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Question(s) from Search: IIT

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1201

One or more than one correct options

The value(s) of 01x4(1x)41+x2dx

is (are)

a) 227π

b) 2105

c) 0

d) 71153π2

One or more than one correct options

The value(s) of 01x4(1x)41+x2dx

is (are)

a) 227π

b) 2105

c) 0

d) 71153π2

IIT 2010
1202

 =

a) True

b) False

 =

a) True

b) False

IIT 1986
1203

For non-zero vectors a, b, c,  holds if and only if

a) a . b = 0, b . c = 0

b) b . c = 0, c . a = 0

c) c . a = 0, a . b = 0

d) a . b = 0, b . c = 0, c . a = 0

For non-zero vectors a, b, c,  holds if and only if

a) a . b = 0, b . c = 0

b) b . c = 0, c . a = 0

c) c . a = 0, a . b = 0

d) a . b = 0, b . c = 0, c . a = 0

IIT 1982
1204

223x21+exdx

equals

a) 8

b) 2

c) 4

d) 0

223x21+exdx

equals

a) 8

b) 2

c) 4

d) 0

IIT 2014
1205

The value of 014x3[d2dx2(1x2)5]dx

is

a) 4

b) 0

c) 2

d) 6

The value of 014x3[d2dx2(1x2)5]dx

is

a) 4

b) 0

c) 2

d) 6

IIT 2014
1206

Let f be a non-negative function defined on the interval [0, 1]. If 0x1(f(t))2dt=0xf(t)dt,0x1

and f(0) = 0, then

a) f(12)<12f(13)>13

b) f(12)>12f(13)>13

c) f(12)<12f(13)<13

d) f(12)>12f(13)<13

Let f be a non-negative function defined on the interval [0, 1]. If 0x1(f(t))2dt=0xf(t)dt,0x1

and f(0) = 0, then

a) f(12)<12f(13)>13

b) f(12)>12f(13)>13

c) f(12)<12f(13)<13

d) f(12)>12f(13)<13

IIT 2009
1207

(One or more correct answers)
If E and F are independent events such that 0 < P (E) < 1 and 0 < P (F) < 1 then

a) E and F are mutually exclusive

b) E and  are independent

c)  are independent

d)

(One or more correct answers)
If E and F are independent events such that 0 < P (E) < 1 and 0 < P (F) < 1 then

a) E and F are mutually exclusive

b) E and  are independent

c)  are independent

d)

IIT 1989
1208

Match the following
Let  

Column 1

Column 2

i) If  then f (x) satisfies

A)  

ii) If  then f (x) satisfies

B)

iii) If  then f (x) satisfies

C)

iv) If then f (x) satisfies

D)

                                                                     

Match the following
Let  

Column 1

Column 2

i) If  then f (x) satisfies

A)  

ii) If  then f (x) satisfies

B)

iii) If  then f (x) satisfies

C)

iv) If then f (x) satisfies

D)

                                                                     

IIT 2007
1209

Let p be the first of the n Arithmetic Means between two numbers and q be the first of n Harmonic Means between the same numbers. Then show that q does not lie between p and

Let p be the first of the n Arithmetic Means between two numbers and q be the first of n Harmonic Means between the same numbers. Then show that q does not lie between p and

IIT 1991
1210

 

a) – 1

b) 2

c) 1 + e−1

d) None of these

 

a) – 1

b) 2

c) 1 + e−1

d) None of these

IIT 1981
1211

One or more than one correct answer

Let P and Q be distinct points on the parabola y2 = 2x such that the circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of triangle OPQ is 32

then which of the following is/are the coordinates of P?

a) (4,22)

b) (9,32)

c) (14,12)

d) (1,2)

One or more than one correct answer

Let P and Q be distinct points on the parabola y2 = 2x such that the circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of triangle OPQ is 32

then which of the following is/are the coordinates of P?

a) (4,22)

b) (9,32)

c) (14,12)

d) (1,2)

IIT 2015
1212

The total number of local maximum and minimum of the function
is

a) 0

b) 1

c) 2

d) 3

The total number of local maximum and minimum of the function
is

a) 0

b) 1

c) 2

d) 3

IIT 2008
1213

The area enclosed by the curve y = sinx + cosx and y = |cosx – sinx| over the interval [0,π2]

is

a) 4(21)

b) 22(21)

c) 2(21)

d) 22(2+1)

The area enclosed by the curve y = sinx + cosx and y = |cosx – sinx| over the interval [0,π2]

is

a) 4(21)

b) 22(21)

c) 2(21)

d) 22(2+1)

IIT 2014
1214

If  and bn = 1 – an then find the least natural number n0 such that bn > an for all n ≥ n0

If  and bn = 1 – an then find the least natural number n0 such that bn > an for all n ≥ n0

IIT 2006
1215

If  are unit coplanar vectors then the scalar triple product  

a) 0

b) 1

c)

d)

If  are unit coplanar vectors then the scalar triple product  

a) 0

b) 1

c)

d)

IIT 2000
1216

One or more than one correct option

If the line x = α divides the area of the region R = {(x, y) ∈ ℝ2 : x3 ≤ y ≤ x, 0 ≤ x ≤ 1 into two equal parts then

a) 2α44α2+1=0

b) α4+4α21=0

c) 12<α<1

d) 0<α<12

One or more than one correct option

If the line x = α divides the area of the region R = {(x, y) ∈ ℝ2 : x3 ≤ y ≤ x, 0 ≤ x ≤ 1 into two equal parts then

a) 2α44α2+1=0

b) α4+4α21=0

c) 12<α<1

d) 0<α<12

IIT 2017
1217

The sides of a triangle inscribed in a given circle subtend angles α, β and γ at the centre. The minimum value of the Arithmetic mean of
 
 

The sides of a triangle inscribed in a given circle subtend angles α, β and γ at the centre. The minimum value of the Arithmetic mean of
 
 

IIT 1987
1218

The value of k=1131sin(π4+(k1)π6)sin(π4+6)

a) 33

b) 2(33)

c) 2(31)

d) 2(2+3)

The value of k=1131sin(π4+(k1)π6)sin(π4+6)

a) 33

b) 2(33)

c) 2(31)

d) 2(2+3)

IIT 2016
1219

Let y(x) be the solution of the differential equation (xlnx)dydx+y=2xlnx,(x1)

. Given that y = 1 when x = 1, then y(e) is equal to

a) e

b) 0

c) 2

d) 2e

Let y(x) be the solution of the differential equation (xlnx)dydx+y=2xlnx,(x1)

. Given that y = 1 when x = 1, then y(e) is equal to

a) e

b) 0

c) 2

d) 2e

IIT 2015
1220

If Cr stands for  then the sum of the series
 
where n is a positive integer, is equal to

a) 0

b) (−)n/2(n + 1)

c) (−)n/2 (n + 2)

d) None of these

If Cr stands for  then the sum of the series
 
where n is a positive integer, is equal to

a) 0

b) (−)n/2(n + 1)

c) (−)n/2 (n + 2)

d) None of these

IIT 1986
1221

Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all x  ℝ, f(x + T) = f(x). If  then the value of  is

a)

b)

c) 3I

d) 6I

Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all x  ℝ, f(x + T) = f(x). If  then the value of  is

a)

b)

c) 3I

d) 6I

IIT 2002
1222

One or more than one correct options

If y(x) satisfies the differential equation y′ − ytanx = 2xsecx and y(0) = 0, then

a) y(π4)=π282

b) y(π4)=π218

c) y(π3)=π29

d) y(π3)=4π3+2π233

One or more than one correct options

If y(x) satisfies the differential equation y′ − ytanx = 2xsecx and y(0) = 0, then

a) y(π4)=π282

b) y(π4)=π218

c) y(π3)=π29

d) y(π3)=4π3+2π233

IIT 2012
1223

The sum if p > q is maximum when m is

a) 5

b) 10

c) 15

d) 20

The sum if p > q is maximum when m is

a) 5

b) 10

c) 15

d) 20

IIT 2002
1224

At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by dPdx=10012x

. If the firm employs 25 more workers then the new level of production of items is

a) 2500

b) 3000

c) 3500

d) 4500

At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by dPdx=10012x

. If the firm employs 25 more workers then the new level of production of items is

a) 2500

b) 3000

c) 3500

d) 4500

IIT 2013
1225

If a, b, c; u, v, w are complex numbers representing the vertices of two triangles such that c = (1 − r)a + rb, w = (1 − r)u + rv where r is a complex number. The two triangles

a) have the same area

b) are similar

c) are congruent

d) none of these

If a, b, c; u, v, w are complex numbers representing the vertices of two triangles such that c = (1 − r)a + rb, w = (1 − r)u + rv where r is a complex number. The two triangles

a) have the same area

b) are similar

c) are congruent

d) none of these

IIT 1985

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