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5401.

Objective function of a LPP is …………

Answer»

a constraint
a FUNCTION to be optimized
a RELATION between the variables
None of these

Answer :B
Discussion
5402.

An A.P. has the property that the sum of first ten terms is half the sum of next ten terms. If the second term is 13, then the common difference is

Answer»

3
2
5
4

Answer :B
Discussion
5403.

underset(x to 0)"Lt" (root3(1+Tan^(-1)3x)-root3(1-Sin^(-1)3x))/(sqrt(1-Sin^(-2)2x)-sqrt(1+Tan^(-1)2x))

Answer»

`-1`
0
1
2

Answer :A
Discussion
5404.

If in a DeltaABC, (a)/(cosA)=(b)/(cosB), then :

Answer»

`2sinAcosB=sinC`
`2sinAsinBsinC=1`
`SIN^(2)A+sin^(2)B=sin^(2)C`
NONE of these

Answer :A
Discussion
5405.

1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

Answer»

`1/3 ROOT(3)(5)`
`1/2 root(3)(5)`
`1/2root(3)(4)`
`root(3)(5)`

Answer :B
Discussion
5406.

The number of ways that 6 questions can be chosen out of 9 questions so that the first and the last questions are always included is

Answer»

35
56
84
60

Answer :A
Discussion
5407.

Solve graphically 3x + 8y gt 24

Answer»

SOLUTION :
Discussion
5408.

int 5^(x+1)*e^(2x-1)dx=....+c

Answer»

`(5^(x+1)*e^(2x-1))/(log5)`
`(5^(x+1)*e^(2x-1))/(log5e)`
`(5^(x+1)*e^(2x-1))/(log5+2)`
`(5^(x+1)*e^(2x))/(5E)`

ANSWER :C
Discussion
5409.

If A=[(4,2,3),(1,5,7)] and B=[(1,3,7),(0,4,1)], then 2A+B is :

Answer»

`[(9,7,13),(2,14,15)]`
`[(9,13,7),(2,14,13)]`
`[(7,9,13),(2,14,15)]`
NONE of these.

Answer :A
Discussion
5410.

Three coins are tossed simultaneously. Let the event E 'three heads or three tails', F 'at least two heads' and G 'at most two heads'. Of the pairs (E, F), (E, G) and (F, G), which are independent? which are dependent.

Answer»


ANSWER :The events (E and F) are independent, and event (E and G) and (F and G) are DEPENDENT.
Discussion
5411.

Three cards are drawn from pack successively with replacement then the probability of getting first king, Second Queen and third Ace is

Answer»

`(1)/(13^(2))`
`(1)/(13^(3))`
`(1)/(4^(2))`
`(1)/(4^(3))`

Answer :B
Discussion
5412.

Resolve the following into partial fractions. (x^(2))/ ((x-1)(x-2))

Answer»


ANSWER :`1 -(1)/(x-1)+(4)/(x-2)`
Discussion
5413.

Coloured balls are distributed in four boxes as shown in the following table: A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III?

Answer»


ANSWER :0.165
Discussion
5414.

E,Fare independenteventsand P(E )neO, P(F )ne O , then…….Is false .

Answer»

<P>`P(E//F ) = P(E ) `
`P(F^1 //E) = 1-P (F //E)`
`P(E^1 //F^1 ) = 1-P ( E)`
`P(E^1 //F^1 )=1-P (E//F)`

ANSWER :A
Discussion
5415.

Let a differentiable function f:RtoR be such that for all x and y in R 2|f(x)-f(y)|le|x-y| and f^(')(x)ge(1)/(2). So then the number of points of intersection of the graph y=f(x) with

Answer»

the line `y=x` is one.
the curve `y=-x^(3)` is one.
the curve `2y=|x|` is three.
the curve `y^(2)=-x` may be more than one.

Solution :We have `2|f(x)-f(y)|lt|x-y|`
`implies|(f(x)-f(y))/(x-y)|lt(1)/(2)implies|f^(')(x)|lt(1)/(2)`
but `f^(')(x)GE(1)/(2)`. So `f^(')(x)=(1)/(2)` so the curve is`y=(x)/(2)+c`
Discussion
5416.

underset(x to 0)"Lt" x sin (1/x)=

Answer»

only I is true
only II is true
both I and II are true
neither I nor II are true

Answer :B
Discussion
5417.

If A and B are symmetric matrices of same order, then AB-BA is

Answer»

NULL MATRIX
Unit matrix
SYMMETRIC matrix
Skew-symmetric matrix

Answer :D
Discussion
5418.

If is given that cosx=k, where x is the radian measure of an angle and pi lt x lt(3pi)/(2). If cos z=-k, which of the following could ul("not") be the value of z ?

Answer»

`x-pi`
`pi-x`
`2pi-x`
`3pi-x`

ANSWER :C
Discussion
5419.

Consider the function f(x)=|x-2|+|x-5|,c inR. Statement 1: f'(4)=0 Statement 2: f is continuous in [2,5], differentiable in

Answer»

Statement 1 is false, statement 2 is true.
Statement 1 is true , Statement 2 is true, statement 2 is CORRECT EXPLANATION for Statement 1.
Statement 1 is true, Statement 2 is trur, STATEMENT2 is no a correct explanation for statement 1.
Statement 1 is true, Statement 2 is false.

Answer :C
Discussion
5420.

Find the co-ordinates of the point on the curve sqrt(x)+sqrt(y)=4 at which tangent is equally inclined to the axes.

Answer»

<P>

ANSWER :P(4, 4)
Discussion
5421.

Find the values of the following integrals int sec^(2) x cosec^(4) x dx

Answer»


ANSWER :`tanx+2cotx-(COT^(3))/(3)+C`
Discussion
5422.

A ladder 5cm long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall at the rate of 2cm/sec. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall?

Answer»


ANSWER :Top END of LADDER is DECREASING at the rate of `8/3` cm/s.
Discussion
5423.

DABC be a tetrahedron such that AD is perpendicular to the base ABC and angleABC=30^(@). The volume of tetrahedron is 18. If value of AB+BC+AD is minimum, then the length of AC is

Answer»

`6sqrt(2-sqrt(3))`
`3(sqrt(6)-sqrt(2))`
`6sqrt(2+sqrt(3))`
`3(sqrt(6)+sqrt(2))`

Solution :Volume `=1/3AD(1/2AB.BCsin30^(@))`
`rArr 18-1/12(AD.AB.BC)`
`rArr AD.AB.BC=216`
Now, `AB+BC + ADge3 (AD.AB.BC)^(1//3)`

`rArr AB+BC+AD ge18`
Minimum VALUE occurs when AB=BC=AD=6
Hence, `AC = sqrt(AB^(2)+BC^(2)-2AB.BC. cos30^(@))`
`=6sqrt(2-sqrt(3))`
Discussion
5424.

Whichof thefollowinghas//havevalueequalto zero ?

Answer»

`|{:(8,,2,,7),(12,,3,,5),(16,,4,,3):}|`
`|{:(1//a,,a^(2),,bc),(1//b,,b^(2),,ac),(1//c,,c^(2),,AB):}|`
`|{:(a+b,,2a+b,,3a+b),(2a+b,,3a+b,,4a+b),(4a+b,,5a+b,,6a+b):}|`
`|{:(2,,43,,6),(7,,35,,4),(3,,17,,2):}|`

Solution :`|{:(8,,2,,7),(12,,3,,5),(16,,4,,3):}|=|{:(8,,2,,7),(4,,1,,-2),(4,,1,,-2):}|"" underset(R_(2) to R_(2)-R_(1))(R_(3) to R^(3) -R_(2)" and")`
`|{:(1//a,,a^(2),,bc),(1//b,,b^(2),,ac),(1//c,,c^(2),,ab):}|=(1)/(ABC) |{:(1,,a^(3),,abc),(1,,b^(3),,abc),(1,,c^(3),,abc):}|`
`[R_(1) to aR_(1),R_(2) to bR_(2) ,R_(3) to cR_(3)]`
`=(abc)/(abc) |{:(1,,a^(3),,1),(1,,b^(3),,1),(1,,c^(3),,1):}|`
[takingabc common from `C_(3)`]
`|{:(a+b,,2a+b,,3a+b),(2a+b,,3a+b,,4a+b),(4a+b,,5a+b,,6a+b):}|=|{:(a+b,,2a+b,,3a+b),(a,,a,,a),(2a,,2a,,2a):}|`
`[R_(3) to R_(3) -R_(2),R_(2) to R_(2)-R_(1)]`
`=0`
`|{:(2,,43,,6),(7,,35,,4),(3,,17,,2):}|=|{:(2,,1,,6),(7,,7,,4),(3,,3,,2):}|""[C_(2) to C_(2) -7 C_(3)]`
`=|{:(1,,1,,6),(0,,7,,4),(0,,3,,2):}|""[C_(2) to C_(1) -C_(2)]`
`=2`
Discussion
5425.

Write minors and cofactors of the elements of following determinant |{:(2,-1,3),(4,2,5),(0,4,-1):}|

Answer»


ANSWER :`M_(11)=-22,M_(12)=-4,M_(13)=16,M_(21)=-11,M_(22)=-2,M_(23)=8,M_(31)=-11,M_(32)=-2,M_(33)=8`
`A_(11)=-22,A_(12)=-4,A_(13)=16,A_(21)=11,A_(22)=-2,A_(23)=-8,A_(31)=-11,A_(32)=2,A_(33)=8`
Discussion
5426.

If 3f(x)-f((1)/(x))= log_(e) x^(4) for x gt 0 ,then f(e^(x))=

Answer»

X
`log_(e)x `
`e^(x)`
none of these

Solution :We have ,
`3f(x)-F((1)/(x))=log_(e) x^(4)`
`implies 3f(x)-f((1)/(x))=4 log_(e)x "" ` ….(i)
`implies 3f((1)/(x))-f(x)=4 log_(e)((1)/(x))""`[Replacing x by 1/x]
`implies 3f((1)/(x))-f(x)=-4 log_(e)x""`…..(ii)
Solving (i) and (ii) , we get
`8f(x)=8log_(e)x implies f(x)=log_(e)ximplies f(e^(x))=x`
Discussion
5427.

If I(m)=int_(0)^(pi)log_(e)(1-2mcosx+m^(2))dx, Then match the following lists and choose the correct code. :

Answer»


Solution :`I(m)=int_(0)^(PI)log_(e)(1-2mcosx+m^(2))dx`
`impliesI(-m)=int_(0)^(pi)log_(e)(1+2mcosx+m^(2))dx`
`=int_(0)^(pi)log_(e)(1+2mcos(pi-x)+m^(2))dx`
`=int_(0)^(pi)log_(e)(1-2mcosx+m^(2))dx`
`=I(m)=I(m)`
`impliesI(m)+I(-m)=int_(0)^(pi)log_(e)(1-2m^(2)cos2x+m^(4))dx`
put `2x=t`
`impliesI(m)+(-m)=I(m^(2))`
`implies2I(m)=I(m^(2))`
`implies(I(m^(2)))/(I(m))=2`
`=(I(9))/(I(3))=2` and `(I(25))/(I(5))=2`
`implies(I(81))/(I(91))=2` and `(I(9))/(I(3))=2`
`implies (I(81))/(I(3))=4`
Discussion
5428.

Statement I In triangle ABC, (a^(2)+b^(2)+c^(2))/(Delta) ge 4 sqrt3 Statement II If a_(i) gt 0,i=1,2,3…,n shich are not (a_(1)^(m)+a_(2)^(m)+...+a_(n)^(m))/(n)gt((a_(1)+a_(2)+...+ +a_(n))/(n))^(m) ,if m lt 0 or m gt1.

Answer»

Both Statement I and Statement II are CORRECT and Statement II is the correct EXPLANATION of Statement I
Both Statement I and Statement II are correct and Statement II is not the correct explanation of Statement I
Statement I is correct but Statement II is incorrect
Statement I is correct but Statement I is incorrect

ANSWER :A
Discussion
5429.

overset((2)/(3))underset(0)int (dx)/(4+9x^(2))=....

Answer»

`(PI)/(6)`
`(pi)/(12)`
`(pi)/(24)`
`(pi)/(4)`

Answer :C
Discussion
5430.

The period of (tan theta -1/3 tan ^(3) theta ) ((1)/(3) - tan ^(2) theta ), when tan ^(2) theta ne 1/3 is

Answer»

`PI/3`
`(2PI)/(3)`
`pi`
`2pi`

ANSWER :A
Discussion
5431.

Find the maximum and the minimum values, if any, of the function given by f(x)=x, x in (0,1).

Answer»


ANSWER :MAXIMUM and MINIMUM VALUES does not EXISTS.
Discussion
5432.

Solve sin(cos ^(-1) x) = (1)/(9)

Answer»

`(4sqrt5)/( 9)`
` ( 2SQRT5)/( 9)`
` ( 4sqrt3)/(5)`
` (2SQRT3)/(5)`

ANSWER :A
Discussion
5433.

Write the range of y= cos^(-1)x

Answer»


ANSWER :The RANGE `[0,PI]`
Discussion
5434.

Evaluate the following integrals int e^(x) (tan x + sec^(2) x ) dx

Answer»


ANSWER :`E^(X) TAN x + C`
Discussion
5435.

The area of the region bounded by y=x^(2),y=x+2,x=-1andx=2 is

Answer»


ANSWER :`((51)/(4))`
Discussion
5436.

If 3^(2x) + 3^(2x) + 3^(2x)=(1/3)^x. What is the value of x ?

Answer»

`-1`
`-1/2`
`-1/3`
`-1/6`

ANSWER :C
Discussion
5437.

Write the following function in the simplest form : tan^(-1)((cosx-sinx)/(cosx+sinx)),(-pi)/4ltxlt(3pi)/4

Answer»


ANSWER :`(PI)/4-x`
Discussion
5438.

Evaluate int sin^(5)x cos^(4) xdx

Answer»


ANSWER :`-((COS^(5)X)/(5)-(cos^(9)x)/(9)-(2COS^(7)x)/(7))+c`
Discussion
5439.

Evaluate the following definite integrals as limit of sums : int_(1)^(3)(2x^(2)+7)dx

Answer»


ANSWER :`(94)/(3)`
Discussion
5440.

If f(n)= 1/n {(n+1)(n+2)....2n}^(1//n) then {:(" "Lt),(n rarr oo):} f(n)=

Answer»

2E
`2//e`
`4//e`
4e

Answer :C
Discussion
5441.

Determine order and degree (if defined) of differential equations ((ds)/(dt))^(4) + 5s(d^(2)s)/(dt^(2)) = 0

Answer»


ANSWER :ORDER 2; DEGREE 1
Discussion
5442.

Solve the following differential equations. (dy)/(dx)-y=-2e^(-x)

Answer»


ANSWER :`y = E^(-X) + C e^(x)`
Discussion
5443.

Let A and B be two sets defined as follows: A = {n in N : 2^(2^(n)) + 1 " ends in 7"} B = {7n : n in N}, then A cup B is equal to

Answer»

B
`N-{1}`
N-B
none of these

ANSWER :B
Discussion
5444.

Solve sqrt((x)/(x-3))+sqrt((x-3)/(x))=(5)/(2) (x != 0, x != 3)

Answer»


ANSWER :{-1, 4}
Discussion
5445.

The pints of intersection of two equal circles which out orthogonally are (2,3) and ( 5,4)Then the radius of each circle is

Answer»

1
` 5sqrt2`
` SQRT5`
` SQRT2`

ANSWER :C
Discussion
5446.

int(1)/(3+2 sin x +cos x)dx

Answer»


Answer :`TAN^(-1) (1+tan .(X)/(2))+c`
Discussion
5447.

Find the number of 4 digited numbers that can be formed using the digits 0,1,2.

Answer»


ANSWER :54
Discussion
5448.

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number " and r be the statement "x is a rational number iff y is a transcendental number". Statement - 1 : r is equivalent to either q or p. Statement -2 : r is equivalent to ~(p harr ~q)

Answer»

S -1 is true , S - 2 is true, S -2 is a CORRECT explanation of S-1
S-1 is true, S- 2 is true, S - 2 is not a correct explanation of S-1
S-1 is true, S - 2 is FALSE
S-1 is false, S - 2 is true

Answer :C
Discussion
5449.

Compute P(X=k) for the binominal distribution, B(n,p) where n=6, p=1/3, k=3

Answer»


ANSWER :`160/729`
Discussion
5450.

Evalute the following integrals int (2x- 3)/(sqrt(2x^(2) + 5x - 6 )) dx

Answer»


ANSWER :`sqrt(2x^(2) + 5X - 6) - (11)/(2 sqrt(2)) "cosh"^(-1) ((4x + 5)/(sqrt(73)) ) + C `
Discussion