Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 71

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The third term of a $G . P .$ is $4$ . The product of the first five terms is equal to -

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Important Questions on Sequences and Series

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 73

Let

x^{2} - 3 x + k = 0

has two positive roots

k_{1}

and

k_{2}

then minimum value of

\frac{4}{k_{1}} + \frac{1}{k_{2}}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 74

Let

x, y, z > 0

and

9 x + 3 y + z = 90

, then maximum value of

\log_{10} x + \log_{10} y + \log_{10} z

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 75

Equation $x^{4} + a x^{3} + b x^{2} + c x + 1 = 0$ has real roots where $a, b, c$ are non-negative then $\min (a + b + c)$ is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 1

If

θ_{1}, θ_{2}, θ_{3}, . . . . . . θ_{n}

are in

A . P

. whose common difference is

d

, then

\sin d [\sec θ_{1} \sec θ_{2} + \sec θ_{2} \sec θ_{3} + . . . . . . . . + \sec θ_{n - 1} \sec θ_{n}] =

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 2

Let

a, b

be the roots of the equation

x^{2} - 4 x + k_{1} = 0

and

c, d

the roots of the equation

x_{2} - 36 x + k_{2} = 0

. If

a < b < c < d

and

a, b, c, d

are in

GP

, then the product

k_{1} k_{2}

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 3

The value of

x + y + z

is

15

if

a, x, y, z, b

are in

A . P .

while the value of

\frac{1}{x} + \frac{1}{y} + \frac{1}{z}

is

\frac{5}{3}

if

a, x, y, z, b

are in

H . P .

the value of

a

and

b

are

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 4

If

x, y, z

are positive reals satisfying

4 x y + 6 y z + 8 z x = 9

, then the greatest possible value of the product

x y z

is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 5

If

a + b + c = 3

and

a > 0, b > 0, c > 0

, then the greatest value of

a^{2} b^{3} c^{2}

is -