### 12th Standard CBSE Maths Study material & Free Online Practice Tests - View and download Sample Question Papers with Solutions for Class 12 Session 2019 - 2020 CBSE

#### 12th CBSE Mathematics Differential Equations Model Question Paper - by Shalini Sharma - Udaipur Aug 12, 2019 - View & Download

• 1)

Write the degree of the differential equation: $5x{ \left( \frac { dy }{ dx } \right) }^{ 2 }-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0.$

• 2)

Write the sum of the order and degree of the differential equation $1+\left( \frac { dy }{ dx } \right) ^{ 4 }=7\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 3 }$

• 3)

Write the degree of the differential equation ${ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+x\left( \frac { dy }{ dx } \right) ^{ 4 }=0$

• 4)

Find the differential equation representing the family of curves $V=\frac { A }{ r } +B$ , where A and B arbitrary constants.

• 5)

Find the integrating factor of the differential equation $\left( \frac { { e }^{ -2\sqrt { x } } }{ \sqrt { x } } -\frac { y }{ \sqrt { x } } \right) \frac { dx }{ dy } =1$ .

#### 12th Standard CBSE Mathematics Unit 8 Application of Integrals Model Question Paper - by Shalini Sharma - Udaipur Aug 05, 2019 - View & Download

• 1)

Find the area of the region by the curve $y=\frac { 1 }{ x }$ , X-axis and between X = 1, X = 4.

• 2)

Find the area of the region bounded by the curve y2 = x and the lines x = 1 , x = 4 and the x -  axis.

• 3)

The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.

• 4)

Using integration, find the area of the triangular region whose sides have the equations:
y = 2x + 1, y = 3x + 1and x = 4.

• 5)

Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is :
(A) $2(\pi -2)$
(B) $\pi -2$
(C) $2\pi -1$
(D) $2(\pi +2)$

#### 12th Standard CBSE Mathematics Unit 7 Integrals Model Question Paper - by Shalini Sharma - Udaipur Aug 03, 2019 - View & Download

• 1)

Evaluate the integral: $\int { {x^2\over1+x^3}dx. }$

• 2)

Evaluate the integral: $\int {(ax\ +\ b)^3}dx$

• 3)

$\int cos^2x\ cosec^2x\ dx.$

• 4)

$\int {x\over \sqrt {x+2}}dx.$

• 5)

Given $\int { { e }^{ x }(tanx+1)secxdx={ e }^{ x }f(x)+c }$. Write f(x) satisfying the above.

#### 12th CBSE Mathematics Unit 6 Application of Derivatives Model Question Paper - by Shalini Sharma - Udaipur Jul 31, 2019 - View & Download

• 1)

The amount of pollution content added in air in a city due to X diesel vehicles is given by P(x)=0.005x3+0.02x2 +30x.Find the marginal increase   in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question?

• 2)

For what value of m,The function f(x)=mx+c,is decreasing for x $\epsilon$ R.

• 3)

Show that f(x)=(x-1) ex+1 is an increasing function for x > 0.

• 4)

For the function y=x3, if x=5 and $\Delta$x=0.01,find $\Delta$y

• 5)

f(x)=9x2+12x+2

#### 12th CBSE Mathematics Unit 5 Continuity and Differentiability Important Question Paper - by Shalini Sharma - Udaipur Jul 29, 2019 - View & Download

• 1)

Examine the continuity of the function f (x)=$\frac { 1 }{ x+3 } ,\quad x\quad \varepsilon \quad R$.

• 2)

Give an example of a function which is continuous at x=1, but not differentiable at x=1.

• 3)

State the points of discountinuity for the function $f(x)= [x]$  in $-3 < x < 3.$

• 4)

If y= sec-1 $\left( \frac { \sqrt { x } +1 }{ \sqrt { x } -1 } \right) +\quad sin^{ -1 }\left( \frac { \sqrt { x } -1 }{ \sqrt { x } +1 } \right) ,\quad find\frac { dy }{ dx } .$

• 5)

Differentiate the following w.r.t. x, or find $\frac { dy }{ dx }$.

$y={ e }^{ x }+{ e }^{ { x }^{ 2 } }+{ e }^{ { x }^{ 3 } }+{ e }^{ { x }^{ 4 } }+{ e }^{ { x }^{ 5 } }.$

#### 12th CBSE Mathematics Unit 4 Determinants Important Question Paper - by Shalini Sharma - Udaipur Jul 27, 2019 - View & Download

• 1)

If A is a square matrix of order 3 and |3A|=k|A|, then write the value of k.

• 2)

What positive value of x makes the following pair of determinants equal?

$\begin{vmatrix} 2x & 3 \\ 5 & x \end{vmatrix},\begin{vmatrix} 16 & 3 \\ 5 & 2 \end{vmatrix}$

• 3)

Write the adjoint of the following matrix $\begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}$

• 4)

Evaluate $\begin{vmatrix} cos15^{ o } & sin15^{ o } \\ sin75^{ o } & cos75^{ o } \end{vmatrix}$

• 5)

Given determinant $\begin{vmatrix} a_{ 11 } & a_{ 12 } & a_{ 13 } \\ a_{ 21 } & a_{ 22 } & a_{ 23 } \\ a_{ 31 } & a_{ 32 } & a_{ 33 } \end{vmatrix}$.Find the value of a11A21+a12A22+a13A23, where Aij is cofactor of element aij

#### 12th Standard CBSE Mathematics Unit 3 Matrices Important Question Paper - by Shalini Sharma - Udaipur Jul 26, 2019 - View & Download

• 1)

If $\left[ \begin{matrix} x & +3y & y \\ 7 & -x & 4 \end{matrix} \right]$=$\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix}$, find the values of x and y.

• 2)

If matrix A=$[\begin{matrix} 1 & 2 & 3 \end{matrix}]$ write AA' , where A' is the transpose of matrix A.

• 3)

If $\left[ \begin{matrix} y & +2x & 5 \\ & -x & 3 \end{matrix} \right] =\begin{bmatrix} 7 & 5 \\ -2 & 3 \end{bmatrix}$, find the value of y.

• 4)

If $A=\left[ { a }_{ ij } \right] =\left[ \begin{matrix} 2 & 3 & -5 \\ 1 & 4 & 9 \\ 0 & 7 & -2 \end{matrix} \right] andb=\left[ { b }_{ ij } \right] =\left[ \begin{matrix} 2 & 1 & -1 \\ -3 & 4 & 4 \\ 1 & 5 & 2 \end{matrix} \right] ,then\quad find\quad { a }_{ 22 }+{ b }_{ 21 }.$

• 5)

If $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\begin{bmatrix} 3 & 1 \\ 2 & 5 \end{bmatrix}=\begin{bmatrix} 7 & 11 \\ k & 23 \end{bmatrix}$, find the value of k.

#### 12th CBSE Maths Unit 2 Inverse Trigonometric Functions Important Question Paper - by Shalini Sharma - Udaipur Jul 24, 2019 - View & Download

• 1)

Evaluate  $sin\left[ \frac { \pi }{ 3 } -{ sin }^{ -1 }\left( -\frac { 1 }{ 2 } \right) \right]$ .

• 2)

Using principal value, evaluate the following:  ${ cos }^{ -1 }\left( cos\frac { 2\pi }{ 3 } \right) +{ sin }^{ -1 }\left( sin\frac { 2\pi }{ 3 } \right)$

• 3)

Show that ${ sin }^{ -1 }\left( 2X\sqrt { 1-{ X }^{ 2 } } \right) =2{ sin }^{ -1 }X$

• 4)

Solve for X, $\quad { tan }^{ -1 }\frac { 1-X }{ 1+X } =\frac { 1 }{ 2 } { tan }^{ -1 }X,\quad X>0.$

• 5)

Write the principal values of the following: ${ cos }^{ -1 }\left( cos\frac { 7\pi }{ 6 } \right)$

#### CBSE 12th Standard Mathematics Unit 1 Important Questions - by Shalini Sharma - Udaipur Jul 18, 2019 - View & Download

• 1)

If f(X)=X+7 and g(X)=X-7, $X\in R,$ find fog(7). ?

• 2)

If the binary operation * on the set of integers Z is defined by a*b=a+3bthen find the value of 2*4.

• 3)

Let * be a binary operation on N given by a*b=HCF(a,b), $a,b\in N$. Write the value of 22*4.

• 4)

If the binary operation * defined on Q is defined as a*b=2a+b-ab, for all $a,b\in Q,$ find the value of 3*4.

• 5)

If f:$R\to R$ be defined by $f(X)=(3-X^3)^{1\over3}$ then find fof(X).

#### Maths CBSE 12 Class Revision Test paper - by Bala Dec 29, 2018 - View & Download

• 1)

For the set A={1,2,3} define a relation R in the set A is follows:

R={(1,1).(2,2),(3,3),(1,3)}. Write the ordered pairs to be added to R to make it the smallest equivalence relation.

• 2)

If matrix A=$[\begin{matrix} 1 & 2 & 3 \end{matrix}]$ write AA' , where A' is the transpose of matrix A.

• 3)

Evaluate : $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { e }^{ x }Isinx+cosx) } dx$

• 4)

Find $\lambda$, if the vectors
$\overrightarrow a=\overset\wedge i+3\overset\wedge j+\overset\wedge k,\overrightarrow b=2\overset\wedge i-\overset\wedge j-\overset\wedge k$ and $\overrightarrow c=\lambda \overset\wedge j+3\overset\wedge k$ are coplanar.

• 5)

How many equivalence relations on the set {1,2, 3} containing (I, 2) and (2, 1) are there in all ? Justify your answer.

#### CBSE Maths First Full Test Class 12 - by Bala Dec 29, 2018 - View & Download

• 1)

Let * be a binary operation on N given by a * b = LCM(a,b) for all a,b $\in$ N. Find 5*7

• 2)

Use elementary column operation ${ C }_{ 2 }\rightarrow { C }_{ 2 }+2{ C }_{ 1 }$ in the following matrix equation :
$\left( \begin{matrix} 4 & 2 \\ 3 & 3 \end{matrix} \right) =\left( \begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix} \right) \left( \begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix} \right)$

• 3)

Evaluate the integral: $\int {(1-x)\sqrt x\ dx}$

• 4)

Find $\lambda$ when the projection of $\overrightarrow { a } =\lambda \hat { i } +\hat { j } +4\hat { k } \quad on\quad \overrightarrow { b } =2\hat { i } +6\hat { j } +3\hat { k }$ is 4 units.

• 5)

Define Reflexive.Give one example.

#### CBSE Class 12 Mathematics Important Question Paper - by Bala Dec 29, 2018 - View & Download

• 1)

Show that the relation R:{1,2,3}$\rightarrow${1,2,3} given by R={(1,1),(2,2),(3,3),(1,2),(2,3)} is reflexive but neither symmetric nor transitive.

• 2)

If $A=\begin{bmatrix} cos\alpha - & sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix}$, then for what value of $\alpha$, A is an identify matrix?

• 3)

Evaluate the integral: $\int {(1-x)\sqrt x\ dx}$

• 4)

Write the value of the area of the parallelogram determined by the vectors $2\hat { i } \quad and\quad 3\hat { j }$

• 5)

Let f and g be real function be $f(x)=\sqrt { x+4 } ,x\ge 4$ find the function fg, $\frac { f }{ g }$

#### Vector Algebra Important Questions CBSE 12th Mathematics - by Bala Dec 14, 2018 - View & Download

• 1)

Find a unit vector in the direction of $\overrightarrow { a } =3\overrightarrow { i } -2\overrightarrow { j } +6\overrightarrow { k }$

• 2)

If p(1,5,4) and Q(4,1,-2) find the direction ratios of $\overrightarrow { PQ }$

• 3)

Write the direction cosines of the vector $-2\hat { i } +\hat { j } -5\hat { k }$

• 4)

If $\overrightarrow { a }$ is a unit vector and $(\overrightarrow { x } -\overrightarrow { a } ).(\overrightarrow { x } +\overrightarrow { a } )=8\quad find\quad \left| \overrightarrow { x } \right|$

• 5)

Find the sum of the vectors $\overset\rightarrow a=\overset\wedge i-2\overset\wedge j+\overset\wedge k,\overset\rightarrow b=-2\overset\wedge i+4\overset\wedge j+5\overset\wedge k,\overset\rightarrow c=\overset\wedge i-6\overset\wedge j-7\overset\wedge k.$

#### 12th CBSE Mathematics Three Dimensional Geometry Important Question Paper - by Bala Dec 10, 2018 - View & Download

• 1)

Find the direction ratios of the line $\frac { x+2 }{ 1 } =\frac { 2y-1 }{ 3 } =\frac { 3-z }{ 5 } .$

• 2)

Find the angle between the line $\vec { r } =(2\hat { i } -\hat { j } +3\hat { k } )+\lambda (3\hat { i } -\hat { j } +2\hat { k } )$  and the plane $\vec { r } .(\hat { i } +\hat { j } +\hat { k } )=3.$

• 3)

What is the distance of the point (p,q,r) from the x-axis?

• 4)

Find the distance of a point (2, 5, - 3) from the plane $\overset { \rightarrow }{ r } (6\hat { i } +3\hat { j+6\hat { 2k } )=4 }$

• 5)

Find the length of the perpendicular drawrt from the origin to the plane 2x - 3y + 6z + 21 = 0

#### 12th CBSE Mathematics Linear Programming Model Question Paper - by Bala Dec 01, 2018 - View & Download

• 1)

The objective function is maximum or minimum, which lies on the boundary of the feasible region.

• 2)

Solve the following problem graphically:
Minimise and Maximise Z=3x+9y subject to the constraints:
$x+3y\le 60,x+y\ge 10,x\le y,x\ge 0,y\ge 0.$

• 3)

Maximise Z=3x+2y
subject to $x+2y\le 10,3x+y\le 15,x,y\ge 0.$

• 4)

Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs RS. 60/kg and Food Q costs RS. 80/kg. Food P contains 3 units/kg of Vitamin A AND 4 units/kg of vitamin B. Food Q contains 5 units/kg Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.

• 5)

A farmer mixes two brands P and Q of cattle feed. Brand P, costing RS.250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of vitamin C. Brand Q costing RS.200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A,B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?

#### 12th CBSE Mathematics Probability Important Question Paper - by Bala Nov 30, 2018 - View & Download

• 1)

If P(A)=0.4, P(B)=p and $P(A\cup B)=0.7$ find the value of p, if A and B are independent events.

• 2)

Given P(A)=0.4, P(B)=0.7 and P(B/A)=0.6, Find $P(A\cup B)$

• 3)

A bag contain 2 red, 6 black and 8 green balls. A ball is drawn at random from the bag. Find the probabilty:
(a) a red ball
(b) a black ball
(c) a green ball
(d) a non-red ball

• 4)

If P(E) =$\frac { 6 }{ 11 }$, P(F) =$\frac { 5 }{ 11 }$ and P(E$\cup$F)=$\frac { 7 }{ 11 }$ then find (a) P(E/F), (b) P(F/E)

• 5)

If P(F) = 0.35 and P(E$\cup$F) = 0.85 and E and F are independent events. Find P(E).

#### 12th Standard Mathematics Revision Model Question Paper 1 - by Bala Nov 29, 2018 - View & Download

• 1)

State the reason for the relation R in the set {1,2,3} given by R={(1,2),(2,1),} not to be transitive.

• 2)

Find the principal value of ${ sin }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2 } \right)$

• 3)

If ${ X }_{ m\times 3 }{ Y }_{ p\times 4 }={ Z }_{ 2\times b }$, for three matrices X,Y and Z, find the values of m,p and b.

• 4)

$\int {x^2-1\over x^2+1}dx.$

• 5)

Let f:$X\rightarrow Y$ be a function Define a relation R on X given be R=[(a,b) ; (f(b)] Show that R is an equivalence relation ?

#### 12th Standard CBSE Mathematics Term Test Question Paper - by Bala Sep 15, 2018 - View & Download

• 1)

If the binary operation * on the set of integers Z is defined by a*b=a+3bthen find the value of 2*4.

• 2)

Let * be a binary operation on N given by a*b=HCF(a,b), $a,b\in N$. Write the value of 22*4.

• 3)

If the binary operation * defined on Q is defined as a*b=2a+b-ab, for all $a,b\in Q,$ find the value of 3*4.

• 4)

Let f:$R\rightarrow R$ is defined by f(x)=|x|. Is function f onto? Give reasons.

• 5)

Let R be a relation in the set of natural numbers N defined by R={(a,b)$\in$NXN;a

#### Probability - Important Questions Model Paper In 12th Maths - by Bala Aug 01, 2018 - View & Download

• 1)

Given P(A)=$1\over2$,P(B)=$1\over3$ and $P(A\cap B)={1\over6}$  Are the events A and B independent?

• 2)

Given P(A)=0.2, P(B)=0.3 and $P(A\cap B)=0.3$ Find P(A/B)

• 3)

Given P(A)=0.4, P(B)=0.7 and P(B/A)=0.6, Find $P(A\cup B)$

• 4)

Events E and F are given to be independent. Find P(F) if it is given that P(E)=0.60 and P(E$\cap$F)=0.35

• 5)

Does the following represent a probability distribution? Give reasons.

 X 0 1 2 P(x) 1/3 1/3 1/6

#### Linear Programming - Important Questions Model Question Paper 1 In 12th Maths - by Bala Aug 01, 2018 - View & Download

• 1)

Solve the following linear programming problem graphically:
Maximise Z=4x+y subject to the constraints:
$\\ x+y\le 50,3x+y\le 90,x\ge 0,y\ge 0.$

• 2)

Solve the following problem graphically:
Minimise and Maximise Z=3x+9y subject to the constraints:
$x+3y\le 60,x+y\ge 10,x\le y,x\ge 0,y\ge 0.$

• 3)

Determine the minimum value of Z=3x+2y (if any), if the feasible region for an LLP is shown in the figure:

• 4)

Solve the following LLP graphically:
Maximise Z=2x+3y, subject to $x+y\le 4,x\ge 0,y\ge 0.$

• 5)

Minimize and Maximize Z=5x+2y, subject to the following constraints:
$x-2y\le 2,3x+2y\le 12,-3x+2y\le 3,x\ge 0,y\ge 0.$

#### Three Dimensional Geometry - Important Questions Model Question Paper 1 In 12th Maths - by Bala Aug 01, 2018 - View & Download

• 1)

Find the distance of the point (2,3,4) from the plane $\overrightarrow { r } .(3\acute { i } -6\acute { j } +2\acute { k } )=-11$.

• 2)

Write the Cartesian equation of the following line given in vector form:

$\overrightarrow { r } =2\hat { i } +\hat { j } +4\hat { k } +\lambda (\hat { i } +\hat { j } -\hat { k } )$

• 3)

Write the vector equation of a line whose Cartesian equation is $\frac { x+3 }{ 2 } =\frac { y-1 }{ 4 } =\frac { z+1 }{ 5 }$.

• 4)

Find the vector normal to the plane $\vec { r } .(3\hat { i } -7\hat { k } )+5=0$.

• 5)

Find the coordinates of a point, where the line $\frac { x+2 }{ 1 } =\frac { y-5 }{ 3 } =\frac { z+1 }{ 5 }$ cuts yz-plane.

#### Vector Algebra - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 31, 2018 - View & Download

• 1)

Find the angle between the vectors $\overrightarrow { a } =\overrightarrow { i } -\overrightarrow { j } +\overrightarrow { k } and\quad \overrightarrow { b } =\overrightarrow { i } +\overrightarrow { j } -\overrightarrow { k }$

• 2)

Find a vector in the direction of $\overrightarrow { a } =\overrightarrow { i } -2\overrightarrow { j }$ whose magnitude is 7.

• 3)

Vectors $\overrightarrow { a } \quad and\quad \overrightarrow { b }$ are such that $\left| \overrightarrow { a } \right| =\sqrt { 3 } ,\left| \overrightarrow { b } \right| =\frac { 2 }{ 3 } and\quad (\overrightarrow { a } \times \overrightarrow { b } )$ is a unit vector. write the angle between $\overrightarrow { a } \quad and\quad \overrightarrow { b }$?

• 4)

If $\overrightarrow { a } =x\hat { i } +2\hat { j } -z\hat { k } \quad and\quad \overrightarrow { b } =3\hat { i } -y\hat { j } +\hat { k }$ are two equal vectors then write the value of x+y+z.

• 5)

If $\left| \overrightarrow { a } \right| =3$ interpret the following:

(i)2$\overrightarrow { a }$   (ii)-5$\overrightarrow { a }$

#### Differential Equations - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 31, 2018 - View & Download

• 1)

What is the degree of the following differential equation?

${ { 5x\left( \frac { dy }{ dx } \right) } }^{ 2 }-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -6y=logx$

• 2)

Write the order and degree of the differential equation $(\frac{{d}^{2}y}{{dx}^{2}})^{3}$ -5$\frac{dy}{dx}$+6=0.

• 3)

Find the differential equation of the family of lines passing through the origin.

• 4)

Write the differential equation representing the curve y2 = 4ax, where a is an arbitrary constant.

• 5)

Find the integrating factor of the differential equation $\left( \frac { { e }^{ -2\sqrt { x } } }{ \sqrt { x } } -\frac { y }{ \sqrt { x } } \right) \frac { dx }{ dy } =1$ .

#### Application Of Integrals - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 31, 2018 - View & Download

• 1)

Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x - axis in the first quadrant.

• 2)

Find the area of the region in the first quadrant enclosed by x - axis and $x=\sqrt { 3 } y$ by the circle ${ x }^{ 2 }+{ y }^{ 2 }=4$.

• 3)

The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.

• 4)

Find the area bounded by the curve x2 = 4y and the line x = 4y - 2.

• 5)

Area lying between the curves y2 = 4x and y = 2x is :
(A) $\frac { 2 }{ 3 }$
(B) $\frac { 1 }{ 3 }$
(C) $\frac { 1 }{ 4 }$
(D) $\frac { 3 }{ 4 }$

#### Integrals - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 31, 2018 - View & Download

• 1)

Evaluate the integral: $\int { {x^2\over1+x^3}dx. }$

• 2)

$\int {1+tan\ x\over 1-tan\ x}dx$.

• 3)

$\int {dx\over x\ cos^2 (1+log\ x)}$.

• 4)

$\int {x^2-1\over x^2+1}dx.$

• 5)

$\int {e^x\over 1+e^x}dx.$

#### Application Of Derivatives - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 30, 2018 - View & Download

• 1)

The amount of pollution content added in air in a city due to X diesel vehicles is given by P(x)=0.005x3+0.02x2 +30x.Find the marginal increase   in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question?

• 2)

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue(marginal revenue).If the total revenue(in rupees)received from the sale of x units of a product is given by R9x)=3x2+36+5,find the marginal revenue,when=5,and write which value does the question indicate?

• 3)

The total cost C(x) associated with provision of free mid-day meals to x students of a school in primary classes is given by

C(x)=0.005x3-0.02x2+30x+50

If the marginal cost is given by rate of change $dC\over dX$of total cost,write the marginal cost of food for 300students.What value is shown here?

• 4)

The total revenue received from the sale of x souvenirs in connection with 'PEACE DAY'is given by R(x)=3x2+40x+10.Find the marginal revenue when 100souvenirs were sold.What is the importance of celebrating Peace Day in our life?

• 5)

A balloon which always remains spherical has a variable diameter ${3\over2}(2x+1)$.Find the rate of change of its volume with respect to x.

#### Continuity And Differentiability - Important Questions Model Paper In 12th Maths - by Bala Jul 30, 2018 - View & Download

• 1)

Examine the continuity of the function f (x) = x2+5 at x=-1

• 2)

Examine the continuity of the function f (x)=$\frac { 1 }{ x+3 } ,\quad x\quad \varepsilon \quad R$.

• 3)

Give an example of a function which is continuous at x=1, but not differentiable at x=1.

• 4)

State the points of discountinuity for the function $f(x)= [x]$  in $-3 < x < 3.$

• 5)

Show that the function f (x)= $\begin{cases} { x }^{ 3 }+3\quad ,\quad if\quad x\neq 0 \\ 1\quad \quad \quad ,\quad if\quad x=0 \end{cases}$ is not continuous at x=0.

#### Determinants - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 30, 2018 - View & Download

• 1)

Find the cofactor of a12 in the following.$\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}$

• 2)

Write the adjoint of the following matrix $\begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}$

• 3)

If $\begin{vmatrix} x+1 & x-1 \\ x-3 & x+2 \end{vmatrix}=\begin{vmatrix} 4 & -1 \\ 1 & 3 \end{vmatrix}$then write the value of x.

• 4)

A is a non-singular matrix of order 3 and |A|=-4. Find |adj A|

• 5)

In the interval  $\frac { \pi }{ 2 } , find the value of x for which that matrix \(\left[ \begin{matrix} 2sinx \\ 1 \end{matrix}\begin{matrix} 3 \\ 2sinx \end{matrix} \right]$ is singular.

#### Matrices - Important Questions Model Question Paper 1 In 12th Maths - by Bala Jul 30, 2018 - View & Download

• 1)

If $\left[ \begin{matrix} x & +3y & y \\ 7 & -x & 4 \end{matrix} \right]$=$\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix}$, find the values of x and y.

• 2)

Write the value of x-y+z from the following equation :

$\left[ \begin{matrix} x+y+z \\ x+z \\ y+z \end{matrix} \right] =\left[ \begin{matrix} 9 \\ 5 \\ 7 \end{matrix} \right]$

• 3)

If ${ A }^{ T }=\left[ \begin{matrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{matrix} \right]$and $B=\left[ \begin{matrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{matrix} \right]$, then find ${ A }^{ T }-{ B }^{ T }$.

• 4)

If matrix $A=\begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$ and ${ A }^{ 2 }=kA$, then write the value of k.

• 5)

A matrix has 18 elements. Write the possible orders of a matrix

#### 12th Maths Model Question Paper 5 - by Bala Jul 27, 2018 - View & Download

• 1)

Show that ${ sin }^{ -1 }\left( 2X\sqrt { 1-{ X }^{ 2 } } \right) =2{ sin }^{ -1 }X$

• 2)

Solve for X, $\quad { tan }^{ -1 }\frac { 1-X }{ 1+X } =\frac { 1 }{ 2 } { tan }^{ -1 }X,\quad X>0.$

• 3)

Write the principal values of the following: sec-1(-2).

• 4)

Write the principal values of the following: ${ cot }^{ -1 }\left( -\sqrt { 3 } \right)$

• 5)

Find the principal value of ${ tan }^{ -1 }\sqrt { 3 } -{ sec }^{ -1 }\left( -2 \right)$

#### 12th Maths Model Question Paper 1 - by Bala Jul 27, 2018 - View & Download

• 1)

If the binary operation * on the set of integers Z is defined by a*b=a+3bthen find the value of 2*4.

• 2)

Let * be a binary operation on N given by a*b=HCF(a,b), $a,b\in N$. Write the value of 22*4.

• 3)

If f:$R\to R$ and g:$R\to R$are given by f(X)=sin x and g(x)=5x2 find gof(x).

• 4)

State the reason for the relation R in the set {1,2,3} given by R={(1,2),(2,1),} not to be transitive.

• 5)

Let f:$R\rightarrow R$ is defined by f(x)=x2. Is f one-one?

#### Inverse Trigonometric Functions - Important Four Marks Questions Model Question Paper In 12th Maths - by AJAY KAKKAR Jun 09, 2018 - View & Download

• 1)

Write in the simplest form: $({ tan }^{ -1 }\left[ \frac { \sqrt { 1+sin\quad x } +{ \sqrt { 1-sin\quad x } }\quad }{ \sqrt { 1+sin\quad x } +{ \sqrt { 1-sin\quad x } } } \right] ,0<x<\frac { \pi }{ 2 }$

• 2)

Solve for X, 2tan-1(sinX)=tan-1(2secX),$X\neq \frac { \pi }{ 2 }$

• 3)

Solve the following equations:

${ cot }^{ -1 }X-{ cot }^{ -1 }\left( X+2 \right) =\frac { \pi }{ 12 }$

• 4)

Solve the following equations:

${ tan }^{ -1 }\frac { X+1 }{ X-1 } +{ tan }^{ -1 }\frac { X-1 }{ X } ={ tan }^{ -1 }\left( -7 \right)$

• 5)

Solve the following equations in term of  $\beta$${ tan }^{ -1 }\left[ \frac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right] =\beta$

#### Inverse Trigonometric Functions - Important Two Marks Questions Model Question Paper In 12th Maths - by AJAY KAKKAR Jun 09, 2018 - View & Download

• 1)

Write in the simplest form : ${ tan }^{ -1 }\left[ \frac { cos\quad x }{ 1+sin\quad x } \right] ,x\left[ -\frac { \pi }{ 2 } ,\frac { \pi }{ 2 } \right]$

• 2)

Show that : ${ tan }^{ -1 }\frac { 3 }{ 4 } +{ tan }^{ -1 }\frac { 3 }{ 5 } -{ tan }^{ -1 }\frac { 8 }{ 19 } =\frac { \pi }{ 4 }$

• 3)

Show that ${ tan }^{ -1 }\frac { x }{ y } -{ tan }^{ -1 }\frac { x-y }{ x+y } =\frac { \pi }{ 4 }$

• 4)

Show that ${ sin }^{ -1 }\frac { 5 }{ 13 } +{ cos }^{ -1 }\frac { 3 }{ 5 } ={ tan }^{ -1 }\frac { 63 }{ 16 }$

• 5)

Evaluate : $4 { tan }^{ -1 }\frac { 1 }{ 5 }$

#### Continuity And Differentiability - Important Two Marks Questions Model Question Paper In 12th Maths - by AJAY KAKKAR Jun 09, 2018 - View & Download

• 1)

Show that the function f (x)= $\begin{cases} { x }^{ 3 }+3\quad ,\quad if\quad x\neq 0 \\ 1\quad \quad \quad ,\quad if\quad x=0 \end{cases}$ is not continuous at x=0.

• 2)

Check the continuity of the function f given by:
f(x)=2x+3 at x=1.

• 3)

Examine whether the function f given by:
f(x)=${ x }^{ 2 }$ is continuous at x=0.

• 4)

Discuss the continuity of the function f given by:
$f(x)=\left| x \right| at\quad x=0.$

• 5)

Show that the function f given by:
$f(x)=\begin{cases} { x }^{ 3 }+3,\quad \quad \quad if\quad x\neq 0 \\ 1,\quad \quad \quad \quad \quad \quad if\quad x=0 \end{cases}$
is not continuous at x=0.

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#### CBSEStudy Material - Sample Question Papers with Solutions for Class 12 Session 2019 - 2020

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