Email
Chat with tutors
Login
Ask Questions, Get Answers
Menu
X
home
ask
tuition
questions
practice
papers
mobile
tutors
pricing
X
Recent questions tagged 2012
Questions
Show that the relation R, defined in the set A of all triangles as \( R = (T_1, T_2):T_2\) is similar to \( T_2\)}, is equivalence relation. Consider three right triangles \( T_1\) , with sides 3, 4, 5; \( T_2\) with sides 5, 12, 13 and \( T_3\) with sides 6, 8, 10. Which triangle among \( T_1, T_2 \: and T_3\) are related?
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \sin \bigg[ \frac{\large \pi}{\large 3}-$$\sin^{-1} \bigg( -\frac{\large 1}{\large 2} \bigg) \bigg]. $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants prove that \( \begin{bmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{bmatrix} = (a-b)(b-c)(c-a)(a+b+c). \)
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Prove that \( \begin{bmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{bmatrix} = (5x+4)(4-x)^2. \)
cbse
class12
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q10-1
p120
medium
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
If \( y = \frac{\large sin-x}{\large \sqrt {1-x^2}}\) show that $ (1+x^2) \large\frac{ d^2y}{ dx^2}$$-3x \large\frac{ dy}{ dx}$$ - y=0. $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
If \( y=x^x-2^{sinx}\) then find \( \frac{\large dy}{\large dx}.\)
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find the derivaties of the function given by \( f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)\) and hence find \( f(1) \)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int \frac{\large cos(x+a)}{\large sin(x+b)}dx$
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int \sin x \sqrt {1+\cos\: x} dx.$
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Verify that \( y=A\cos x - B\sin x\), is a solution of the differential equation \( \frac{\large d^2y}{\large dx^2}+y=0.\)
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Solve the following differential equation : $(y^2-x^2)dy = 3xy\: dx.$
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Solve the differential equation : $\large \frac{dy}{dx}-\frac{y}{x}=\bigg( \frac{x-1}{x} \bigg)$$ e^x. $
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Show that each of the given three vectors is a unit vector : $\large \frac{1}{7}$$ (2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7} $$(3\hat i - 6\hat j + 2\hat k),\large\frac{1}{7} $$(6\hat i + 2\hat j - 3\hat k)$ (Also show that they are mutually perpendicular to each other).
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find the equation of the \( \bot \) drawn from point (2, 4, -1) to the line \( \frac{\large x+5}{\large 1}=\frac{\large y+3}{\large 4}=\frac{\large z-6}{\large -9}. \)
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find the length and the foot of \( \bot \) drawn from point (2, -1, 5) to the line \( \frac{\large x-11}{\large 10}=\frac{\large y+2}{\large -4}=\frac{\large z+8}{\large -11}. \)
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
A speaks truth 8 times out of 10 times. A dice is tossed. He reports that it was 5. What is the probability that it was actually 5?
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Jan 9, 2013
by
thanvigandhi_1
1
answer
The cost of 4 kg onion , 3 kg wheat and 2 kg rice of Rs.60. The cost of 2 kg onion , 4 kg wheat and 6 kg rice is Rs. 90. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is Rs. 70. Find cost of each item per kg by matrix method.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 9, 2013
by
thanvigandhi_1
1
answer
Using matrix method solve the following system of linear equations : $x+2y+z=7; x+3z=11 ; 2x-3y = 1$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find the equation of the line through the point P(3, 4) which cuts from the first quadrant a triangle of the minimum area. Also find the area of the triangle.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find the area of the region bounbed by \( y^2=4x, \: x=1, \: x=4\) and \( x\) - axis in the first quadrant.
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int_0^2 (x^2+x+1)dx$ as limit of a sum.
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int_0^{\pi} \large\frac{dx}{5+4cos\: x}. $
cbse
class12
modelpaper
2012
sec-c
q26
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Show that the line joining the origin to the point (2, 1, 1) is perpendicular the line determined by the point (3, 5, -1),(4, 3, -1).
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
There are two types of fertilisers \( F_1 and F_2. F_1\) contain 10% nitrogen and 6% phosphoric acid and \( F_2\) consists of 5% of nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14kg of phosphoric acid for the crop. If \( F_1 \) costs Rs.6/kg and \( F_2 \) costs Rs. 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
cbse
class12
modelpaper
2012
q28
math
sec-c
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
An electronic assembly consists of two subsystems say A and B. From the previous testing procedures, the following probabilities are assumed to be known : P(A fails)=0.2, P(B fails alone)=0.15. Evaluate the following probabilities : (i) P(A fails / B has failed) (ii) P(A fails alone).
cbse
class12
modelpaper
2012
sec-c
q29
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Let * be a operation on N given by a*b=H.C.F, (a, b), a,b \( \in \) N. Write the value of 22*4.
cbse
class12
modelpaper
2012
sec-a
q1
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Using principal value, calculate the following : \( \sin^{-1} \bigg( \sin \large\frac{3\pi}{5} \bigg). \)
cbse
class12
modelpaper
2012
sec-a
q2
math
asked
Jan 8, 2013
by
thanvigandhi_1
1
answer
Find the value of x if $ \begin{bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 8, 2013
by
thanvigandhi_1
1
answer
If A is an invertible matrix of order 3 and |A|=5 then find [adj.A].
cbse
class12
modelpaper
2012
sec-a
q4
math
asked
Jan 8, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int \large\frac{\sec^2x}{3+tan\: x}$$dx$
cbse
class12
modelpaper
2012
sec-a
q6
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int \large\frac{\sin\: \sqrt x}{\sqrt x}$$dx.$
cbse
class12
modelpaper
2012
sec-a
q7
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Find the value of \( p\) if \( (2\hat i + 6\hat j + 27\hat k) \times (\hat i + 3\hat j + p\hat k) =0.\)
cbse
class12
modelpaper
2012
sec-a
q8
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
If \( p\) is a unit vector and \( (\overrightarrow x - \overrightarrow p)(\overrightarrow x+\overrightarrow p)=80\) then find |x|.
cbse
class12
modelpaper
2012
sec-a
q9
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Write the value of \(\overrightarrow P \) for which \( \overrightarrow a = 3\hat i + 2\hat j + 9\hat k \: and \: \overrightarrow b = \hat i + p\hat j + 3\hat k\) are parallel vectors.
cbse
class12
modelpaper
2012
sec-a
q10
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Show that the relation R in the set A of points, given by R: {P, Q): distance of the point P from the origin is the same as the distance of Q from the origin }, is an equivalence relation. Further, show that the set of all points related to P = (0, 0) is the circle passing through P with origin as the centre.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Prove that : $ \cot^{-1} \bigg(\large \frac{ \sqrt{1+\sin x}+\sqrt{1-\sin\: x}}{\sqrt{1+\sin\: x}-\sqrt{1-\sin x}} \bigg)=\frac{x}{2}.$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove that : $ \begin{bmatrix} a^2+2a & 2a+1 & 1 \\ 2a+1 & a+2 & 1 \\ 3 & 3 & 1 \end{bmatrix} = (a-1)^3. $
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Using the properties of determinants, prove that : $ \begin{bmatrix} x-3 & x-4 & x-\alpha \\ x-2 & x-3 & x-\beta \\ x-1 & x-2 & x-\gamma \end{bmatrix} = 0, \: where\: \alpha, \beta, \gamma \: are \: in \ A.P. $
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
For what value of k is the following function continuous at x = 2? $ f(x) = \left\{ \begin{array}{l l} 2x+1, & \quad { x < 2}\\ k, & \quad \text{ $x$ = 2} \\ 3x-1, & \quad \text{ $x$ > 2} \end{array}. \right.$
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 7, 2013
by
thanvigandhi_1
1
answer
If \( y = log \sqrt {\large\frac{1-\cos2x}{1+\cos2x}},\) show that $ \large\frac{dy}{dx} $$= 2 cosec\: 2x.$
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Find the derivative of \( \sin (3x+2)\) w.r.t \(x\) from the first principal.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Evaluate : $\int \large\frac{x^2+1}{x^4+1}$$dx.$
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Solve the following differential equation: $ (x^2-y^2)dx+2xy.dy = 0\: given \: that\: y=1\: when \: x = 1.$
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Solve the differential equation : $ \large\frac{dy}{dx} $$+y=\cos x - \sin x.$
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Solve the differential equation : $ \large\frac{dy}{dx} $$= \log (x+1).$
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Find the shortest distance between the following two lines : $ \overrightarrow r = (1+\lambda)\hat i + (2-\lambda)\hat j + (\lambda + 1)\hat k ; \overrightarrow r = (2\hat i -\hat j -\hat k) + \mu (2\hat i + \hat j +\hat k).$
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Find the value of \( \lambda \), so that lines $\large \frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{5z-10}{11} $ and $ \large \frac{7-7x}{3\lambda}=\large\frac{y-5}{1}=\frac{6-z}{5} $ are perpendicular to each other.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
The probability that a student entering an university will graduate is 0.4. Find the probability that out of 3 students of the university: (i) none will graduate (ii) only one will graduate (iii) all will graduate.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 7, 2013
by
thanvigandhi_1
1
answer
An insurance company issued 2000 scooters and 3000 motor cycles. The probability of an accident involving a scooter is 0.01 and that of a motor cycle is 0.02. An insured vehicle met with an accident. Find the probability that the accident vehicle was a motor cycle.
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
If \( A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} \), find \( A^{-1} \) . Use it to solve the following system of equations: $ \begin{array}{1 1} 2x-3y+5z=16 \\ 3x+2y-4z = -4 \\ x+y-2z=-3 \end{array} $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Page:
« prev
1
...
30
31
32
33
34
35
36
...
40
next »
Home
Ask
Tuition
Questions
Practice
Your payment for
is successful.
Continue
...