Maths | CBSE Board | Grade 12 | 2014
Q. Find the particular solution of the differential equation dydx=1+x+y+xy, given that y=0, when x=1.
View Solution
Q. If tan1(x2x4)+tan1(x+2x+4)=π4, find the value of x.
View Solution
Q. A manufacturing company makes two types of teaching aids A and B of Mathematics for Class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs.80 on each piece of type A and Rs.120 on each piece of type B. How many pieces of type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?
View Solution
Q. If R={(x, y):x+2y=8} is a relation on N, write the range of R.
View Solution
Q. Show that the altitude of the right circular cone of maximum volume that can be described in a sphere of radius r is 4r3. Also show that the maximum volume of the cone is 827 of the volume of the sphere.
View Solution
Q. Evaluate: x+2x2+5x+6dx.
View Solution
Q. If f(x)=x0tsintdt, then write the value of f(x).
View Solution
Q. Evaluate: π04xsinx1+cos2xdx.
View Solution
Q. A dealer in rual area wishes to purchase a number of sewing machines. He has only Rs 5, 760 to invest and has space for at most 20 items for storage. An electronic sewing machine costs him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy how should he invest his money in order to maximize his profit? Formulate this problem mathematically and then solve it.
View Solution
Q. If [xyz2xyw]=[1405], find the value of x+y.
View Solution
Q. Find the value of dydx at θ=π4 if x=aeθ(sinθcosθ) and y=aeθ(sinθ+cosθ).
View Solution
Q. Evaluate: 42xx2+1dx
View Solution
Q. If tan1x+tan1y=π4, xy<1, then write the value of x+y+xy.
View Solution
Q. Two school A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs.x each, Rs.y each and Rs.z each for the three respective values to 3, 2 and 1 students respectively with a total award money of Rs.1, 600. School B wants to spend Rs.2, 300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs.900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.
View Solution
Q. Find the value of p for which the vectors 3^i+2^j+9^k and ^i+p^j+3^k are parallel.
View Solution
Q. Find the particular solution of the differential equation dydx=x(2logx+1)siny+ycosy given that y=π2 when x=1.
View Solution
Q. A line passes through (2, 1, 3) and it is perpendicular to the lines r=(^i+^j^k)+λ(2^i2^j+^k) and r=(2^i^j3^k)+μ(^i+2^j+2^k). Obtain its equation in vector and Cartesian form.
View Solution
Q. Find the equation of the tangent and normal to the curve x2a2y2b2=1 at point (2a, b).
View Solution
Q. Find the particular solution of the differential equation ex1y2dx+yxdy=0, given that y=1 when x=0.
View Solution
Q. Find the value(s) of x for which y=[x(x2)]2 is a increasing function.
View Solution
Q. Solve the differential equation (1+x2)dydx+y=etan1x.
View Solution
Q. Prove that: tan1[1+x1x1+x+1x]=π412cos1x, 12x1.
View Solution
Q. Using properties of determinants, prove that x+yxx5x+4y4x2x10x+8y8x3x=x3
View Solution
Q. If 3x724=8764, find the value of x.
View Solution
Q. Find a(b×c), if a=2^i+^j+3^k, b=^i+2^j+^k and c=3^i+^j+2^k.
View Solution
Q. If A is a square matrix such that A2=A, then write the value of 7A(I+A)3, where I is an identity matrix.
View Solution
Q. Show that the four points A, B, C and D with position vectors 4^i+5^j+^k, ^j^k, 3^i+9^j+4^k and 4(^i+^j+^k) respectively are coplanar.
View Solution
Q. If y=Peax+Qebx, show that d2ydx2(a+b)dydx+aby=0.
View Solution
Q. Find the particular solution of the differential equation x(1+y2)dxy(1+x2)dy=0, given that y=1 when x=0.
View Solution
Q. The scalar product of the vector a=^i+^j+^k with a unit vector along the sum of vectors b=2^i+4^j5^k and c=λ^i+2^j+3^k is equal to one. Find the value of λ and hence find the unit vector along b+c.
View Solution