Maths | CBSE Board | Grade 12 | 2017
Q. Two tailors, A and B, earn Rs. 300 and Rs. 400 per day, respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP and find the number of days A and B worked.
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Q. Determine the value of 'k' for which the following function is continuous at x=3:
f(x)=(x+3)236x3, x3k, x=3
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Q. If xy+yx=ab, then find dydx.
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Q. Find the particular solution of the differential equation (xy)dydx=(x+2y), given that y=0 when x=1.
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Q. Find the distance between the planes 2xy+2z=5 and 5x2.5y+5z=20.
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Q. Find: exdx(ex1)2(ex+2)
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Q. Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer.
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Q. If ey(x+1)=1, then show that d2ydx2=(dydx)2.
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Q. Find matrix A such that 211034A=1812922
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Q. Evaluate: 41{|x1|+|x2|+|x4|}dx
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Q. Find : dx58xx2
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Q. Find : sin2xcos2xsinxcosxdx
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Q. Find the area of the ABC, coordinates of whose vertices are A(4, 1), B(6, 6) and C(8, 4).
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Q. A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.
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Q. There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.
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Q. If A is a skew-symmetric matrix of order 3, then prove that det A=0.
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Q. Solve the following linear programming problem graphically:
Maximize Z=7x+10y
subject to the constraints
4x+6y240
6x+3y240
x10
x0, y0
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Q. If tan1x3x4+tan1x+3x+4=34, then find the value of x.
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Q. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light trough the whole opening.
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Q. The x-coordinate of a point on the line joining the points P(2, 2, 1) and Q(5, 1, -2) is 4. Find its z-coordinate.
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Q. Find the area enclosed between the parabola 4y=3x2 and the straight line 3x2y+12=0
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Q. If for any 2×2 square matrix A, A(adjA)=[8008], them write the value of det[A].
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Q. Show that the points A, B, C with position vectors 2ˆiˆj+ˆk, ˆi3ˆj5ˆk and 3ˆi4ˆj4ˆk respectively, are the vertices of a right angled triangle. Hence find the area of the triangle.
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Q. Find the general solution of the differential equation
dydxy=sinx.
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Q. Show that the function f(x)=x33x2+6x100 is increasing on R.
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Q. Find the value of c in Rolle's theorem for the function f(x)=x33x in [3, 0].
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Q. Using properties of determinants, prove that
∣ ∣a2+2a2a+112a+1a+21331∣ ∣=(a1)3
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Q. The volume of a sphere is increasing at the rate of 8cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12cm.
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Q. Evaluate: x0xtanxsecx+tanxdx
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Q. If a=2ˆiˆj2ˆk and b=7ˆi+2ˆj3ˆk, then express b in the form of b=b1+b2, where b1 is parallel to a and b2 is perpendicular to a.
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