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6701.

Find the one-sided limits of the functions : f(x) ={{:(,-2x+3,if x le 1),(,3x-5, if x gt 1):} as x to 1: (b) f(x)=(x^(2)-1)/(|x-1|) as x to 1 (c ) f(x)=(sqrt(1-cos 2x))/(x)" as "x to 0 (d) f(x)=3+(1)/(1+7^(1//(1-x)) as x to 1 (e) f(x)=cos(pi/2)as x to 0 (f) f(x)=5//(x-2)^(3) as x to 2

Answer»


ANSWER :(B) F(1-0)=-2, f(1+0)=2; (f) f(2-0) `=-OO f(2+0)=+oo`
Discussion
6702.

Evaluate the definite integrals int_((pi)/(6))^((pi)/(3))(sinx+cosx)/(sqrt(sin2x))dx.

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ANSWER :`2SIN^(-1)((sqrt3-1))/2`
Discussion
6703.

A large healthclub with more than 5,000 members has a swimming pool , weight room , aerobic classes , and a gym, not all of which are used by all of the members . A staff member conducted a survey concerning the temperature of the weight room . For one month, every tenth member who signed in at the club was asked if the weight room temperaturewas too high , too low , or just right . Which of the following factors is most likely to invalidate the conclusion drawn about the temperature of the weight room ?

Answer»

The MEMBERSHIP SIZE
The sample size
The NUMBER of people who refused to respond
The COMPOSITION of the sample

ANSWER :D
Discussion
6704.

If cos(cot^(-1)(1/2))=cos (cos^(-1)x) then a vaue of x is

Answer»

`1/SQRT6`
`(-1)/sqrt12`
`2/sqrt6`
`(-2)/sqrt6`

ANSWER :A
Discussion
6705.

Show that two pairs of lines3x^(2)+8xy-3y^(2)=0 and 3x^(2)+8xy-3y^(2)+2x-4y-1=0 forms a square.

Answer»


ANSWER :`(1/5,-2/5)`
Discussion
6706.

A small pack of cards consists of 5 green cards 4 blue cards and 3 black cards. The pack is shuffled through and first three cards are turned face up. The probability that there is exactly one card of each colour is :

Answer»

`(9)/(55)`
`(4)/(11)`
`(3)/(11)`
`(8)/(55)`

Answer :C
Discussion
6707.

If ((x+1)^(2))/(x^(3)+x)=(A)/(x)+(Bx+C)/(x^(2)+1), then "cosec"^(-1) ((1)/(A)) + cot^(-1) ((1)/(B))+sec^(-1)C=______

Answer»

a. `(PI)/(2)`
B. `(pi)/(6)`
c. 0
d.`(5pi)/(6)`

Answer :D
Discussion
6708.

Integrate the following functions : xcotxcosec^(2)x

Answer»


ANSWER :`-(1)/(2)[XCOSEC^(2)x+cotx]+C`
Discussion
6709.

The point at which the maximum value of Z = 3x + 2y subject to the constraints x+2y le 2, x ge 0, y ge 0 is ……….

Answer»

(0, 0)
(1.5, -1.5)
(2, 0)
(0, 2)

ANSWER :C
Discussion
6710.

The maximum value of x^4+3x^3-2x^2-9x+6 is

Answer»

only I is TRUE
only II is true
both I and II are true
NEITHER I nor II true

Answer :B
Discussion
6711.

Match the following The correct answer is

Answer»

A-II, B-IV, C - III, D - I
A-II, B-IV, C-V, D-I
A-II, B-I, C -III, D - V
A-III, B-II, C-I, D - IV

Answer :A
Discussion
6712.

The Solution set of the inequation x+2y> 3 is

Answer»

UPPER PLANE CONTAINING the origin
upper HALF plane not containing the origin
first quadrant
none of this

Answer :B
Discussion
6713.

Let f'(x)=e^(x)""^(2)and f(0)=10.If Altf(1)ltB can be concluded from the mean value theorem, then the largest volume of (A-B) equals

Answer»

E
`1-e`
`e-1`
`1+e`

ANSWER :B
Discussion
6714.

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results :{:(,,"Firm A",,"Firm B"),("No. of wage earners",,586,,648),("Mean of monthly wages",,Rs.5253,,Rs.5253),("Variance of the distribution of wages",,100,,121):}Which firm, A or B, shows greater variability in individual wages?

Answer»

A
B
None
can not be determined

Answer :B
Discussion
6715.

Find the area of the surface generated by revolving about the x-axis a closed contour OABCO formed by the curves y= x^(2) and x= y^(2)

Answer»


Answer :`(67 sqrt(5PI))/(48) - (PI)/(32) ln (2 + SQRT5) - (pi)/(6)`
Discussion
6716.

Solve (dy)/(dx)=sqrt(4x+2y-1)

Answer»


ANSWER :x+c
Discussion
6717.

Which of the following is correct for data -1, 0, 1,2,3,5,5,6,8,10,11

Answer»

MEAN = MODE = median
mean = 5
mean = mode
mode = median

Answer :D
Discussion
6718.

IF12 ^2 -10 xy+ 2y ^2+ 11x-5 y+kis resolvableintotwolinearfactorsfactorsthenk=

Answer»

2
1
0
4

Answer :A
Discussion
6719.

Haldan effect explain :-

Answer»

DISSOCIATION of `HbO_(2)` on lungs surface
Dissociation of `HbO_(2)` on TISSUE surface
Dissociation of carbamino Hb on tissue surface
Dissociation of carbamino Hb on LUNG surface

Answer :A
Discussion
6720.

Integrate the following function : int(dx)/(9x^(2)-7)

Answer»


ANSWER :`(1)/(6sqrt7)LOG|(3x-sqrt7)/(3x+sqrt7)|+C`
Discussion
6721.

If x ge 0, y ge 0, x+y le 1, 3x+y ge 1 then the minimum value of f=2x+3y is

Answer»

2
3
`4//3
`1//3`

ANSWER :B
Discussion
6722.

Find the values in the interval (1,2) of the mean value theorem satisfied by the function f(x)=x-x^(2) "for" 1 le x le 2.

Answer»


ANSWER :`C=(3)/(2)`
Discussion
6723.

A line of fixed length a + b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of a point which divides this line into portions of length a and b is

Answer»


ANSWER :`sqrt5/3`
Discussion
6724.

Find the derivative of y=sinx(sin^(-1)x)^(2).

Answer»


ANSWER :A::B
Discussion
6725.

Choose the correct answer. The corner points of the feasible region determined by the following system of linear in equalities. 2x + y le 10, x + 3y le 15, x,y ge 0are (0,0) , (5,0), (3,4) and (0,5). Let z = px + qy where p,q gt 0. Condition on p and q so that the maximum of z occurs at both (3,4) and (0,5) is

Answer»

<P>p = Q
p = 2Q
p = 3q
q = 3P

ANSWER :D
Discussion
6726.

Find the coefficient of term independent of x in the expansion of ((x+1)/(x^(2//3) -x^(1//3) +1) -(x-1)/(x-x^(1//2)))^(10)

Answer»


SOLUTION :N/A
Discussion
6727.

Find underset(0)overset(pi)int xsin^(7)x cos^(6)x dx

Answer»


ANSWER :`(16pi)/(3003)`
Discussion
6728.

Show that the points (0,-1),(-2,3),(6,7) and (8,3) are vertices of a rectangle.

Answer»

Solution :
`THEREFORE absbar(AB) = sqrt((0 + 2)^2 + (-1-3)^2)`
`sqrt(4+6) = sqrt(20)`
`absbar(AB) = sqrt((-2-6)^2 + (3-7)^2)`
`sqrt(64+16) = sqrt(80)`
`absbar(CD) = sqrt((6-8)^2 + (7-3)^2)`
`sqrt(4+16) = sqrt(20)`
`absbar(AD) = sqrt((8-0)^2 + (3+1)^2)`
= `sqrt(64+16) = sqrt(80)`
`therefore` the opposite sides are EQUAL and two CONSECUTIVE sides are perpendicular So it is a rectangle.
Discussion
6729.

Let f : R to (1, infty) be defined by f(x) = log_(5) (sqrt(3x^(2) - 4x + a+ 5)). If f is surjective, then

Answer»

`a= 4/3`
`a LT 1/3`
`a GT 4/3`
`a = 1/3`

ANSWER :A
Discussion
6730.

If alpha and beta are the least and the greatest values of f(x)= (sin^(-1)x)^(2) + (cos^(-1)x)^(2) for all x inR respectively, then 8 (alpha + beta)=

Answer»

A `PI^(2)`
B`11pi^(2)`
C`9pi^(2)`
D`25pi^(2)`

ANSWER :B
Discussion
6731.

int(sec x dx)/(sqrt(cos 2x))=...

Answer»

`SIN^(-1)(tanx)`
`tanx`
`COS^(-1)(tanx)`
`(sinx)/(sqrt(COSX))`

Answer :A
Discussion
6732.

Find dy/dx if y^x =c

Answer»

SOLUTION :`y^X = C IMPLIES x In y = In c
In y + x/y dy/dx = 0 implies dy/dx = (y In y)/x`
Discussion
6733.

If the coefficient of x^(11) and x^(12) in the binomial expansion of (2+(8x)/(3))^(n) are equal, find n.

Answer»


ANSWER :N = 20
Discussion
6734.

Determine the truth of falsity of the a in{{a,b),b},a!= b propositions with reasons.

Answer»

SOLUTION :`a in{{a,B},b},a!=b` It is FALSE, as .a. is not an ELEMENT of the SET {{a, b},b}
Discussion
6735.

If a variable takes the discrete values alpha + 4, alpha - (7)/(2), alpha - (5)/(2), alpha - 3, alpha - 2, alpha + (1)/(2), alpha - (1)/(2), alpha +5 where (alpha gt 0) then the Median is

Answer»

`ALPHA - (1)/(2)`
`alpha - 2`
`alpha - (5)/(4)`
`alpha + (1)/(2)`

Answer :C
Discussion
6736.

Find the domain and the range of the function y=f(x), where f(x) is given by tanx

Answer»


ANSWER :`R-{(2n+1)(PI)/(2),N=-,+-1,+2,…}`
Discussion
6737.

Integration of a binomialdifferential int(dx)/(x(1+3sqrt(x))^(2)).

Answer»


ANSWER :`In (ROOT(3)(X))/(1+root(3)(x))+(3)/(1+root(3)(x))+C.`
Discussion
6738.

A particle is thrown with 50 m/s vertically upward from the ground.Upward direction is +y direction and projection point is y=0. Which graph is CORRECT for velocity-time (v-t) ?

Answer»




Discussion
6739.

For the parabola y^(2)+6y-2x+5=0 Statement I The vertex is (-2,-3) Statement II The directrix is y+3=0 Which of the following is correct?

Answer»

Both I and II are TRUE
I is true, II is FALSE
I is false, II is true
Both I and II are false

Answer :B
Discussion
6740.

The tangent to (at^(2), 2at) is perpendicular to X - axis at

Answer»

(4A, 4a)
(a, 2A)
(0, 0)
(a, -2a)

ANSWER :C
Discussion
6741.

By using the properties of definite integrals, evaluate the integrals int_(0)^(2)x(2-x)dx

Answer»
Discussion
6742.

C=60+0.25d The equation represents the monthly cost of a cell phone that includes up to 1 gigabyte of data after which there is a charge for d gigabytes of any additional data. Which of the following must be true? I. The cost of each additional megabyte of data is $60.25. II. The y-intercept of the graph of the cost equation represents the charge for each additional megabytes of data used. III. If betwee 5 and 6 megabytes of data are used in month, the monthly charge is $61.25.

Answer»

I and II only
I and III only
II only
III only

Answer :D
Discussion
6743.

A particle moves along x-axis so that its position is given by x=2t^(3)-3t^(2) at times t seconds. What is the time interval during which the particle will be on the negative half of the axis ?

Answer»

`0 LT t lt (2)/(3)`
`0 lt t lt 1`
`0 lt t lt 3//2`
`(1)/(2) lt t lt 1`.

ANSWER :C
Discussion
6744.

Differentiate x^2log_2x+secx

Answer»

SOLUTION :`y=x^2log_2x+SECX`
`dy/dx=d/dx(x^2)cdotlog_2x+x^2cdotd/dx(log_2x)+d/dx(secx)`
`=2X cdotlog_2x+x^2cdot1/xlog_2e+secx CDOT TANX`
Discussion
6745.

One solutions of the euqation 4x^(3) - 2x^(2) + x + 7 = 0 is x = -1. Which of the following describes the other 2 solutions?

Answer»

Both are NEGATIVE REAL numbers
One is a negative real NUMBER, and the other is a POSITIVE real number.
Both are positive real number.
Both are complex numbers that are not real.

Answer :D
Discussion
6746.

If A is a non-singular matrix, such that I+A+A^(2)+… +A^(n)=0, then A^(-1)=

Answer»

`A^(N)`
`-A^(n)`
`-(I+A+A^(2)+… +A^(n))`
`A^(2)`

ANSWER :A
Discussion
6747.

If vec(a),vec(b),vec(c ) are unit vectors such that vec(a)+vec(b)+vec(c )=0, then the value of vec(a).vec(b)+vec(b).vec(c )+vec(c ).vec(a) is equal to

Answer»

1
3
`-(3)/(2)`
`(3)/(2)`

ANSWER :C
Discussion
6748.

Find the equation of the ellipse whose length of minor axis is 10 and length of latus rectum is 6.

Answer»
Discussion
6749.

If the slope of focal chord of y^(2) = 16x is 2 then the length of the chord is

Answer»

8
12
20
24

Answer :C
Discussion
6750.

The total cost function is given by C(x) = 2x^(3)-3.5x^(2) +x. Find the marginal average cost function.

Answer»


SOLUTION :N/A
Discussion