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Recent questions and answers in Math
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CBSE XII
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Math
Math
Model Papers
(2025)
Relations and Functions
(349)
Inverse Trigonometric Functions
(193)
Matrices
(341)
Determinants
(197)
Continuity and Differentiability
(393)
Application of Derivatives
(352)
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(457)
Application of Integrals
(107)
Differential Equations
(258)
Vector Algebra
(204)
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(158)
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Probability
(305)
A letter is known to have come either from TATA NAGAR or from CALCUTTA.On the envelope,just two consecutive letter TA are visible.What is the probability that the letter came from TATA NAGAR.
cbse
class12
ch13
q44
p277
exemplar
math
sec-b
answered
Jul 30
by
Prathapchaithanya99
2
answers
A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Jul 28
by
pady_1
1
answer
A retired person has 70000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type of bond yields 10% per annum. As per norms, he has to invest minimum of 10000 in the first type and not more than 30000 in the second type. How should he plan his investment, so as to get maximum return after one year of investment. Make it an L.P.P. and solve the above problem.
cbse
class12
modelpaper
2012
sec-c
q28
math
answered
Jul 28
by
yashingrodiya1212
1
answer
Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q21
p4
math
sec-b
answered
Jul 20
by
saurabh.kumarshukla1995
1
answer
Give an account of Hershey and Chase experiment. What did it conclusively prove? If both DNA and pro
cbse
class12
ch6
exemplar
theoryquestion
biology
sec-e
molecular basis of inheritance
answered
Jul 5
by
pady_1
1
answer
If the line ax+by+c = 0 is normal to the curve xy = 1 then \[(a)\;a>0,b>0 \qquad (b)\;a<0,b<0 \qquad(c)\;a<0,b>0\qquad(d)\;a<0,b<0.\]
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q13
p17
math
answered
Jul 5
by
toshit.jain
1
answer
During reproduction, the chromosome number (2n) reduces to half (n) in the gametes and again the ori
cbse
class12
ch3
exemplar
theoryquestion
biology
sec-a
human reproduction
answered
Jun 14
by
pady_1
1
answer
Form the differential equation of the family of circles having centre on $y$-axis and radius $3$ units.
cbse
class12
bookproblem
ch9
sec3
q10
p391
sec-b
math
answered
Jun 5
by
rslv8331
2
answers
The total revenue received from the sale of x units of a product is given by $ R(x) = 13x^2 + 26x + 15 $ Find the marginal revenue when x = 7.
cbse
class12
modelpaper
2012
sec-a
q5
math
answered
Jun 3
by
ranjani.hogwarts
1
answer
Find the area included between the parabolas $ y^2=4ax\;and\;x^2=4ay$
cbse
class12
additionalproblem
kvquestionbank2012
ch8
q3
p31
math
answered
May 24
by
sai.manohar044
1
answer
Find the equation of the plane passing through the point (1,6,3) and perpendicular to the plane 2x+3y-z = 7
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q5
p37
math
answered
May 22
by
vikkyravi0106
1
answer
find intervals in which function given by f(x) = sin 3x where x belongs [0, pi/2] is 1 increasing 2 decreasing
answered
May 13
by
nikunjjain285
1
answer
The ground state energy of hydrogen atom is $-13.6\;eV$ 1.What are the potential and kinetic energy of an electron in the 3rd excited state? 2.If the electron jumps to the ground state from the third excited state, calculate the frequency of the photon emitted.
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
May 11
by
balaramshil1
1
answer
A company has two plants to manufacture bicycles. Plant I manufactures 70% of the bicycles and plant II manufactures 30%. At plant I 80% of the bicycles are rated as of standard quality and a plant II 90% of the bicycles are rated as of standard quality. A bicycle is choosen at random and is found to be of standard quality. What is the probability that it has come from plant II?
cbse
class12
modelpaper
2012
sec-c
q29
math
answered
Apr 14
by
shrutibhagat2215
1
answer
A company sells two different products A and B. The products are produced in a common production process which has total capacity of 500 man hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The demand in the market shows that the maximum number of units of A that can sold is 70 and that of B is 125. Profit on each unit of A is Rs. 20 and on B is Rs.15. How many units of A and B should be produced to maximise the profit? Form an L.P.P and solve it graphically.
cbse
class12
modelpaper
2012
sec-c
q28
math
answered
Feb 16
by
meena.p
1
answer
If \( \overrightarrow a \: and \: \overrightarrow b\) are two vectors such that \( | \overrightarrow a. \overrightarrow b| = | \overrightarrow a\) x \( \overrightarrow b |\), then what is the angle between \( \overrightarrow a \: and \: \overrightarrow b\)?
cbse
class12
modelpaper
2012
sec-a
q9
math
answered
Feb 16
by
suganyadevi.p
1
answer
Using properties of determinants, solve the following for x : $\begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $
cbse
class12
modelpaper
2012
sec-b
q12
ch4
bookproblem
misc
q5
p141
math
answered
Feb 16
by
meena.p
1
answer
Solve the differential equation : $(x+y)dy + (x-y) dx=0$
cbse
class12
modelpaper
2012
sec-c
q26
math
answered
Feb 16
by
suganyadevi.p
1
answer
A card from a pack of 52 playing cards is lost. Two cards are drawn from the remaining cards and found to be both spade. (i) Find the probability of lost card being a spade card.(ii)While playing in ground you found a purse containing rupees and some other documents,what will you do?
cbse
class12
modelpaper
2012
sec-c
q29
math
answered
Feb 16
by
meena.p
1
answer
If vectros $ \overrightarrow a = 2\hat i + 2\hat j +3\hat k , \overrightarrow b = -\hat i + 2\hat j +\hat k \: and \: \overrightarrow c = 3\hat i + \hat j $ are such that \( \overrightarrow a +\lambda \overrightarrow b\) is perpendicular to \( \overrightarrow c \), then find the value of \( \lambda \)
cbse
class12
modelpaper
2012
sec-b
q20
math
answered
Feb 16
by
suganyadevi.p
1
answer
If $x=a(\theta - \sin \theta) \quad ; y= a(1+\cos \theta) $ find $\large\frac{d^2y}{dx^2}$ at $\theta =\large\frac{\pi}{2}$
cbse
class12
ch5
additionalproblem
sec-b
q7
answered
Feb 16
by
meena.p
1
answer
The scalar product of the vector $ \overrightarrow a = \hat i + \hat j + \hat k$ with a unit vector along the sums of vectors $ \overrightarrow b = 2 \hat i + 4\hat j - 5 \hat k$ and $ \overrightarrow c = \lambda \hat i + 2 \hat j + 3 \hat k$ is equal to one. Find the value of $ \lambda $ and hence find the unit vector along $ \overrightarrow b + \overrightarrow c$
modelpaper-2014-chennai
cbse
class12
math
sec-b
answered
Feb 16
by
meena.p
1
answer
Evaluate : \[ \int_{-a}^a \sqrt{\frac{a-x}{a+x}}dx \]
cbse
class12
modelpaper
2012
sec-c
q26
math
answered
Feb 16
by
meena.p
1
answer
If $x^{my^n}=(x+y)^{m+n}$, prove that $\large\frac{dy}{dx}=\frac{y}{x}$
cbse
class12
math
modelpaper
mock-test-series-2015
sec-b
answered
Feb 15
by
meena.p
1
answer
If $A$ is a square matrix such that $A^2=A$, then write the value of $7A -(I+A)^3$ where $I$ is an identity matrix.
modelpaper-2014-chennai
cbse
class12
math
sec-a
answered
Feb 15
by
meena.p
1
answer
A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
cbse
class12
modelpaper
2005
sec-c
q17
math
answered
Feb 15
by
meena.p
1
answer
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is \( \frac{5}{6} \), What is the probability that he will knock down fewer than 2 hurdles.
cbse
class12
modelpaper
2012
sec-b
q21
math
answered
Feb 15
by
meena.p
1
answer
Assume that the chances of a patient having a heart attack is 40%. It is assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time, a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
cbse
class12
modelpaper
2012
sec-c
q29
math
answered
Feb 15
by
meena.p
1
answer
If a point charge be rotated in an arc of radius r around a change q, what will be the workdone ? explain
cbse
class12
physics
ch-1
sec-a
q48
difficult
answered
Feb 15
by
meena.p
1
answer
Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semivertical angle $ \alpha, \: is \: \large\frac{4}{27}$$ \pi \: h^3\: tan^2\: \alpha $
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Feb 15
by
asewa44
1
answer
A variable plane is at constant distance p from the origin and meet the axes in A, B & C. Show that the locus of the centroid of the tetrahedron $\bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{16}{p^2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q25
p38
math
answered
Feb 4
by
loserlady2lol
1
answer
A variable plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B & C. Show that the locus of the centroid of the $ \bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q24
p38
math
answered
Feb 4
by
loserlady2lol
1
answer
Which one of the following is a bird flu virus?
cbse
class12
biology
zoology
neet
sec-a
asked
Jan 25
by
priyanka.c
0
answers
A firm makes two types of furniture : chairs and tables. The contribution to profit for each product as calculated by the accounting department is Rs.20 per chair and Rs.30 per table. Both products are to be processed on three machines $ M_1,M_2 and M_3.$ The time required in hours by each product and total time available in hours per week on each machine are as follows:
cbse
class12
additionalproblem
kvquestionbank2012
ch12
q4
p39
math
answered
Jan 9
by
stefanosstvm
1
answer
If the points $(1,1,p)$ and $(-3,0,1)$ are at equidistant from the plane $\overrightarrow {r} . (3 \hat {i} +4 \hat {j} -12 \hat {k}) + 13 = 0, $ then find the value of p.
cbse
class12
maths
ch10
sec-c
answered
Dec 28, 2016
by
priyanka.c
1
answer
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
cbse
class12
maths
ch9
sec-c
answered
Dec 27, 2016
by
priyanka.c
1
answer
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. Assuming that the transportation cost of 10 litres of oil is Rs 1 per km, How should the delivery be scheduled in order that the transportation cost is minimum ? What is the minimum cost? The distance (In km) between the depots and the petrol pumps is given in the following table :
cbse
class12
maths
ch1
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Suppose a girl throws a die. If she throws a 5 or 6, she tosses a coin 3 times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with a die?
cbse
class12
maths
ch13
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Find the area of the region $\{ (x,y) : 0 \leq y \leq x^2, 0 \leq y \leq x+2 , 0 \leq x \leq 3\}$
cbse
class12
maths
ch1
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Find the image of the point (1, 3. 4) in the plane $x-y+z =5$. Hence show that the image lies on the plane $x -2y +z -7 = 0$
cbse
class12
maths
ch1
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Radioactive wastes is to be disposed of in full enclosed lead boxes of inner volume $200 cm^3$. The base of the box has dimension in the ratio 2:1 . What is the inner length of the box. Find the minimum inner surface area of the box.
cbse
class12
maths
ch1
sec-e
answered
Dec 22, 2016
by
priyanka.c
1
answer
Rent -a-car has three different makes of vehicles P, Q and R for hire. These cars are located at stations A and B on either side of a city. Some cars are being rented. In total they have 150 cars. At station A, they have 20% of P, 40% of Q and 30% of R which is 46 cars in total. At station B they have 40% of P, 20% of Q and 50% of R which is 54 cars in total. How many of each cars types does Rent-a -car have ?
cbse
class12
maths
ch1
sec-e
answered
Dec 22, 2016
by
priyanka.c
1
answer
Integrate $\begin{align*} \int \frac{\sin(x+a)}{\sin (x+b)} dx\end{align*} $
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Express the matrix $A = \begin{bmatrix} 3 & 2 & 3 \\ 4 & 5 & 3 \\ 2 & 4 & 5 \end{bmatrix}$ as the sum of a symmetric and a skew symmetric matrix.
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
(a) The youngest is a girl.
(b) At least one is a girl.
Pre-natal *** determination is a crime. What will you do if you come to know that some of your known is indulging in pre-natal *** determination ?
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Evaluate $\begin{align*} \int_{-1}^{3/2} |x \sin {\pi \; x}| dx \end{align*}$
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Find the condition that the curves $2x= y^2$ and $2xy = k $ intersect orthogonally.
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
Differentiate $x ^{\sin ^{-1} x}$ w.r.t $\sin^{-1} x$
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
For what value of $a$ and $b$ is the function $f(x) = \begin{cases} x^2 ,& x \leq c \\ ax+b , & x> c \end{cases} $ is differentiable at $x=c$
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
Evaluate : $\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & b+a & c \end{vmatrix} $
cbse
class12
maths
ch4
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
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