(1 + x)n â‰¥ ____ for all n âˆˆ N,where x > -1

1.1 + nx

2.1 â€“ nx

3.1 + nx/2 (

4.1 â€“ nx/2

**Posted Date**:-2021-12-25 08:30:50

(Aâ€™)â€™ = ?

1.âˆª â€“ A

2.Aâ€™

3.âˆª

4.A

**Posted Date**:-2021-12-24 19:39:00

(nÂ² + n) is ____ for all n âˆˆ N.

1.Even

2.odd

3.Either even or odd

4.None of these

**Posted Date**:-2021-12-25 08:28:35

1/(1 âˆ™ 2 âˆ™ 3) + 1/(2 âˆ™ 3 âˆ™ 4) + â€¦â€¦.. + 1/{n(n + 1)(n + 2)} =

1. {n(n + 3)}/{4(n + 1)(n + 2)}

2.(n + 3)/{4(n + 1)(n + 2)}

3.n/{4(n + 1)(n + 2)}

4.None of these

**Posted Date**:-2021-12-25 08:25:16

1/(1 âˆ™ 2) + 1/(2 âˆ™ 3) + 1/(3 âˆ™ 4) + â€¦.. + 1/{n(n + 1)}

1. n(n + 1)

2.n/(n + 1)

3.2n/(n + 1)

4.3n/(n + 1)

**Posted Date**:-2021-12-25 08:22:18

102n-1 + 1 is divisible by ____ for all N âˆˆ N

1.9

2.10

3.11

4.13

**Posted Date**:-2021-12-25 08:31:24

A â€“ B is read as?

1.Difference of A and B of B and A

2.None of the above

3. Difference of B and A

4. Both a and b

**Posted Date**:-2021-12-24 19:39:47

A function f(x) is said to be an odd function if

1.f(-x) = f(x)

2.f(-x) = -f(x)

3. f(-x) = k * f(x) where k is a constant

4.None of these

**Posted Date**:-2021-12-25 07:53:36

A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if xÂ² + yÂ² = 16 then the domain of R is

1. (0, 4, 4)

2.(0, -4, 4)

3. (0, -4, -4)

4.None of these

**Posted Date**:-2021-12-25 07:59:32

Empty set is a?

1. Finite Set

2. Invalid Set

3.None of the above

4.Infinite Set

**Posted Date**:-2021-12-24 19:52:43

Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

1.n(n+1)(n+2)/3

2. n(n+1)(n+2)/6

3.n(n+2)/6

4.(n+1)(n+2)/6

**Posted Date**:-2021-12-25 08:27:36

For all n âˆˆ N, 3Ã—52n+1 + 23n+1 is divisible by

1.19

2.17

3.23

4.25

**Posted Date**:-2021-12-25 08:29:14

For all nâˆˆN, 72n âˆ’ 48nâˆ’1 is divisible by :

1.25

2.2304

3.1234

4.26

**Posted Date**:-2021-12-25 08:32:23

For any natural number n, 7n â€“ 2n is divisible by

1.3

2.4

3.5

4.7

**Posted Date**:-2021-12-25 08:24:39

How many rational and irrational numbers are possible between 0 and 1?

1. 0

2.Finite

3.Infinite

4.1

**Posted Date**:-2021-12-24 19:52:05

If 3 Ã— tan(x â€“ 15) = tan(x + 15), then the value of x is

1.30

2.45

3. 60

4.90

**Posted Date**:-2021-12-25 08:12:13

IF A = [5, 6, 7] and B = [7, 8, 9] then A âˆª B is equal to

1.[5, 6, 7, 8, 9]

2.[5, 6, 7]

3. [7, 8, 9]

4.None of these

**Posted Date**:-2021-12-24 19:41:50

If A = [5, 6, 7] and B = [7, 8, 9] then A U B is equal to

1. [5, 6, 7, 8, 9]

2. [5, 6, 7]

3.[7, 8, 9]

4.None of these

**Posted Date**:-2021-12-24 19:53:34

If A, B and C are any three sets, then A â€“ (B âˆª C) is equal to

1.(A â€“ B) âˆª (A â€“ C)

2.(A â€“ B) âˆª C

3. (A â€“ B) âˆ© C

4.(A â€“ B) âˆ© (A â€“ C)

**Posted Date**:-2021-12-24 19:38:04

If A, B and C are any three sets, then A Ã— (B âˆª C) is equal to

1.(A Ã— B) âˆª (A Ã— C)

2. (A âˆª B) Ã— (A âˆª C)

3.(A Ã— B) âˆ© (A Ã— C)

4.None of these

**Posted Date**:-2021-12-24 19:41:01

If A, B, C be three sets such that A âˆª B = A âˆª C and A âˆ© B = A âˆ© C, then,

1. B = C

2.A = C

3.A = B = C

4. A = B

**Posted Date**:-2021-12-24 19:50:44

If aÃ—cos x + b Ã— cos x = c, then the value of (a Ã— sin x â€“ bÂ²cos x)Â² is

1.aÂ² + bÂ² + cÂ²

2.aÂ² â€“ bÂ² â€“ cÂ²

3.aÂ² â€“ bÂ² + cÂ²

4. aÂ² + bÂ² â€“ cÂ²

**Posted Date**:-2021-12-25 08:07:02

If cos a + 2cos b + cos c = 2 then a, b, c are in

1.2b = a + c

2. bÂ² = a Ã— c

3.a = b = c

4.None of these

**Posted Date**:-2021-12-25 08:08:05

If f is an even function and g is an odd function the fog is a/an

1.Even function

2.Odd function

3.Either even or odd function

4.Neither even nor odd function

**Posted Date**:-2021-12-25 08:00:52

If f(x) = (a â€“ x)1/n, a > 0 and n âˆˆ N, then the value of f(f(x)) is

1. 1/x

2.x

3.xÂ²

4. x1/2

**Posted Date**:-2021-12-25 07:49:32

If f(x) = ex and g(x) = loge x then the value of fog(1) is

1.0

2. 1

3.-1

4.None of these

**Posted Date**:-2021-12-25 07:51:00

If f(x) = log3 x and A = (3, 27) then f(A) =

1.(1, 1)

2.(3, 3)

3. (1, 3)

4. (2, 3)

**Posted Date**:-2021-12-25 07:56:17

If f(x) =(3x â€“ 2)/(2x â€“ 3) then the value of f(f(x)) is

1.x

2.xÂ²

3.xÂ³

4.None of these

**Posted Date**:-2021-12-25 07:58:06

If f(x) is an odd differentiable function on R, then df(x)/dx is a/an

1.Even function

2.Odd function

3.Either even or odd function

4.Neither even nor odd function

**Posted Date**:-2021-12-25 07:54:15

If n is an odd positive integer, then an + bn is divisible by :

1.aÂ² + bÂ²

2. a + b

3.a â€“ b

4.None of these

**Posted Date**:-2021-12-25 08:21:37

IF R = {(2, 1),(4, 3),(4, 5)}, then range of the function is?

1.Range R = {2, 4}

2. Range R = {1, 3, 5}

3.Range R = {2, 3, 4, 5}

4.Range R {1, 1, 4, 5}

**Posted Date**:-2021-12-24 19:45:42

If tan A â€“ tan B = x and cot B â€“ cot A = y, then the value of cot (A â€“ B) is

1.x + y

2.1/x + y

3. x + 1/y

4.1/x + 1/y

**Posted Date**:-2021-12-25 08:18:40

If tanÂ² Î¸ = 1 â€“ eÂ², then the value of sec Î¸ + tanÂ³ Î¸ Ã— cosec Î¸ is

1. 2 â€“ eÂ²

2.(2 â€“ eÂ²)1/2

3. (2 â€“ eÂ²)Â²

4.(2 â€“ eÂ²)3/2

**Posted Date**:-2021-12-25 08:15:23

If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is

1.4 : (âˆš5 â€“ 1)

2.5 : 4

3.(âˆš5 â€“ 1) : 4

4.None of these

**Posted Date**:-2021-12-25 08:10:09

If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is

1. 2Ï€/3

2.Ï€/3

3.Ï€/2

4. Ï€/6

**Posted Date**:-2021-12-25 08:16:48

If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

1. Ï€/3

2. Ï€/2

3.2Ï€/3

4.3Ï€/2

**Posted Date**:-2021-12-25 08:12:52

if z lies on |z| = 1, then 2/z lies on

1.a circle

2. an ellipse

3.a straight line

4. a parabola

**Posted Date**:-2021-12-25 08:41:56

In 2nd quadrant?

1. X < 0, Y < 0

2. X < 0, Y > 0

3.X > 0, Y > 0

4.X > 0, Y < 0

**Posted Date**:-2021-12-24 19:51:23

In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?

1.19

2.41

3.21

4.57

**Posted Date**:-2021-12-24 19:47:41

In a class of 50 students, 10 did not opt for math, 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science.

1.24

2.25

3.26

4.27

**Posted Date**:-2021-12-24 19:55:16

In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals

1. c/a

2.1

3.a/c

4.None of these

**Posted Date**:-2021-12-25 08:09:28

In last quadrant?

1.X < 0, Y > 0

2. X < 0, Y < 0

3. X > 0, Y < 0

4. X > 0, Y > 0

**Posted Date**:-2021-12-24 19:56:03

Let A = {-2, -1, 0} and f(x) = 2x â€“ 3 then the range of f is

1.{7, -5, -3}

2.{-7, 5, -3}

3.{-7, -5, 3}

4. {-7, -5, -3}

**Posted Date**:-2021-12-25 08:03:07

Let R be the set of real numbers. If f(x) = xÂ² and g(x) = 2x + 1, then fog(x) is equal to

1. 2x + 1

2.2xÂ² + 1

3.(2x + 1)Â²

4.None of these

**Posted Date**:-2021-12-25 07:58:45

n(n + 1)(n + 5) is a multiple of ____ for all n âˆˆ N

1.2

2.3

3.5

4.7

**Posted Date**:-2021-12-25 08:26:56

The domain of tan-1 (2x + 1) is

1. R

2.R -{1/2}

3.R -{-1/2}

4.None of these

**Posted Date**:-2021-12-25 07:56:51

The domain of the definition of the real function f(x) = âˆš(log12 xÂ² ) of the real variable x is

1.x > 0

2. |x| â‰¥ 1

3. |x| > 4

4.x â‰¥ 4

**Posted Date**:-2021-12-25 07:50:18

The domain of the function f(x) = 1/(xÂ² â€“ 3x + 2) is

1. {1, 2}

2.R

3.R â€“ {1, 2}

4.R â€“ {1, -2}

**Posted Date**:-2021-12-25 08:01:29

The domain of the function f(x) = sin-1 (tan x) is

1. -Ï€/4 â‰¤ x â‰¤ Ï€/4

2.nÏ€ â€“ Ï€/4 â‰¤ x â‰¤ nÏ€ + Ï€/4

3.nÏ€ â€“ Ï€/3 â‰¤ x â‰¤ nÏ€ + Ï€/3

4.-Ï€/3 â‰¤ x â‰¤ Ï€/3

**Posted Date**:-2021-12-25 08:02:25

The function f(x) = sin (â€ŽÏ€x/2) + cos (Ï€x/2) is periodic with period

1.4

2.6

3.12

4.24

**Posted Date**:-2021-12-25 07:55:25

the function f(x) = x â€“ [x] has period of

1.0

2.1

3.2

4.3

**Posted Date**:-2021-12-25 07:57:26

The general solution of âˆš3 cos x â€“ sin x = 1 is

1. x = n Ã— Ï€ + (-1)n Ã— (Ï€/6)

2. x = Ï€/3 â€“ n Ã— Ï€ + (-1)n Ã— (Ï€/6)

3.x = Ï€/3 + n Ã— Ï€ + (-1)n Ã— (Ï€/6)

4.x = Ï€/3 â€“ n Ã— Ï€ + (Ï€/6)

**Posted Date**:-2021-12-25 08:14:35

The members of the set S = {x | x is the square of an integer and x < 100} is

1. {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}

2.{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

3.{1, 4, 9, 16, 25, 36, 64, 81, 85, 99}

4.{0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

**Posted Date**:-2021-12-24 19:46:46

The nth terms of the series 3 + 7 + 13 + 21 +â€¦â€¦â€¦. is

1. 4n â€“ 1

2.nÂ² + n + 1

3.n + 2

4.None of these

**Posted Date**:-2021-12-25 08:26:02

The number of binary operations on the set {a, b} are

1.2

2.4

3.8

4.16

**Posted Date**:-2021-12-25 08:00:07

The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

1.30Â°

2.90Â°

3.60Â°

4.120Â°

**Posted Date**:-2021-12-25 08:11:29

The period of the function f(x) = sin4 3x + cos4 3x is

1.Ï€/2

2.Ï€/3

3. Ï€/4

4.Ï€/6

**Posted Date**:-2021-12-25 08:04:23

The range of the function 7-xPx-3 is

1. {1, 2, 3, 4, 5}

2.{3, 4, 5}

3. {1, 2, 3}

4.None of these

**Posted Date**:-2021-12-25 08:03:50

The range of the function f(x) = 3x â€“ 2â€š is

1.(- âˆž, âˆž)

2.R â€“ {3}

3.(- âˆž, 0)

4.(0, â€“ âˆž)

**Posted Date**:-2021-12-24 19:49:51

The sum of the series 1Â² + 2Â² + 3Â² + â€¦â€¦â€¦..nÂ² is

1.n(n + 1)(2n + 1)

2.n(n + 1)(2n + 1)/2

3.n(n + 1)(2n + 1)/3

4.n(n + 1)(2n + 1)/6

**Posted Date**:-2021-12-25 08:22:57

The sum of the series 1Â³ + 2Â³ + 3Â³ + â€¦â€¦â€¦..nÂ³ is

1.{(n + 1)/2}Â²

2. {n/2}Â²

3.n(n + 1)/2

4.{n(n + 1)/2}Â²

**Posted Date**:-2021-12-25 08:20:42

The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is

1.tan 6x

2.2 tan 6x

3.3 tan 6x

4. 4 tan 6x

**Posted Date**:-2021-12-25 08:19:21

The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is

1.tan 6x

2.2 tan 6x

3.3 tan 6x

4. 4 tan 6x

**Posted Date**:-2021-12-25 08:20:01

The value of 4 Ã— sin x Ã— sin(x + Ï€/3) Ã— sin(x + 2Ï€/3) is

1.sin x

2.sin 2x

3.sin 3x

4.sin 4x

**Posted Date**:-2021-12-25 08:17:52

The value of âˆš(-144) is

1.12i

2.-12i

3. Â±12i

4.None of these

**Posted Date**:-2021-12-25 08:36:42

The value of âˆš(-16) is

1. -4i

2.4i

3.-2i

4.2i

**Posted Date**:-2021-12-25 08:35:57

The value of âˆš(-25) + 3âˆš(-4) + 2âˆš(-9) is

1. 13i

2. -13i

3.17i

4. -17i

**Posted Date**:-2021-12-25 08:41:00

The value of cos 180Â° is

1.0

2.1

3. -1

4.infinite

**Posted Date**:-2021-12-25 08:10:54

The value of cos 20 + 2sinÂ² 55 â€“ âˆš2 sin65 is

1.0

2.1

3.-1

4.None of these

**Posted Date**:-2021-12-25 08:16:06

The value of cos 5Ï€ is

1. 0

2.1

3.-1

4.None of these

**Posted Date**:-2021-12-25 08:08:41

The value of cosÂ² x + cosÂ² y â€“ 2cos x Ã— cos y Ã— cos (x + y) is

1.sin (x + y)

2.sinÂ² (x + y)

3.sinÂ³ (x + y)

4.sin4 (x + y)

**Posted Date**:-2021-12-25 08:06:20

The value of tan 20 Ã— tan 40 Ã— tan 80 is

1. tan 30

2.tan 60

3.2 tan 30

4.2 tan 60

**Posted Date**:-2021-12-25 08:13:31

The value of tan 20 Ã— tan 40 Ã— tan 80 is

1. tan 30

2.tan 60

3.2 tan 30

4.2 tan 60

**Posted Date**:-2021-12-25 08:13:31

Two finite sets have N and M elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second test. Then the value of M and N are

1.7, 6

2.6, 4

3.7, 4

4.6, 3

**Posted Date**:-2021-12-24 19:49:08

Two functions f and g are said to be equal if f

1. the domain of f = the domain of g

2. the co-domain of f = the co-domain of g

3.f(x) = g(x) for all x

4.All of the above

**Posted Date**:-2021-12-25 07:51:40

Which of the following sets are null sets

1.{x: |x |< -4, x ?N}

2.2 and 3

3. Set of all prime numbers between 15 and 19

4. {x: x < 5, x > 6}

**Posted Date**:-2021-12-24 19:42:33

Which of the following two sets are equal

1. A = {1, 2} and B = {1}

2.A = {1, 2} and B = {1, 2, 3}

3.A = {1, 2, 3} and B = {2, 1, 3}

4.A = {1, 2, 4} and B = {1, 2, 3}

**Posted Date**:-2021-12-24 19:54:39

{ (A, B) : AÂ² +BÂ² = 1} on the sets has the following relation

1.reflexive

2.symmetric

3.none

4.reflexive and transitive

**Posted Date**:-2021-12-24 19:48:26

{1 â€“ (1/2)}{1 â€“ (1/3)}{1 â€“ (1/4)} â€¦â€¦. {1 â€“ 1/(n + 1)} =

1.1/(n + 1) for all n âˆˆ N.

2.1/(n + 1) for all n âˆˆ R

3.n/(n + 1) for all n âˆˆ N

4. n/(n + 1) for all n âˆˆ R

**Posted Date**:-2021-12-25 08:23:46

{1/(3 âˆ™ 5)} + {1/(5 âˆ™ 7)} + {1/(7 âˆ™ 9)} + â€¦â€¦. + 1/{(2n + 1)(2n + 3)} =

1. n/(2n + 3)

2.n/{2(2n + 3)}

3.n/{3(2n + 3)}

4.n/{4(2n + 3)}

**Posted Date**:-2021-12-25 08:33:26

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