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1003107203

Level:

Insert such

3

numbers between the roots of the equation

x^{2} - 10 x - 119 = 0

, so that together with the roots of the equation they form

5

consecutive arithmetic sequence terms. What is the central term?

5

17

6

- 1

- 7

1003107202

Level:

The second term of an arithmetic sequence is

- 21

, the fifth term is

21

. How many of the first consecutive terms do we have to add up to get a sum of more than

50

8

7

6

9

5

1003107201

Level:

The sum of the first ten terms of an arithmetic sequence with odd subscripts is

190

, the sum of the first ten terms with even subscripts is

230

. Find the first term.

- 17

- 34

5

4

10

1003124304

Level:

Given a function

f (x) = a x^{4} + b x

, find real numbers

a

and

b

, such that

\int_{0}^{1} f (x) d x = 27

and

\int_{- 1}^{0} f (x) d x = 57

a = 210

b = - 30

a = 210

b = 30

a = 75

b = 60

a = 30

b = 210

1003124308

Level:

Which of the values of a real number

a \in (π; 2 π)

makes the equality

\int_{π}^{a + π} \sin 2 x d x = 1

true?

a = \frac{3}{2} π

a = \frac{3}{4} π

a = \frac{1}{2} π

a = \frac{2}{3} π

1003124307

Level:

Which of the positive values of a real number

a

makes the equality

\int_{a}^{7} \frac{6 x - 5}{3 x^{2} - 5 x} d x = \ln 56

true?

a = 2

a = 1

a = 3

a = 5

1003124306

Level:

Which of the positive values of a real number

a

makes the equality

\int_{1}^{a} \frac{3}{3 x + 5} d x = \ln \frac{7}{4}

true?

a = 3

a = 2

a = 4

a = 5

1003124305

Level:

Given a function

f (x) = a x^{6} + b x^{3} + c x + 8

, find real numbers

a

b

and

c

, such that

\int_{0}^{1} f (x) d x = \frac{35}{4}

f^{'} (0) = 2

and

f^{'} (1) = 180

a = 7

b = - 5

c = 2

a = 7

b = 5

c = 2

a = - 7

b = - 5

c = 2

a = - 7

b = 5

c = - 2

1003124303

Level:

Which of the given values of real numbers

a

b \in (0; \frac{π}{2})

, such as

a < b

, makes the equality

\int_{a}^{b} \cos x d x = 2 \cos \frac{π}{4} \cdot \sin \frac{π}{12}

true?

a = \frac{π}{6}

b = \frac{π}{3}

a = \frac{π}{3}

b = \frac{π}{6}

a = \frac{π}{3}

b = \frac{π}{4}

a = \frac{π}{4}

b = \frac{π}{3}

1003124302

Level:

Which of the given values of a real number

a \in (\frac{π}{2}; π)

makes the equality

\int_{a}^{2 a} (3 \sin x - 4 x) d x = - 6 a^{2}

true?

a = \frac{2}{3} π

a = \frac{5}{6} π

a = \frac{3}{4} π

a = \frac{7}{8} π

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