Maths-

#### Sum of divisors of 2^{5 }·3^{7 }·5^{3 }· 7^{2} is –

Maths-General

- 2
^{6} · 3^{8} · 5^{4} · 7^{8}
- 2
^{6} · 3^{8} · 5^{4} · 7^{3} – 2 · 3 · 5 · 7
- 2
^{6} · 3^{8} · 5^{4} · 7^{3} – 1
- None of these

^{6}· 3^{8}· 5^{4}· 7^{8}^{6}· 3^{8}· 5^{4}· 7^{3}– 2 · 3 · 5 · 7^{6}· 3^{8}· 5^{4}· 7^{3}– 1#### Answer:The correct answer is: None of theseAny divisor of 2^{5} · 3^{7} · 5^{3} · 7^{2} is of the type of 2^{l} 3^{m} 5^{n} 7^{p}, where 0 *l* 5, 0 m 7, 0 n 3 and 0 p 2

Hence the sum of the divisors

= (1 + 2 + …… + 2^{5}) (1 + 3 + ……. + 3^{7}) (1 + 5 + 5^{2} + 5^{3}) (1 + 7 + 7^{2})

=

=.

^{l}

## Book A Free Demo

+91

Grade*

Select Grade

### Related Questions to study

maths-

#### The length of the perpendicular from the pole to the straight line is

#### The length of the perpendicular from the pole to the straight line is

maths-General

maths-

#### The condition for the lines and to be perpendicular is

#### The condition for the lines and to be perpendicular is

maths-General

maths-

#### If f : R →R; f(x) = sin x + x, then the value of (f^{-1} (x)) dx, is equal to

#### If f : R →R; f(x) = sin x + x, then the value of (f^{-1} (x)) dx, is equal to

maths-General

maths-

#### The polar equation of the straight line with intercepts 'a' and 'b' on the rays and respectively is

#### The polar equation of the straight line with intercepts 'a' and 'b' on the rays and respectively is

maths-General

maths-

#### The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is

#### The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is

maths-General

maths-

#### The polar equation of axy is

#### The polar equation of axy is

maths-General

maths-

#### If x, y, z are integers and x 0, y 1, z 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -

Let y = p + 1 and z = q + 2.

Then x 0, p 0, q 0 and x + y + z = 15

x + p + q = 12

The reqd. number of values of (x, y, z) and hence of (x, p, q)

= No. of non-negative integral solutions of x + p + q= 12

= Coeff. of x

= Coeff. of x

= Coeff. of x

=

Then x 0, p 0, q 0 and x + y + z = 15

x + p + q = 12

The reqd. number of values of (x, y, z) and hence of (x, p, q)

= No. of non-negative integral solutions of x + p + q= 12

= Coeff. of x

^{12}in (x^{0}+ x^{1}+ x^{2}+ ……)^{3}= Coeff. of x

^{12}in (1 – x)^{–3}= Coeff. of x

^{12}in [^{2}C_{0}+^{3}C_{1}x +^{4}C_{2}x^{2}+ ….]=

^{14}C_{12}= = = 91.#### If x, y, z are integers and x 0, y 1, z 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -

maths-General

Let y = p + 1 and z = q + 2.

Then x 0, p 0, q 0 and x + y + z = 15

x + p + q = 12

The reqd. number of values of (x, y, z) and hence of (x, p, q)

= No. of non-negative integral solutions of x + p + q= 12

= Coeff. of x

= Coeff. of x

= Coeff. of x

=

Then x 0, p 0, q 0 and x + y + z = 15

x + p + q = 12

The reqd. number of values of (x, y, z) and hence of (x, p, q)

= No. of non-negative integral solutions of x + p + q= 12

= Coeff. of x

^{12}in (x^{0}+ x^{1}+ x^{2}+ ……)^{3}= Coeff. of x

^{12}in (1 – x)^{–3}= Coeff. of x

^{12}in [^{2}C_{0}+^{3}C_{1}x +^{4}C_{2}x^{2}+ ….]=

^{14}C_{12}= = = 91.maths-

#### If then the equation whose roots are

#### If then the equation whose roots are

maths-General

maths-

#### Let p, q {1, 2, 3, 4}. Then number of equation of the form px^{2} + qx + 1 = 0, having real roots, is

#### Let p, q {1, 2, 3, 4}. Then number of equation of the form px^{2} + qx + 1 = 0, having real roots, is

maths-General

maths-

#### ax^{2} + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –

#### ax^{2} + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –

maths-General

maths-

#### The cartesian equation of is

#### The cartesian equation of is

maths-General

maths-

#### The castesian equation of is

#### The castesian equation of is

maths-General

maths-

#### The equation of the directrix of the conic whose length of the latusrectum is 5 and eccenticity is 1/2 is

#### The equation of the directrix of the conic whose length of the latusrectum is 5 and eccenticity is 1/2 is

maths-General

maths-

#### The equation of the directrix of the conic is

#### The equation of the directrix of the conic is

maths-General

maths-

#### The equation of the circle touching the initial line at pole and radius 2 is

#### The equation of the circle touching the initial line at pole and radius 2 is

maths-General