Test Details

All Syllabus Test

After submission, hard copy in single pdf should be send to me in 12th math group with rename pdf as your name in limited time.

Nov 14, 5:00 PM

90 minutes

Nov 14, 6:30 PM

50.0 marks

MCQ

27 questions

Dipesh Panigrahi

Dipesh has a B.Sc.(Hons) and M.Sc. B.Ed. in Mathematics from GGV Bilaspur, and 5+ year of teaching experience in the Mathematics. Over the course of his career , several students taught by him were able to secure full marks in Mathematics section in Various entrance examination .

Class Details

Mathematics

Class 12th

Mathematics

In this classroom, we cover entire syllabus of mathematics prescribed by CGBSE for standard XII

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Question Text

Question 3 :
If two angles of a triangle are $\tan ^{ -1 }{ (2) } $ and $\tan ^{ -1 }{ (3) } $, then the third angle is

Question 4 :
Consider the following : 1. ${\sin}^{-1}\dfrac{4}{5}+{\sin}^{-1}\dfrac{3}{5}=\dfrac{\pi}{2}$ 2. ${\tan}^{-1}\sqrt{3}+{\tan}^{-1}1=-{\tan}^{-1}(2+\sqrt{3})$ Which of the above is/are correct?

Question 5 :
What is the order of the product $ \begin{bmatrix} x &  y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ ?

Question 6 :
If $3\begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}-2\begin{bmatrix} -2 & 1 \\ 3 & 2 \end{bmatrix}+\begin{bmatrix} x & -4 \\ 3 & y \end{bmatrix}=0$ then $\left(x,y\right)=$

Question 7 :
If$\displaystyle a_{ij}=0\left ( i\neq j \right )$ and$\displaystyle a_{ij}=1\left ( i= j \right )$ then the matrix A=$\displaystyle \left [ a_{ij} \right ]_{n\times n}$ is a _____ matrix

Question 8 :
Find number of all such functions $y = f(x)$ which are one-one?

Question 9 :
If $f:R\rightarrow R$ given by $f(x)={ x }^{ 3 }+({ a+2)x }^{ 2 }+3ax+5$ is one-one, then $a$ belongs to the interval

Question 10 :
The function $f: R\rightarrow R$ given by $f(x) = x^{3} - 1$ is

Question 11 :
$\begin{vmatrix} 2^3 & 3^3 & 3.2^2+3.2+1\\ 3^3 & 4^3 & 3.3^2+3.3+1\\ 4^3 & 5^3 & 3.4^2+3.4+1\end{vmatrix}$ is equal to?

Question 12 :
If $m = \begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}$ and $n = \begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$, then what is the value of the determinant of $m \cos \theta - n \sin \theta$?

Question 13 :
If $A=\begin{vmatrix} 10 & 2 \\ 30 & 6 \end{vmatrix}\\ $ then $\left|A\right|=$

Question 15 :
Area bounded by the curve $y= sin^{-1}x, y-axis$ and $y = cos^{-1}x$ is equal to

Question 16 :
The area bounded by $y^{2}=4ax$ and $y=mx$ is $\displaystyle \frac{a^{2}}{3}$ sq. units then $\mathrm{m}$

Question 17 :
The radius of a circle is uniformly increasing at the rate of $3cm/s$. What is the rate of increase in area, when the radius is $10cm$?

Question 18 :
The velocity $v$ of a particle moving along a straight line and its distance $s$ from a fixed point on the line are related by $ v^2 = a^2 + s^2$, then its acceleration equals

Question 19 :
A spherical iron ball $10 cm$ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 cm^3/min$. When the thickness of ice is $5 cm$, then the rate of which the thickness of ice decreases, is.

Question 22 :
$\displaystyle \int \dfrac{1}{\sqrt{x}} \tan^4 \, \sqrt{x} \, \sec^2 \, \sqrt{x} \, dx = $

Question 23 :
The integral $\displaystyle \int { \left( 1+2{ x }^{ 2 }+\frac { 1 }{ x } \right) } { e }^{ { x }^{ 2-\frac { 1 }{ x } } }dx$ is equal to

Question 25 :
If $f(x)=\displaystyle\frac{\log(1+ax)-log(1-bx)}{x}$ for $x\neq 0$ and $f(0)=k$ and $f(x)$ is continuous at $x=0$, then $k$ is equal to:

Question 26 :
If $f\left( x \right) =\left\{ \begin{matrix} x& \text{if}\,\, x\,\, \text{is rational} \\ -x& \text{if}\,\, x\,\, \text{is irratonal} \end{matrix} \right. $, then $f(x)$ is:

Question 27 :
Consider the function $f(x)=\begin{cases}-2\sin x & if & x\le -\dfrac{\pi}{2} \\ A\sin x+B & if & -\dfrac{\pi}{2} < x < \dfrac{\pi}{2} \\ \cos x & if & x \ge \dfrac{\pi}{2}\end{cases}$ which is continuous everywhere. The value of A is

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