Tag: mathematics and statistics

Questions Related to mathematics and statistics

Calculate the amount and the compound interest on Rs. $12,500$ in $3$ years when the rates of interest for successive years are $8 \%$, $10 \%$ and $10 \%$ respectively. 

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. Rs. $16,335$ and Rs. $3,835$

  2. Rs. $14,853$ and Rs. $2,353$

  3. Rs. $15,664$ and Rs. $3,164$

  4. Rs. $17952$ and Rs.$5,452$


Show answer
Correct Option: A
Explanation:

$P=Rs.12,500$

$T=3$ years
$R=8 \%,10 \%, 10 \%,$ 
$A=?,C.I.=?$
$A=P\left(1+\cfrac{R}{100} \right )^T$

$=12500\left(1+\cfrac{8}{100}\right)\left(1+\cfrac{10}{100}\right)\left(1+\cfrac{10}{100}\right)$
$=12500\times \cfrac{108}{100}\times \cfrac{110}{100}\times \cfrac{110}{100}$
$=\cfrac{125\times 108\times 121}{100}$
$A=Rs.  16,335$
$C.I.=A-P$
$C.I=16335-12500$
$C.I=Rs. 3835$ 

Raj borrows Rs.$16,000$; out of which Rs.$9,000$ at $5\%$ and remaining at $6\%$. Find the total interest paid by him in $4$ years.

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. $1600$

  2. $3480$

  3. $3600$

  4. $3300$

Show answer
Correct Option: B
Explanation:

${ I } _{ 1 }=\dfrac { P\times R\times T1 }{ 100 } =\dfrac { 9000\times 5\times 4 }{ 100 } =Rs.1800$


${ I } _{ 2 }=\dfrac { 7000\times 6\times 4 }{ 100 } =Rs.1680$


$\therefore $ Total Interest $=Rs.1800+Rs.1680=Rs.3480$

Value of $ \displaystyle \sin 45^{\circ} \cos 45 \left ( \tan 45^{\circ}+\cot 45^{\circ} \right )^{2}   $  is 

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: B
Explanation:

$ \displaystyle \sin 45^{\circ} \cos 45 \left ( \tan 45^{\circ}+\cot 45^{\circ} \right )^{2}   $

$=\dfrac{1}{\sqrt2} \times \dfrac{1}{\sqrt2} (1+1)^2 $


$=\dfrac42$

$=2$

Two angles are called adjacent if

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. they lie in the same plane and have a common vertex

  2. they have a ray in common

  3. the intersection of their interiors is empty

  4. all the above

Show answer
Correct Option: D
Explanation:

Two angles are called adjacent if
they lie in same plane and have a common vertex,they have a ray in common and the intersection of their interiors is empty.
do (D) all the above is correct

In a cyclic quadrilateral ABCD, $\displaystyle \angle ABC=60^{\circ}$ and if O be the centre of the circle then the measure of $\displaystyle \angle OAC$ is

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. $\displaystyle 20^{\circ}$

  2. $\displaystyle 30^{\circ}$

  3. $\displaystyle 40^{\circ}$

  4. $\displaystyle 50^{\circ}$

Show answer
Correct Option: B

Triangle measurement is called as _______.

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. pythagoras

  2. trigonometry

  3. calculus

  4. area of square

Show answer
Correct Option: B
Explanation:
Trigonometry is the study of triangle measurement.
Hence, the answer is trigonometry.

In the early 9th century AD, _________ produced accurate sine and cosine tables, and the first table of tangents.

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. Habash al-Hasib al-Marwazi

  2. Muhammad ibn Jabir al-Harrani al-Battani

  3. Muhammad ibn Musa al-Khwarizmi

  4. Abu al-Wafa al-Buzjani

Show answer
Correct Option: C
Explanation:

In the early 9th century AD, Muhammad ibn Mūsā al-Khwārizmī produced accurate sine and cosine tables, and the first table of tangents. He was also a pioneer in spherical trigonometry.

Who is the founder of trigonometry?

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. Euclid

  2. Issac Newton

  3. William Rowan Hamilton

  4. Hipparchus

Show answer
Correct Option: D
Explanation:

Hipparchus the founder of trigonometry. 

So, option D is correct.

The history of trigonometry goes back to the earliest recorded mathematics in Egypt and _____.

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. German

  2. Indian

  3. Babylon

  4. Japanese

Show answer
Correct Option: C
Explanation:

The history of trigonometry goes back to the earliest recorded mathematics in Egypt and Babylon.

So, option C is correct.

Trigonometry is used mainly due to the purpose of time keeping and _____.

mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

  1. space

  2. stars

  3. astronomy

  4. planets

Show answer
Correct Option: C
Explanation:

Trigonometry is used mainly due to the purpose of time keeping and astronomy.

So, option C is correct.