The angles of a quadrilateral ABCD are `x^(@),(x+1)^(@),(x+2)^(@)` and `(x+3)^(@)`, taken in the same order. Then the quadrilateral ABCD is necessarily a
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If A, B, and C are three square matrices of the same order, then `AB=AC implies B=C`. Then
If `|A| ne 0`, then `AB=AC` or `A^(-1) AB=A^(-1) AC` or `B=C` Also, if A is orthogonal matrix, then `A A^(T)=I` `implies |A A^(T)|=1 implies |A|^(2)=1implies` is invertible
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A cube and a sphere of the same material and same total surface area are placed in the sae space turn by turn, after heating them to the same temperat
Correct Answer - 1.38
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vectors `veca,vecb and vecc` are of the same length and when taken pair-wise they form equal angles. If `veca=hati+hatj and vecb=hatj+hatk` then find
`Let vecc=xhati+yhatj+zhatk`. Then `|veca|=|vecb|=|vecc|Rightarrowx^(2)+y^(2)+z^(2)=2` it is given that the angles between the vectors taken in pairs are equal, say `theta` . Therefore, `cos theta=(veca.vecb)/(|veca||vecb|)= (0+1+1)/(sqrt2sqrt2)=1/2` `Rightarrow (veca.vecc)/(|veca||vecc|)=1/2and (vecb.vecc)/(|vecb||vecc|)=1/2` `(x+y)/(sqrt2sqrt2)=1/2 and(y+z)/(sqrt2sqrt2)=1/2` `Rightarrow...
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The area of any cyclic quadrilateral ABCD is given by `A^(2) = (s -a) (s-b) (s-c) (s-d)`, where `2s = a + b ++ c + d, a, b, c and d` are the sides of
Correct Answer - A Using A.M. `ge` G.M for `s -a, s-b, s-c, s-d`, we have `(s-a + s-b + s-c + s-d)/(4) ge sqrtA` or `(4s -2s)/(4) ge 1` or...
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If `A`, `B` are two square matrices of same order such that `A+B=AB` and `I` is identity matrix of order same as that of `A`,`B` , then
Correct Answer - A::C `(a,c)` `A+B=AB` `impliesI-(A+B-AB)=I` `implies(I-A)(I-B)=I` `implies|I-A||I-B|=I` `implies |I-A|`, `|I-B|` are non zero Also `(I-B)(I-A)=I` `impliesI-B-A+BA=I` `impliesA+B=B+A` `impliesAB=BA` `implies(a)` and `(c )` are correct
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Four small spheres carrying `+(5)/(3),+(10)/(3),+(5)/(3)` and `-(5)/(3)`nC are placed in order at the angular points of a sqare ABCD of 10 cm sides. C
Correct Answer - `6xx10^(6)`N from O to D
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The sum of the interior angles in a6-sided figure is `720^(@)` and the six angles are x,y,z,z,y, and x. Express the relation among x,y, and z by makin
Correct Answer - `z=360^(@)-(x+y)`
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A swimmer takes 4 second in crossing some distance in downstream and taken 6 second in upstream for same distance then find the time taken by him to c
Correct Answer - 4.8 sec
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If the angles of a triangle are in the ratio `2: 3: 4,` determine three angles.
Correct Answer - `40^(@),60^(@),80^(@)`
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The sides of a quadrilateral ABCD taken in order are 6 cm, 8 cm, 12 cm and 14 cm respectively and the angle between the first two sides is a right ang
Correct Answer - 82.8 `cm^(2)`
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