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One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is

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The nonzero verctors $a$, $b$and $c$are related by $a=8b and c=−7b$. Then the angle between $a$and $c$is

The projections of a vector on the three coordinate axis are $6,3,2$ respectively. The direction cosines of the vector are(A) $6,−3,2$ (B) $56 ,5−3 ,52 $ (C) $76 ,7−3 ,72 $ (D) $7−6 ,7−3 ,72 $

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume \displaystyle{V}_{}

The shortest distance between the line $yx=1$ and the curve $x=y_{2}$ is(A) $832 $(B) $823 $(C) $532 $ (D) $43 $

Solid Ba $(NO_{3})_{2}$ is gradually dissolved in 1 $1.0×10_{−4}M Na_{2}CO_{3}$ solution. At what concentration of $Ba_{2+}$ will a precipitate begin to form ? $(K_{sp}forBaCO_{3}=5.1×10_{−9})$

If P and Q are the points of intersection of the circles $x_{2}+y_{2}+3x+7y+2p5=0$and $x_{2}+y_{2}+2x+2yp_{2}=0$, then there is a circle passingthrough P, Q and $(1,1)$for

Statement 1: The variance of first n even natural numbers is $4n_{2}−1 $Statement 2: The sum of first n natural numbers is $(n2n+1 $and the sum of squares of first n natural numbers is $(n(n+1)62n+1 $

Consider a uniform sqare plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is