28278 + Interview Questions in Maths in Class 12

1.	Everybody in a room shakes hand with everybody else. The total number of handshakes is 66. The total number of persons in the room is :
Answer» 9 10 5 15 Answer :B

Discussion

2.	Examine the consistency of the system of linear equtions in 1 to 6 5x-y+4z=5 2x+3y+5z=2 5x-2y+6z=-1
Answer» ANSWER :`51 NE 0`

Discussion

3.	Evalute the following integrals int e^(x) ((cos x - sin x)/(1 - cos 2 x ))dx
Answer» Answer :`- (E^(x))/(2) "COSEC" x + C`

Discussion

4.	If N denotes the set of all positive integers and if f : N to N is defined byf(n) = the sum of positive divisors of n then, f(2^(k)3), where k is a positive integer, is
Answer» `2^(k+1)-1` `2(2^(k+1)-1)` `3(2^(k+1)-1)` `4(2^(k+1)-1)` ANSWER :D

Discussion

5.	Let X be a random variable such that P(X=-2)=P(X-1)=P(X=2)=P(X=1)=(1)/(6) and P(X=0)=(1)/(3). Find the mean and variance of X.
Answer» ANSWER :`=(5)/(3)`

Discussion

6.	The measure of dispersion which is used to find more consistent data is
Answer» STANDARD DEVIATION MEAN deviation Quartile deviation Range Answer :A

Discussion

7.	13 persons sit a round a table. Find the odds in favour of two specified persons sitting together.
Answer» ANSWER :`1 : 5`

Discussion

8.	Match column I & II. {:(,"Column-I",,"Column-II"),((a),"Monophyodont teeth",(1),(2)/(2)","(1)/(1)","(0)/(0)","(2)/(2)),((b),"Adolescence teeth",(2),(2)/(2)","(1)/(1)","(2)/(2)","(2)/(2)),((c),"Adult teeth",(3),(2)/(2)","(1)/(1)","(2)/(2)","(3)/(3)),((d),"Child teeth",(4),(0)/(0)","(0)/(0)","(2)/(2)","(1)/(1)):}
Answer» a-1, b-3, c-2, d-4 a-4, b-2, c-3, d-1 a-1, b-4, c-2, d-3 a-2, b-4, c-3, d-1 Answer :A

Discussion

9.	Find the numerically greatest term in the expansion of (2+5x)^(21) when x =2/5.
Answer» ANSWER :`T_(11) = T_(12)= .^(21)C_(10) 2^(21)`

Discussion

10.	Calculate the area of the triangle ABC (by vector method) where A(1,1,2), B(2,2,3), C(3,-1,-1)
Answer» Solution : =`-hati+5hatj-4hatk` Area of `TRIANGLE ABC` =`1/2 sqrt(1+25+16) = sqrt(42)/2` SQ. UNITS.

Discussion

11.	L (1, 3) and L^(1) = (1, -1) are the ends of latus rectum of a parabola, then area of quadrilateral formed by tangents and normals at L and L^(1) ( in Square Units ) is
Answer» 2 4 8 16 Answer :C

Discussion

12.	Evaluate lim_(n rarr oo)(2^(k) + 4^(k) + 6^(k)+…+(2n)^(k))/(n^(k+1)) by using the method of finding definite integral as the limit of a sum.
Answer» ANSWER :`(2^(K))/(k+1)`

Discussion

13.	Match the following lists:
Answer» Solution : a. Hence, `agt0`. Therfore. `UNDERSET(xtooo)lim("("sqrt("("x^(2)-x+1")")-ax-b")""("sqrt(x^(2)-x+1")")+ax+b")")/("("sqrt("("x^(2)-x+1")")+ax+b")")` `=0` or `underset(xtooo)lim((x^(2)-x+1)-(ax+b)^(2))/(sqrt((x^(2)-x+1))+ax+b)=0` or `underset(xtooo)lim((1-a^(2))x^(2)-(1+2ab)x+(1-b^(2)))/(sqrt((x^(2)-x+1))+ax+b)=0` or `underset(xtooo)lim((1-a^(2))x-(1+2ab)+((1-b^(2)))/(x))/(sqrt(1-(1)/(x)+(1)/(x^(2))+a+(b)/(x)))=0` This is POSSIBLE only when `1-a^(2)=0" and "1+2ab=0` `:.""a=+-1` or `a=1""(becauseagt0)""(1)` `:.""b=-1//2` `:.""(a,2b)-=(1,-1)` b. Divide numerator and denominator by `e^(1//x)`. Then, `underset(xtooo)lim((1+a^(3))e^(-(1)/(x))+8)/(e^(-(1)/(x))+(1-b^(3)))=2` or `(0+8)/(0+1-b^(3))=2` or `""1-b^(3)=4` `:.""b^(3)=-3" or "b=-3^(1//3)` Then, `ainR.` Therefore, `(a,b^(3))-=(a,-3)` c. `underset(xtooo)lim"("sqrt("("x^(4)-x^(2)+1)")"-ax^(2)-b")"=0` Put `s=(1)/(t)`.Then `underset(t TO0)lim(sqrt(((1)/(t^(4))-(1)/(t^(2))+1))-(a)/(t^(2))-b)=0` or `underset(t to0)lim(sqrt((1-t^(2)+t^(4)))-a-bt^(2))/(t^(2))=0""(1)` Since R.H.S. is finite, numerator must be equal to 0 at `t to0.` Therefore,`1-a=0" or "a=1.` From equation (1), `underset(t to0)lim(sqrt((1-t^(2)+t^(4)))-1-bt^(2))/(t^(2))=0` `underset(t to0)lim(-1+t^(2))(((1-t^(2)+t^(4))^(1//2)-(1)^(1//2))/((1-t^(2)+t^(4))-1))=b` or `(-1)((1)/(2))=b" or "a=1,b=-(1)/(2)" or "(a,-4b)-=(1,2)` d. `underset(xto-a)lim(x^(7)-(-a)^(7))/(x-(-a))=7" or "7a^(6)=7" or "a^(6)=1" or "a=-1`

Discussion

14.	Match the following lists:
Answer» Solution : a. `LET" x"+1=H`. Then, `underset(xto-1)lim(root(3)((7-x))-2)/((x+1))=underset(hto0)lim((8-h)^(1//3)-2)/(h)` `=underset(hto0)lim(2(1-(h)/(8))^(1//3)-2)/(h)` `=2underset(hto0)lim((1-(1)/(3)(h)/(8))-1)/(h)` `=-(1)/(12)` b. We have `underset(xto pi//4)lim(tan^(3)x-TANX)/(cos(x+pi//4))` `=underset(xto pi//4)lim(tanx(tanx-1)(tanx+1))/(cos(x+pi//4))` `=underset(xto pi//4)lim(tanx(sinx-cosx)(tanx+1))/(cosxcos(x+pi//4))` `=-underset(xto pi//4)lim(tanx(cosx-sinx)(tanx+1))/(cosxcos(x+pi//4))` `=-sqrt(2)underset(xto pi//4)lim(tanx((1)/(sqrt(2))cosx-(1)/(sqrt(2))sinx)(tanx+1))/(cosxcos(x+pi//4))` `=-sqrt(2)underset(xto pi//4)lim(tanx(tanx+1))/(cosx)` `=-sqrt(2)xx2xxsqrt(2)=-4` `underset(xto1)lim((2x-3)(sqrt(x-1)))/(2x^(2)+x-3)=underset(xto1)lim((2x-3)(sqrt(x)-1))/((2x+3)(x-1))` `=underset(xto1)lim((2x-3)(sqrt(x)-1))/((2x+3)(sqrt(x)-1)(sqrt(x)+1))` `=underset(xto1)lim((2x-3))/((2x+3)(sqrt(x)+1))` `=(2-3)/((2+3)(sqrt(1)+1))=-1//10` d. `underset(xtooo)lim(LOGX^(n)-[x])/([x])=underset(xtooo)lim(logx^(n))/([x])-underset(xtooo)lim([x])/([x])` `=0-1=-1`

Discussion

15.	Match the following lists:
Answer» Solution : We know that `underset(xto0)lim(sinx)/(x)=1` (but a VALUE is smaller than 1) or `[underset(xto0)lim100(sinx)/(x)]=99` and `[underset(xto0)lim100(x)/(sinx)]=100` ALSO, `underset(xto0)lim(sin^(-1)x)/(x)=1""`(but a value is more than 1) or `[underset(xto0)lim100(sin^(-1)x)/(x)]=100` and `[underset(xto0)lim100(x)/(sin^(-1)x)]=99` `underset(xto0)lim(tanx)/(x)=1""`(but a value is bigger than 1) or `[underset(xto0)lim100(tanx)/(x)]=100` and `[underset(xto0)lim100(tan^(-1)x)/(x)]=99` Hence, a. `underset(xto0)lim([100(sinx)/(x)]+[100(tanx)/(x)])=199` b. `underset(xto0)lim([100(x)/(sinx)]+[100(tanx)/(x)])=200` c. `underset(xto0)lim([100(sin^(-1)x)/(x)]+[100(tan^(-1)x)/(x)])=199` d. `underset(xto0)lim([100(x)/(sin^(-1)x)]+[100(tan^(-1)x)/(x)])=198`

Discussion

16.	Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of
Answer» p+q+r=0 `p^(2)+q^(2)+r^(2)=pq+qr+rp` `p^(3)+q^(3)+r^(3)=3PQR` p+q-r=0 Answer :C

Discussion

17.	iff(x)= (x-1)/(x+1) thef(2x )is
Answer» `(F(X) +1)/(f(x) +3)` `(3f(x)+1)/(f(x) +3)` `(f(x)+3 )/(f(x) +1)` `(f(x)+3)/(3f(x)+1)` Answer :B

Discussion

18.	Using the identity sin^(4) x=3/8-1/2 cos 2x+1/8 cos 4x or otherwise, if the value of sin^(4)(pi/7)+sin^(4)((3pi)/(7))+sin^(4)((5pi)/(7))=a/b, where a and b are coprime, find the value of (a-b).
Answer» ANSWER :5

Discussion

19.	Find the probability of drawing 2 red balls in succession from a bag containing 4 red balls and 5 black balls when the ball that is drawn first is (i) not replaced (ii) replaced.
Answer» ANSWER :The first ball is REPLACED, `R_(1), R_(2)` are INDEPENDENT

Discussion

20.	int(e^(exlog_(e)x)+(log_(e)x)(e^(exlog_(e)x)))dx=...+c
Answer» `(x^(-EX))/(e)` `(x^(ex))/(e)` `-(x^(ex))/(e)` `LOG(x*e)` ANSWER :B

Discussion

21.	Compute the magnitude of the following vectors :veca=hati+hatj+k,vecb=2hati-7hatj-3hatk,vecc=(1)/(sqrt(3))hati+(1)/(sqrt(3))hatj-(1)/(sqrt(3))hatk
Answer» ANSWER :`VEC( C )=1`

Discussion

22.	intsec^(6//5) x. "cosec"^(4//5) x dx
Answer» ANSWER :`5(TANX)^(1//5) +C`

Discussion

23.	If ""^(12)P_r=1320 find r
Answer» ANSWER :r=3

Discussion

24.	If vecu=veca-vecb,vecv=veca+vecb and \|veca\|=\|vecb\|=2, then \|vecuxx vecc\| is :
Answer» `2sqrt(16 - (veca.vecb)^(2))` `2sqrt(4-(veca.vecb)^(2))` `SQRT(16-(veca.vecb)^(2))` `sqrt(4-(veca.vecb)^(2))` ANSWER :A

Discussion

25.	sin alpha=sinbeta, cos alpha=cos beta then
Answer» `SIN((alpha+beta)/2=0` `COS(((alpha+beta))/2)=0` `sin(((alpha-beta))/2)=0` `cos(((alpha-beta))/2)=0` Answer :C

Discussion

26.	Let x > - 1, then statement P(n) : (1 + x)^(n) > 1 + nx is true for
Answer» all `N in N` all `NGT1` all `ngt1` provided `XNE0` NONE of these Answer :C

Discussion

27.	Observe the following statements Assertion (A) : X is binomial variate with parameters 2n+1 and p = 1/2 then P(x = odd values) = 1/2 Reason ( R ) : If ""^(n)C_(r)=C_(r) then C_(1)+C_(3)+C_(5)+……=2^(n-1). Then
Answer» A is FALSE, R is TRUE A is true, R is true but `R cancelimpliesA` A is true, R is true and R `implies` A A is true, R is false ANSWER :C

Discussion

28.	if 2^((log_3 5)(log_x 81)-6(25)^(log_x^2)+8=0, then :-
Answer» NUMBER of solutions is 3 sum of solutions is 30 solutions are twin PRIME sum of solutions is 6

Discussion

29.	If I_(a) = int_(0)^(pi//4) tan^(n) theta d theta for n=1,2,3,…, then I_(n-1) + I_(n+1) is equal to
Answer» 0 1 `1/n` `(1)/(n+1` ANSWER :C

Discussion

30.	The two curves x^(3)-3xy^(2)+2=0 and 3x^(2)y-y^(3)-2=0:
Answer» 1)Touch each other 2)Cut each other at right angle 3)Cut at an angle `pi//3` 4)Cut at an angle `pi//4` Answer :B

Discussion

31.	The slope of tangent to the curve x=t^(2)+3t-8, y=2t^(2)-2t-5 at the point (2,-1) is …………..
Answer» `(22)/(7)` `(6)/(7)` `-(6)/(7)` `-6` ANSWER :B

Discussion

32.	If f:R to R is a differentible function such that f(x+y) = f (x). F(y) for all x,y in R and if f'(4) =24 and f'(0) = 3 then f(4) =
Answer» 72 5 11 8 Answer :D

Discussion

33.	Total number of 6 digited numbers in which all the odd digits and only odd digits appear is
Answer» `(5)/(2)ANGLE6` `angle6` `(1)/(2)angle6` `(5)/(2)angle5` ANSWER :A

Discussion

34.	Let f:[0,1] to Rbe an injective continuous function that satisfies the condition -1 lt f(0) lt f(1) lt 1 Then the number of functions g:[-1,1] to [0,1]such that (gof)x =xfor all x in [0,1] is
Answer» 0 1 more than 1, but finite infinite Solution :Only condition that g(x) should satisfy for`GOF(x)=x Aax in [0,1]` is that g(x) shold attain all VALUES in [0,1] when RANGE of f(x) s SUBSET of `(-1,1)` is used as image for g(x). Thus there can be infinite such functions g(x) with domain [-1,1] and range [0,1]

Discussion

35.	Statement-I: The area bounded by x=2 cos theta,y=3sin theta is 36pi sq. units. Statement-II : The area bounded by x=2cos theta, y=2 sin theta is 4pi sq. units. Which of the above statement is correct.
Answer» only I only II Both I and II NEITHER I nor II ANSWER :B

Discussion

36.	If the median and the range of four numbers{x,y, 2x+ y,x -y} , "where"0 lt y lt x lt 2yare 10 and 28 respectively, then the mean of numbers is
Answer» 18 10 5 14 Answer :D

Discussion

37.	Let veca=hati+hatj+hatk,vecb=2hati+3hatk,vecc=hati-hatj and vecd=6hati+2hatj+3hatk. If vecd=x(vecbxxvecc)+y(veccxxveca)+z(vecaxxvecb) where x, y and z are scalars then the value of x+y+z is k. the number of prime factors of 5k is.
Answer» Solution :`veca.vecd=X[vecavecbvecc]` `x=(veca.vecd)/([vecavecbvecc]),y=(vecbvecd)/([vecavecbvecc]),z=(veccvecd)/([vecavecbvecc])` `((veca+vecb+vecc).vecd)/([vecavecbvecc])=(34)/(5)`

Discussion

38.	If f (x) = min [ x ^(2), sin ""(x)/(2), (x -2pi) ^(2)], the area bounded by the curve y=f (x), x-axis, x=0 and x=2pi is given by Note: x_(1) is the point of intersection of the curves x ^(2) and sin ""(x)/(2),x _(2) is the point of intersection of the curves sin ""x/2 and (x-2pi)^(2))
Answer» `int_(0)^(x _(1))(SIN ""(x)/(2)) dx + int _(x_(1))^(pi) x ^(2) dx + int _(pi)^(x _(2)) (x-2pi)^(2) dx + int _(x _(2))^(2pi) (sin ""(x)/(2)) dx` `int _(0) ^(x_(1)) x ^(2) dx +int _(x _(1))^(x _(3))(sin""(x)/(2)) dx + int _( x_(2)) ^(2pi) (x-2pi)^(2) dx,` where `x _(1) in (0, (pi)/(3)) and x _(2) in ((5PI)/(3), 2pi)` `int _(0)^(x_(1)) x ^(2) dx + int _(x _(1)) ^(x_(2))sin ((x )/(2)) dx + int _( x_(2))^(2pi) (x-2pi) ^(2)dx,` where `x _(1) in ((pi)/(3), (pi)/(2)) and x _(2) in ((3pi)/(2) , 2pi)` `int _(0)^(x _(1))x ^(2) dx + int _(x _(1)) ^(x_(2)) sin ((x )/(2)) dx + int _( x_(2))^(2pi) (x-2pi) ^(2) dx`, where `x _(1) in ((pi)/(2), (2pi)/(3)) and x _(2) in (pi, 2pi)` Answer :B

Discussion

39.	Prove the equality int_(-a)^(a) f(x) dx = int_(0)^(a) [f(x) + f(-x)] dxfor any continuous function f(x)
Answer» ANSWER :X = - t

Discussion

40.	5 balls of different colours are to be placed in 3 boxes of different sizes. Each box can hold all 5 balls. No. of different ways the balls can be placed so that no box remain empty is
Answer» 50 150 300 350 Answer :B

Discussion

41.	Statement 1: F a,b,c are real positive numbers with abc =1 and AA^(T)=1 where A= [{:( a,b,c),( b,c,a),( c,a,b) :}] then a^(3) +b^(3) + c^(3) =4. Statement 2: (1)/(a) +( 1)/(b) +(1)/( C) = 0.
Answer» STATEMENT -1 is True ,Statement -2 is True ,Statement -2 is CORECT 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

42.	If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= a(cos t+ log tan (t)//(2))y= a sin t.
Answer» ANSWER :`TAN t`

Discussion

43.	If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= (sin^(3)t)/(sqrt(cos 2t)), y= (cos^(3)t)/(sqrt(cos 2t)).
Answer» ANSWER :`-COT 3T`

Discussion

44.	Find k if the following pairs of circles are orthogonal x^(2)+y^(2)-16y+k-0, x^(2)+y^(2)+4x+8=0
Answer» ANSWER :`k=-8`

Discussion

45.	Match the following . {:("Circles"," Radical centre"),(I.x^(2) + y^(2) = 1" ," x^(2) + y^(2) - 2x = 1 "," x^(2) + y^(2) - 2y = 1 , "a)(0,0)"),(II. x^(2) + y^(2) - x + 3y - 3 = 0 ", " x^(2) + y^(2) - 2x+ 2y + 2 = 0 ", " x^(2) + y^(2) + 2x + 3y - 9 = 0,"b)(2,3)"),(III.x^(2) + y^(2) - 8x + 40 = 0 "," x^(2) + y^(2) - 5x + 16 = 0"," x^(2) + y^(2) - 8x + 16y + 160 = 0 ,"c)(8,-15/2)"):}
Answer» a,B,C b,c,a c,a,b a,c,b Answer :A::B

Discussion

46.	If theroots ofx^4+5x^3 - 30 x^2- 40x+64=0are inG.Pthen roots ofx^4 - 5 x^3- 30 x^2 + 40 x+ 64 =0 arein
Answer» A.P G.P H.P A.G.P Answer :B

Discussion

47.	For what x is the 4th term in the expansion of [(5^(1/3))^(-1/2log_(10)(6-sqrt8x))+(5^(log_(10)(x-1))/(25^(log_(10)5)))^(1/6)]^(m) is equal to 84/5, if it is known that 14/9 of binomial coefficient of 3rd term, binomial coefficient of 4th term and binomial coefficient of 5th term in the expansion constitute a G.P.
Answer» ANSWER :2

Discussion

48.	If the straight lines (x-1)/k = (y-2)/2 = (z-3) and (x-2)/3 = (y-3)/k = (z-1)intersect at a point, then the integer k is equal to
Answer» `-5` 5 2 `-2` ANSWER :A

Discussion

49.	int_(-1)^(1) (x-[x])dx=
Answer» 0 1 -1 2 Answer :B

Discussion

50.	Evaluate : int(dx)/(sinx+sin2x)
Answer» ANSWER :`(1)/(2)log\|cosx+1\|+(1)/(6)\|cosx-1\|-(2)/(3)log\|2cosx+1\|+c`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Everybody in a room shakes hand with everybody else. The total number of handshakes is 66. The total number of persons in the room is :

Examine the consistency of the system of linear equtions in 1 to 6 5x-y+4z=5 2x+3y+5z=2 5x-2y+6z=-1

Evalute the following integrals int e^(x) ((cos x - sin x)/(1 - cos 2 x ))dx

If N denotes the set of all positive integers and if f : N to N is defined byf(n) = the sum of positive divisors of n then, f(2^(k)3), where k is a positive integer, is

Let X be a random variable such that P(X=-2)=P(X-1)=P(X=2)=P(X=1)=(1)/(6) and P(X=0)=(1)/(3). Find the mean and variance of X.

The measure of dispersion which is used to find more consistent data is

13 persons sit a round a table. Find the odds in favour of two specified persons sitting together.

Find the numerically greatest term in the expansion of (2+5x)^(21) when x =2/5.

Calculate the area of the triangle ABC (by vector method) where A(1,1,2), B(2,2,3), C(3,-1,-1)

L (1, 3) and L^(1) = (1, -1) are the ends of latus rectum of a parabola, then area of quadrilateral formed by tangents and normals at L and L^(1) ( in Square Units ) is

Evaluate lim_(n rarr oo)(2^(k) + 4^(k) + 6^(k)+…+(2n)^(k))/(n^(k+1)) by using the method of finding definite integral as the limit of a sum.

Match the following lists:

Match the following lists:

Match the following lists:

Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of

iff(x)= (x-1)/(x+1) thef(2x )is

Using the identity sin^(4) x=3/8-1/2 cos 2x+1/8 cos 4x or otherwise, if the value of sin^(4)(pi/7)+sin^(4)((3pi)/(7))+sin^(4)((5pi)/(7))=a/b, where a and b are coprime, find the value of (a-b).

Find the probability of drawing 2 red balls in succession from a bag containing 4 red balls and 5 black balls when the ball that is drawn first is (i) not replaced (ii) replaced.

int(e^(exlog_(e)x)+(log_(e)x)(e^(exlog_(e)x)))dx=...+c

Compute the magnitude of the following vectors :veca=hati+hatj+k,vecb=2hati-7hatj-3hatk,vecc=(1)/(sqrt(3))hati+(1)/(sqrt(3))hatj-(1)/(sqrt(3))hatk

intsec^(6//5) x. "cosec"^(4//5) x dx

If ""^(12)P_r=1320 find r

If vecu=veca-vecb,vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxx vecc| is :

sin alpha=sinbeta, cos alpha=cos beta then

Let x > - 1, then statement P(n) : (1 + x)^(n) > 1 + nx is true for

Observe the following statements Assertion (A) : X is binomial variate with parameters 2n+1 and p = 1/2 then P(x = odd values) = 1/2 Reason ( R ) : If ""^(n)C_(r)=C_(r) then C_(1)+C_(3)+C_(5)+……=2^(n-1). Then

if 2^((log_3 5)(log_x 81)-6(25)^(log_x^2)+8=0, then :-

If I_(a) = int_(0)^(pi//4) tan^(n) theta d theta for n=1,2,3,…, then I_(n-1) + I_(n+1) is equal to

The two curves x^(3)-3xy^(2)+2=0 and 3x^(2)y-y^(3)-2=0:

The slope of tangent to the curve x=t^(2)+3t-8, y=2t^(2)-2t-5 at the point (2,-1) is …………..

If f:R to R is a differentible function such that f(x+y) = f (x). F(y) for all x,y in R and if f'(4) =24 and f'(0) = 3 then f(4) =

Total number of 6 digited numbers in which all the odd digits and only odd digits appear is

Let f:[0,1] to Rbe an injective continuous function that satisfies the condition -1 lt f(0) lt f(1) lt 1 Then the number of functions g:[-1,1] to [0,1]such that (gof)x =xfor all x in [0,1] is

Statement-I: The area bounded by x=2 cos theta,y=3sin theta is 36pi sq. units. Statement-II : The area bounded by x=2cos theta, y=2 sin theta is 4pi sq. units. Which of the above statement is correct.

If the median and the range of four numbers{x,y, 2x+ y,x -y} , "where"0 lt y lt x lt 2yare 10 and 28 respectively, then the mean of numbers is

Let veca=hati+hatj+hatk,vecb=2hati+3hatk,vecc=hati-hatj and vecd=6hati+2hatj+3hatk. If vecd=x(vecbxxvecc)+y(veccxxveca)+z(vecaxxvecb) where x, y and z are scalars then the value of x+y+z is k. the number of prime factors of 5k is.

If f (x) = min [ x ^(2), sin ""(x)/(2), (x -2pi) ^(2)], the area bounded by the curve y=f (x), x-axis, x=0 and x=2pi is given by Note: x_(1) is the point of intersection of the curves x ^(2) and sin ""(x)/(2),x _(2) is the point of intersection of the curves sin ""x/2 and (x-2pi)^(2))

Prove the equality int_(-a)^(a) f(x) dx = int_(0)^(a) [f(x) + f(-x)] dxfor any continuous function f(x)

5 balls of different colours are to be placed in 3 boxes of different sizes. Each box can hold all 5 balls. No. of different ways the balls can be placed so that no box remain empty is

Statement 1: F a,b,c are real positive numbers with abc =1 and AA^(T)=1 where A= [{:( a,b,c),( b,c,a),( c,a,b) :}] then a^(3) +b^(3) + c^(3) =4. Statement 2: (1)/(a) +( 1)/(b) +(1)/( C) = 0.

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= a(cos t+ log tan (t)//(2))y= a sin t.

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= (sin^(3)t)/(sqrt(cos 2t)), y= (cos^(3)t)/(sqrt(cos 2t)).

Find k if the following pairs of circles are orthogonal x^(2)+y^(2)-16y+k-0, x^(2)+y^(2)+4x+8=0

If theroots ofx^4+5x^3 - 30 x^2- 40x+64=0are inG.Pthen roots ofx^4 - 5 x^3- 30 x^2 + 40 x+ 64 =0 arein

If the straight lines (x-1)/k = (y-2)/2 = (z-3) and (x-2)/3 = (y-3)/k = (z-1)intersect at a point, then the integer k is equal to

int_(-1)^(1) (x-[x])dx=

Evaluate : int(dx)/(sinx+sin2x)