class 12

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JEE Main

Bromination of cyclohexene under conditions given below yields :

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Let f(x) be a polynomial of degree four having extreme values at $x=1$and $x=2$. If $(lim)_{x0}[1+x_{2}f(x) ]=3$, then f(2) is equal to :

A complex number z is said to be unimodular if . Suppose $z_{1}$and $z_{2}$are complex numbers such that $2−z_{1}z_{2}z_{1}−2z_{2} $is unimodular and $z_{2}$is not unimodular. Then the point $z_{1}$lies on a :

Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choice given below the list :

If f and g are differentiable functions in [0, 1] satisfying \displaystyle{f{{\left({0}\right)}}}\text{}=\text{}{2}\text{}={g}

Two short bar magnets of length 1 cm each have magnetic moments $1.20Am_{2}and1.00Am_{2}$ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centres is close to (Horizontal component of earths magnetic induction is $3.6×10_{−5}Wb/m_{2})$

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

Let $a,b$and $c$ be three non-zero vectors such that no two of them are collinear and $(a×b)×c=31 ∣c∣∣∣ b∣∣ ∣a∣$. If $θ$is the angle between vectors $b$and $c$then a value of $sinθ$is :

A uniformly charged solid sphere of radius R has potential $V_{0}$ (measured with respect to $∞$ ) on its surface. For this sphere the equipotential surface with potentials $23V_{0} ,45V_{0} ,43V_{0} and4V_{0} $ have radius \displaystyle{R}_{}