quadrant and bounded by y=4x^2, x=0,y=1 and y=4.

If vec(a) = xhat(i) + yhat(j) + zhat(k), vec(b) = yhat(i) + zhat(j) + xhat(k) and vec(c) = zhat(i) + xhat(j) + yhat(k), then vec(a) xx (vec(b) xx vec(c)) is

Evaluate the following integrals int x cos x dx

If int(e^(4x)-1)/(e^(2x))log((e^(2x)+1)/(e^(2x-1)))dx=(t^(2))/(2)logt-(t^(2))/(4)-(u^(2))/(2)logu+(u^(2))/(4)+C, then

B and C are two points on the circle x^2+y^2=a^2point A (b,c)lies on that circle such that AB = AC = d, then the equation of the line harr(BC) is

lim_(theta rarr 0) ("cosec" theta - cot theta)/(theta) is :

If A= [[-1,2,3],[5,7,9],[-2,1,1]] and B=[[-4,1,-5],[1,2,0],[-1,3,1]] then verify that (A+B)^T=A^T +B^T

If A^T=[[3,4],[-1,2],[0,1]] and B=[[-1,2,1],[1,2,3]] then verify that (A-B)^T=A^T-B^T

If p and q are chosen randomly from the set {1, 2, 3, 4, 5} with replacement. Find the probability that the roots of the equation x^(2) + px + q = 0 are equal.

If a = (1,1,1) c = (0,1, -1) are given vectors then a vector b satisfying the equntions a xx b = c and a.b= 3 is

Integrate the following functions sin(ax+b) cos(ax+b).

Find the sum if Ist n terms of the series 3,6,15,42,123……

Obtain following definite integrals : overset(pi) underset(0) int x sin x cos^(2)x dx

If (e^(x) -1)^(2) =a_0 +a_(1)x +a_(2) x^2 + ......oothen a_4 =

Using differentials, find the approximate value of : root5(33).

Let f:D rarr R, D sube R , c in Dand r be a non zero real number. Consider the following statements : I. c is an extreme point of f rArr cis an extremepoint of rf II. cis anextreme point of f rArrcis an extreme point of r+f Which of the following is correct ?

If f(x) =int_(1//x^(2) ) ^(x^2) cos sqrt(t) dt, then f'(1) is equal to

Prove that (i) sin^(2)0lt 0sin(sin)) for 0lt0ltpi/2 (ii) cos(sinx)gt sin(cosx),0ltxltpi/2.(iii) (a+b)^(p) lea^(p), a, bgt0,0ltplt1.

Let f (x) =1+ int _(0) ^(1) (xe ^(y) + ye ^(x)) f (y) dy where x and y are independent vartiables. If complete solution set of 'x' for which function h (x) = f(x) +3x is strictly increasing is (-oo, k) then [(4) e ^(k/3) ] equals to: (where [.] denotes greatest integer function):

The value of int_((-pi)/(2))^((pi)/(2))(x^(3)+xcosx+tan^(5)x+1)dx is

If -1 +iis arootofx^4 + 4x^3 + 5x^2 + k=0 thenits realrootsare

Find the value of k if f(x)= {(kx^(2),if x le 2),(3, if x gt2):} is continuous at x=2

Evaluate{:|(1,x,y),( 1,x+y,y),( 1,x,x+y)|:}

Prove that the line of intersection of x + 2y + 3z=0 and 3x + zy+ z=0 is equally inclined to the X and Z axes and that it makes an angletheta with the Y-axis where sec 2 theta=3.

The locus of foot of perpendicular from the focus upon any tangent to the parabola y^(2) = 4ax is

Solve (x^(3)+3xy^(2))dx+3x^(2)y)dy=0

Does there exist an integer such that its cube is equal to 3n^(2) + 3n + 7, n in I ?

If the line y=4x-5 touches to the curve y^2=ax^3+b at the point (2,3) then 7a+2b=