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3151.

Assertion (A) : The maximum value of quadratic function -x^(2)+3x+1is (11)/(4) Reason (R ) : The maximum value of ax^(2)+bx+cis (4ac-b^(2))/(4a)if alt0

Answer»

Both A and R are TRUE and R is the correct explanation of A
Both A and R are true and R is not the correct explanation of A
A is true and R is FALSE
A is false and R is true

Answer :D
Discussion
3152.

Sketch roughly the lines satisfyingthe givenconditions and write their equations: x intercept = 7, and distance from the origin = 2.

Answer»


ANSWER : `2x+3sqrt(5Y)=14 and 2x-3sqrt(5y)=14`
Discussion
3153.

Number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^(-1)(sinx) where -pi le x le pi

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0
1
2
4

Answer :C
Discussion
3154.

If f'(x) =4x -4 and f(0) = -3,find f(x)

Answer»


ANSWER :`2(X^(2))-5(x)-3 '
Discussion
3155.

Find distance between following pair of points : (-3, 7, 2) and (2, 4, -1)

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ANSWER :`sqrt43` UNIT
Discussion
3156.

Sum to n terms the series 1+3+7+15+31+...

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ANSWER :`2N^(N+1) -2 -n`
Discussion
3157.

Evaluate the following limits : Lim _(x to 0) (1+sinx)^(cotx)

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ANSWER :E
Discussion
3158.

If A -={a,e,I,o,u}, C-={p,q,r,…,z} and X-={a,b,c….,z} is the universal set, then (A uuC)'=

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`A NNC`
`A'nnC'`
`A'uuC'`
`(ANNC)'`

ANSWER :B
Discussion
3159.

For what values of a and b, the equation x^(2)+(2a-3)x=3b+4 should have both the roots zero?

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ANSWER :`a=(3)/(2),B=-(4)/(3)`.
Discussion
3160.

lim_(xtoa)(sinx-sina)/(x-a)=…….

Answer»

COS a
sin a
a
0

Answer :A
Discussion
3161.

Which of the following sets are finite or infinite {1, 2, 3, . . .}

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ANSWER :INFINITE
Discussion
3162.

If sin^3xsin3x=sum_(m=0)^(6)c_mcos^(m)x , where c_(0),c_1,......c_6 are constants then

Answer»

`c_0+c_2+c_4+c_6=0`
`c_(1)+c_(3)+c_(5)=6`
`2c_(2)+3c_6=0`
`c_(4)+2c_(6)=0`

ANSWER :A
Discussion
3163.

If X-axis lies in a plane which is perpendicular to Z-axis then a line parallel to Y-axis is

Answer»

PERPENDICULAR to the plane
parallel to the plane
parallel to the NORMAL of the plane
normal to the plane

Answer :B
Discussion
3164.

Find the mean deviation about the median for the following data: 11, 3, 8, 7, 5, 14, 10, 2, 9

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ANSWER :3
Discussion
3165.

Find the derivative of (i)2x-(3)/(4) (ii) (5x^(3)+3x-1)(x-1) (iii) x^(-3)(5+3x) (iv) x^(5)(3-6x^(-9)) (v) x^(-4)(3-4x^(-5)) (vi) (2)/( x+1)-(x^(2))/(3x-1)

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Solution :(i) Let `y=2x-(3)/(4)`
`rArr (dy)/(dx)=(d)/(dx)(2x-(3)/(4))`
`=2(d)/(dx)(X)-(d)/(dx)((3)/( 4))`
`=2(1)-0=2`
(ii) Let `y=(5x^(3)+3X-1)(x-1)`
`rARr (dy)/(dx)=(d)/(dx)[(5x^(3)+3x-1)(x-a)]`
`=(5x^(3)+3x-1)(d)/(dx)(x-1)+(x-1)(d)/(dx)(5x^(3)+3x-1)`
`(5x^(3)+3x-1)(1-0)+(x-1)(15X^(2)+3)`
`=5x^(3)+3x-1+15x^(3)+3x-15x^(2)-3`
`=20x^(3)-15x^(2)+6x-4`
(iii) Let `y=x^(-3)(5+3x)`
`=5x^(-3)+3x^(-2)`
`rArr (dy)/(dx)=(d)/(dx)(5x^(-3)+3x^(-2))`
`=5(d)/(dx)x^(-3)+3(d)/(dx)x^(-2)`
`=5(-3)x^(-4)+ 3(-2)x^(-3)`
`=-(15)/(x^(4))-(6)/(x^(3))=-(3)/(x^(3))((5)/(x)+2)`
(iv) Let `y=x^(5)(3-6x^(-9))`
`=3x^(5)-6x^(-4)`
`rArr(dy)/(dx)=(d)/(dx)(3x^(5)-6x^(-4))`
`=d(d)/(dx)x^(5)-6(d)/(dx)x^(-4)`
`=3(5x^(4))-6(-4x^(-5))`
`=(15x^(4)+(24)/(x^(5)))`
(v) Let `y=x^(-4)(3-4x^(-5))=3x^(-4)-4x^(-9)`
`rArr(dy)/(dx)=(d)/(dx)(3x^(-4)-4x^(-9))`
`=3(d)/(dx)x^(-4)-4(d)/(dx)x^(-9)`
`=3(-4x^(-5))-4(-9X^(-10))`
`=-(12)/(x^(5)+(36)/(x^(10))=-(12)/(x^(5))(1-(3)/(x^(5)))`
(vi) Let `y=(2)/(x+1)-(x^(2))/(3x-1)`
`rArr(dy)/(Dx)=(d)/dx)[(2)/(x+1)-(x^(2))/(3x-1)]`
`=(d)/(dx)((2)/(x+1))-(1)/(dx)((x^(2))/(3x-1))`
`=((x+1)(d)/(dx)2-2(d)/(dx)(x+1))/((x+1)^(2))`
`((3x-1)(d)/(dx)x^(2)-x^(2)(d)/(dx)(3x-1))/((3x-1)^(2))`
`=(0-2)/((x+1)^(2))-((3x-1).2x-x^(2).3)/((3x-1)^(2))`
`=(-2)/((x+1)^(2))-(3x^(2)-2x)/((3x-1)^(2))`
`=-(1)/((x+1)^(2))=(x(3x-2))/((3x-1)^(2))`.
Discussion
3166.

If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis, then 2fgh=

Answer»

`AF^(2)+ch^(2)`
`bg^(2)+ch^(2)`
`af^(2)+bg^(2)`
`bg^(2)+h^(2)`

ANSWER :B
Discussion
3167.

Let A={1,2,3,4}, B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

Answer»


ANSWER :1
Discussion
3168.

If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)""1/x=tan^(-1)""1/3, then x is equal to

Answer»

1
2
3
`SQRT(2)`

ANSWER :B
Discussion
3169.

Find the term independent of x in the expansion of (root(3)(x)+1/2root(3)(x))^18,x > 0.

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ANSWER :The REQUIRED TERM is `^18`Cunderset9 `1/2^9`.
Discussion
3170.

Find the ratio in which YZ-plane divides the line joining A(2,4,5),B(3,5,-4). Find the point of intersection.

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ANSWER :`2:-3,(0,2,23)`
Discussion
3171.

If f(x)={:{(x",","x is rational"),(1-x",","x is irrational"):} then f(f(x)) is

Answer»

`X AA x in R`
`{:{(x",","x is IRRATIONAL"),(1-x",",x " is RATIONAL"):}`
`{:{(x",","x is rational"),(1-x"," ,"x is irrational"):}`
`{:(x",","x is rational"),(1+x"," ,x " is irrational"):}`

Answer :A
Discussion
3172.

Goods are sold is 3 retail outlets,X Y,Z in the ratio 2:3:5. If 90% of the item from X 80% of item from Y and 95% of item from Z are in good condition (i)what is the probability that an item chosen at random is in good condition.(ii)If a selected item is not in good condition what is the probability that it is from outlet Y?

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ANSWER :`0.895,(48)/(179)`
Discussion
3173.

Find the equation of the bisectors of the angles between the line 3x+4y=5, 12x-5y=41 and distinguish them.

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ANSWER :`3x-11y=20`
Discussion
3174.

Derive the formula for the distance between two points(x_1,y_1,z_1) and (x_2,y_2,z_2) and hence find the distance between P(1,-3,4) and Q(-4,1,2).

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ANSWER :` PQ= sqrt((x_(2)-x_(1))^(2)+ (y_(2)-y_(1))^(2)+(z_(2)-z_(1))^(2))`
Discussion
3175.

Find the approximate value of sqrt(25.001)

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ANSWER :`~-5.0001`
Discussion
3176.

Ifsigma _x =10 ,sigma _y =10 , then the value of Cov(x,y) is

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`100 `
` SQRT(10)`
` 10 `
` 0`

ANSWER :A
Discussion
3177.

10 C_(1)+10 C_(3) +10 C_(5) +10 C_(7) +10 C_(9) = …….

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`2^(9)`
`2^(10)`
`2^(10-1)`
NONE of these

ANSWER :A
Discussion
3178.

Let f(x)= underset(n to 00) (Lt) (x^(2n)-1)/(x^(2n)+1), then

Answer»

`f(X)=1"for" |x|=1 `
`f(x)={{:(1",", "for" |x| gt 1),(-1"m,", "for" |x| lt 1):}`
`f(x){{:(1",", "for" |x| gt 1),(-1"m,", "for" |x| le 1):}`
f is not defined for any VALUE of 'x'

Answer :B
Discussion
3179.

The value of sin ^(3) 10^(@) + sin ^(3) 50^(@) - sin ^(3) 70^(@) is equal to

Answer»

`-3/2`
`3/4`
`-3/4`
`-3/8`

ANSWER :D
Discussion
3180.

If cos (alpha + beta) = (4)/(5), sin (alpha - beta) = (5)/(13) and alpha and betalie between0 and (pi)/(4), find tan 2 alpha .

Answer»


ANSWER :`(56)/(33)`
Discussion
3181.

If f Q to Q is defined as f(x) =x^(2), f^(-1)(9)is equal to .

Answer»

3
`-3`
`{-3,3}`
`PHI`

ANSWER :C
Discussion
3182.

If vec(AB)= vec(b) and vec(AC)= vec( c), then the length of the perpendicular from A to the line BC is

Answer»

`|(vec(b) XX vec(C ))/(vec(b) + vec(c ))|`
`|(vec(b) xx vec(c ))/(vec(b)-vec(c ))|`
`(1)/(2) |(vec(b) xx vec(c ))/(vec(b) -vec(c ))|`
`2|(vec(b) xx vec( c))/(vec(b) -vec(c ))|`

Answer :B
Discussion
3183.

y = cos(m sin^(-x)) and (1-x^(2))y_(2) - xy_(1) + ky = 0, find a:

Answer»

`-m^(2)`
`2M`
`m^(2)`
m

Answer :C
Discussion
3184.

2x + 5y ge 10

Answer»





NONE of these

Solution :
Discussion
3185.

If f(x)=(x^(2)-10x+25)/(x^(2)-7x+10)"for "x ne 5 and f is continuous at x=5 then f(5)=

Answer»

0
5
10
25

Answer :A
Discussion
3186.

Define the gravitational field. Give its unit.

Answer»

Solution :The SPACE surrounding material BODY within while its GRAVITATIONAL force of ATTRACTION can be expensed is called its gravitational FIELD.
` vecE = - (Gm_1)/(r^2) hatr`
Discussion
3187.

f(x)= 3x^(2)-1 and g(x)= 3 + x. If f= g then the value of x is…….

Answer»

1
`(4)/(3)`
`-(4)/(3)`
`(3)/(4)`

ANSWER :B
Discussion
3188.

A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like product B, what is the least number that must have liked both products?

Answer»


ANSWER :`= 170`
Discussion
3189.

If the pair of lines ax^(2)+2hyx+by^(2)+2gx+2fy+c=0 intersect on the x-axis, then ac=

Answer»

`G^(2)`
`f^(2)`
`FG`
`2g^(2)`

ANSWER :A
Discussion
3190.

If |bar(a) xx bar(b)|= bar(a).bar(b), then find the angle between the vectors bar(a) and bar(b).

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ANSWER :`(PI)/(4)`
Discussion
3191.

Find the derivative of the w.r.to x. (2x + 3) ^(x-5)

Answer»


Answer :`(2x + 3 ) ^( x -5) [ (2 (x-5) )/( 2x +3) + LOG (2x + 3)]`
Discussion
3192.

Determine the number of terms of geometric progression {a_(n)} if a_(1)=3, a_(n)=96, S_(n)=189.

Answer»


ANSWER :6
Discussion
3193.

If 0 le x le pi, 4^(sin^(2)) + 4 ^(cos^(2)x) = 5, then x =

Answer»

`(pi)/(6)`
`(pi)/(3)`
`(pi)/(4)`
`(pi)/(2)`

ANSWER :D
Discussion
3194.

If the displacement in time t of a particle is given by s = ae^(t) + be^(-t). Then the acceleration is equal to

Answer»

`velocity`
`DISPLACEMENT`
`INITIAL velocity`
`a(E)^t`

Answer :B
Discussion
3195.

Find the transformed equation of 3x^(2) + 10xy + 3y^(2) = 9 when the axes are rotated through an angle (pi)/(4)

Answer»


ANSWER :`8X^(2) - 2Y^(2) = 9`
Discussion
3196.

The solution set of (5 + 4 cos theta)(2 cos theta + 1) = 0 in the interval [0, 2 pi ] is

Answer»

`{(PI)/(3), (2PI)/(3)}`
`{(pi)/(3),pi}`
`{(2 pi)/(3), (4 pi)/( 3)}`
`{(2 pi)/(3), (5 pi)/(3)}`

ANSWER :C
Discussion
3197.

If bara+barb+barc=bar0 and absbara=3, absbarb = 4, absbarc =sqrt37, " then " (bara,barb) =

Answer»

`pi/4`
`pi/2`
`pi/6`
`pi/3`

ANSWER :D
Discussion
3198.

Area of the triangle formed by the lines y^(2)-mxy=0 and x+y-m=0 is

Answer»

`(m^(2))/(2(1+m))`
`(m^(3))/(2(1+m))`
`(m^(3))/(2(1+m)^(2))`
`(m^(2))/(2)`

ANSWER :B
Discussion
3199.

What is the relation between torque and angular momentum?

Answer»

Solution :An EXTERNAL torque on a rigid body fixed to an axis produces RATE of change of angular MOMENTUM in the body about that axis.
` T = (dL)/(dt)`
Discussion
3200.

Use De-Moivere's theorem to find (sqrt3-i)^9 and (sqrt3-i)^(-1) in rectangular form (x+iy form)

Answer»


ANSWER :0+5.12i, `2^(-2)+0I
Discussion