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Maths-

General

Easy

Question

$open parentheses 1 plus x plus x squared plus horizontal ellipsis plus x to the power of p close parentheses to the power of n equals a subscript 0 plus a subscript 1 x plus a subscript 2 x squared plus horizontal ellipsis$ $plus a subscript n p end subscript x to the power of n p end exponent not stretchy rightwards double arrow a subscript 1 plus 2 a subscript 2 plus 3 a subscript 3 plus horizontal ellipsis plus n p$

$\frac{n p (p + 1)^{n}}{2}$
$\frac{n p (p + 1)^{n}}{4}$
$\frac{n p (p - 1)^{n}}{4}$
$\frac{n p (p - 1)^{2 n}}{4}$

The correct answer is: $fraction numerator n p left parenthesis p plus 1 right parenthesis to the power of n over denominator 2 end fraction$

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Compounds (A) and (B) are –

Compounds (A) and (B) are –

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$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

parallel

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 $m s to the power of negative 1 end exponent$ to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 $m s to the power of negative 1 end exponent$ to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

physics-General

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In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a $capital delta A B C open parentheses fraction numerator a to the power of 2 end exponent over denominator sin invisible function application A end fraction plus fraction numerator b to the power of 2 end exponent over denominator sin invisible function application B end fraction plus fraction numerator c to the power of 2 end exponent over denominator sin invisible function application C end fraction close parentheses times s i n invisible function application fraction numerator A over denominator 2 end fraction s i n invisible function application fraction numerator B over denominator 2 end fraction s i n invisible function application fraction numerator C over denominator 2 end fraction$ simplifies to

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In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

parallel

A bullet of mass $m$ is fired with a velocity of 50 $m s to the power of negative 1 end exponent$ at an angle $theta$ with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length $l equals 10 divided by 3$ m and gets embedded in the bob. After the collision, the string moves to an angle of 120 $degree$ . What is the angle $theta ?$

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A spherical hollow is made in a lead sphere of radius $R$ such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?

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parallel

Three identical blocks $A comma B$ and $C$ are placed on horizontal frictionless surface. The blocks $A$ and $C$ are at rest. But $A$ is approaching towards $B$ with a speed 10 $m s to the power of negative 1 end exponent$ . The coefficient of restitution for all collisions is 0.5. The speed of the block $C$ just after collision is

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physics-General

In the given figure four identical spheres of equal mass $m$ are suspended by wires of equal length $l subscript 0 end subscript$ , so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is

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