Biology
General
Easy
Question
Folder upper part of dermis is known as
- Skin papilla only
- Hair papilla only
- Dermal papilla only
- (A) and (B) both
The correct answer is: Dermal papilla only
Related Questions to study
maths-
A flag staff stands vertically on a pillar The height of the flag staff being double the height of the pillar Aman on the ground at a distance finds both pillar and the flag staff subtends equal angle
at his eye then ![theta equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAANCAYAAAC6hw6qAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ9JREFUeNpjYMAE1kC8DoifAvFBIDZnoCEwh1rGBOWLAvFdWlp4AYil0cR2ALEeLSxzAeL5WMSXA7EXLSycDcRBWMRBQeyGQ89/IjBOcA2PJnFq+w6USD6RIE4xAPlgLxZxUyBeg0cf2UEKyw7ooB6IE2nhQx5olkAGgkB8DojZaJUHrwBxHpStAcTHgdiHlpleD+rLX0B8CYj9GIYDAADc+i+zvWx1LgAAAFl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PG1vPj08L21vPjwvbWF0aD7cv019AAAAAElFTkSuQmCC)
A flag staff stands vertically on a pillar The height of the flag staff being double the height of the pillar Aman on the ground at a distance finds both pillar and the flag staff subtends equal angle
at his eye then ![theta equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAANCAYAAAC6hw6qAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ9JREFUeNpjYMAE1kC8DoifAvFBIDZnoCEwh1rGBOWLAvFdWlp4AYil0cR2ALEeLSxzAeL5WMSXA7EXLSycDcRBWMRBQeyGQ89/IjBOcA2PJnFq+w6USD6RIE4xAPlgLxZxUyBeg0cf2UEKyw7ooB6IE2nhQx5olkAGgkB8DojZaJUHrwBxHpStAcTHgdiHlpleD+rLX0B8CYj9GIYDAADc+i+zvWx1LgAAAFl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PG1vPj08L21vPjwvbWF0aD7cv019AAAAAElFTkSuQmCC)
maths-General
Maths-
Assertion A : The radius of the circle inscribed in the triangle obtained by joining the middle points of the sides of
ABC is equal to half the radius of incircle of
ABC.
Reasons R : In
ABC, D, E, F be midpoints of the sides of
ABC,
',2s' denote area and perimeter of ΔDEF then
' =
/ 4 and s' = s / 2
Assertion A : The radius of the circle inscribed in the triangle obtained by joining the middle points of the sides of
ABC is equal to half the radius of incircle of
ABC.
Reasons R : In
ABC, D, E, F be midpoints of the sides of
ABC,
',2s' denote area and perimeter of ΔDEF then
' =
/ 4 and s' = s / 2
Maths-General
Maths-
Let ABC be a triangle such the
,then
equal to
Let ABC be a triangle such the
,then
equal to
Maths-General
Maths-
In this question, we have to find the sum of the series. Separate the series in even and odd series, and replace with Log ( 1 – x2) and Log ( 1 + x / 1-x ) .
Maths-General
In this question, we have to find the sum of the series. Separate the series in even and odd series, and replace with Log ( 1 – x2) and Log ( 1 + x / 1-x ) .
maths-
If
and principal value be considered then value of z is-
If
and principal value be considered then value of z is-
maths-General
maths-
maths-General
maths-
The conditional
is
The conditional
is
maths-General
maths-
If p and q are simple propositions, then
is true when
If p and q are simple propositions, then
is true when
maths-General
maths-
Using Simpson’s
rule, the value of
for the following data, is
![](data:image/png;base64,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)
Using Simpson’s
rule, the value of
for the following data, is
![](data:image/png;base64,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)
maths-General
maths-
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506990/1/977896/Picture4.png)
By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506990/1/977896/Picture4.png)
By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is
maths-General
maths-
With the help of trapezoidal rule for numerical integration and the following table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508625/1/977890/Picture3.png)
the value of
is
With the help of trapezoidal rule for numerical integration and the following table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508625/1/977890/Picture3.png)
the value of
is
maths-General
maths-
A river is 80 metre wide. Its depth d metre and corresponding distance x metre from one bank is given below in table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508624/1/977888/Picture2.png)
Then approximate area of cross-section of river by Trapezoidal rule, is
A river is 80 metre wide. Its depth d metre and corresponding distance x metre from one bank is given below in table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508624/1/977888/Picture2.png)
Then approximate area of cross-section of river by Trapezoidal rule, is
maths-General
maths-
A curve passes through
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508623/1/977887/Picture244.png)
Then area bounded by x=1 and x=4 by Trapezoidal rule, is
A curve passes through
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508623/1/977887/Picture244.png)
Then area bounded by x=1 and x=4 by Trapezoidal rule, is
maths-General
maths-
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508622/1/977885/Picture31.png)
By Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=1, x=5, is
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508622/1/977885/Picture31.png)
By Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=1, x=5, is
maths-General
maths-
From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=7.47, x=7.52, is
![](data:image/png;base64,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)
From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=7.47, x=7.52, is
![](data:image/png;base64,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)
maths-General