Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 70

HARD

JEE Main/Advance

IMPORTANT

Earn 100

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is equal to -

50% studentsanswered this correctly

Important Questions on Sequences and Series

MEDIUM

JEE Main/Advance

IMPORTANT

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

The third term of a

G . P .

is

4

. The product of the first five terms is equal to -

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 72

Consider an infinite

G . P .

with first term

a

and common ratio

r

. If its sum is

4

and the second term is

\frac{3}{4}

then value of

r

is equal to -

HARD

JEE Main/Advance

IMPORTANT

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

HARD

JEE Main/Advance

IMPORTANT

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

HARD

JEE Main/Advance

IMPORTANT

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 -

MEDIUM

JEE Main/Advance

IMPORTANT

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}] =

MEDIUM

JEE Main/Advance

IMPORTANT

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

MEDIUM

JEE Main/Advance

IMPORTANT

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