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

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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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Important Questions on Sequences and Series

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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 -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 6

Let

C

be a circle with centre

P_{0}

and

A B

be a diameter of

C

. Suppose

P_{1}

is the midpoint of line segment

P_{0} B, P_{2}

the midpoint of line segment

P_{1} B

and so on. Let

C_{1}, C_{2}, C_{3}

be circles with diameters

P_{0} P_{1}, P_{1} P_{2}, P_{2} P_{3}, . . . .

respectively Suppose the circles

C_{1}, C_{2}, C_{3} . . .

are all shaded. The ratio of the area of the unshaded portion of

C

to that of the original circle is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 7

If

b - c, 2 b - x

and

b - a

are in H.P., then

a - (x / 2), b - (x / 2)

and

c - (x / 2)

are in