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The area bounded by the xaxis and the curve y = 4x  x^{2}  3 is
Multiply R_{1}, R_{2}, R_{3} by a, b, c respectively and divide by abc
Take abc common from C_{3} so that C_{1}, C_{3} are identical
The solution of the differential equation x^{2} dy/dxxy=1+cos y/x is
The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is
The valuie of sin^{1} cos(sin^{1} x) + cos^{1} sin (cos^{1} x) is
Consider the sentence: x < 5
Which of the following integers makes this open sentence true?
The only number less than 5 in the list of answers is 4.
If A represents the determinant of a square matrix of order 3 then (2A)=
If B is a nonsingular matrix and A is a square matrix, then det (B^{1}AB) =
Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?
Two dice are thrown simultaneously. The probability of obtaining a total score of seven is
There are six possible ways as to the number of points on the first die; and to each of these ways, there corresponding 6 possible numbers of points on second die.
Hence total number of ways S = 6 x 6 = 36
We now find out how many ways are favorable to the total of 7 points.
This may happen only in following ways:
(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3).
Hence, required Probability = 6/36 =1/6.
If S is a sample space, , where A, B are two mutually exclusive events, then P(A) =
For a frequency distribution mean deviation from mean is computed by
The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by (1/2) kg ; the weight of the teacher is
If x = 2 + i √3, then the value of, 4x^{2} + 8x + 13 is____
A quadratic equation whose one root is the square root of 47+8√3 is
The intersection of the spheres x^{2} + y^{2} + z^{2} + 7x  2y  z = 13 and x^{2} + y^{2} + z^{2}  3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane
The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 is
A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (1, 1, 2). Then the angle between the faces OAB and ABC will be
The angle between the two straight lines represented by 6y^{2}  xy  x^{2} + 30y + 36 = 0 is
Let a, b and c be distributed nonvegetative numbers. If the vectors aî + aĵ + ck̂, î + k̂ and cî̂ + cĵ̂ + bk̂ lie in a plane, then c is
If vectors i+2j+3k and 3i2j+k represents the adjacent sides of a parallelogram, the area of parallelogram is
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