A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

A cubic polynomial f(x) = ax³ + bx² + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

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A cubic polynomial f(x) = ax³ + bx² + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b $sin invisible function application fraction numerator pi over denominator 2 end fraction x$ , 1 £ x £ 2 then which of the following is correct?

The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval $open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction close square brackets$ is -

physics

The relation between time and displacement of a moving particle is given by $t equals 2 a x squared$ where $alpha$ is a constant. The shape of the graph is $x not stretchy rightwards arrow y$ is....

physicsGeneral

If P (q) and Q $open parentheses fraction numerator pi over denominator 2 end fraction plus theta close parentheses$ are two points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , then locus of the mid – point of PQ is

If CP and CD are semi – conjugate diameters of an ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 comma$ then CP² + CD² =

The normals to the curve x = a ( $theta$ + sin $theta$ ), y = a (1 – cos $theta$ ) at the points $theta$ = (2n + 1) $pi$ , n $element of$ I are all -

The normal to the curve x = 3 cos $theta$ – $cos cubed theta$ , y = 3 sin $theta$ – $sin cubed$ $theta$ at the point $theta$ = $pi$ /4 passes through the point -

The normal of the curve given by the equation x = a (sin $theta$ + cos $theta$ ), y = a (sin $theta$ – cos $theta$ ) at the point Q is -

If the tangent at ‘t’ on the curve y = $8 t cubed space minus 1$ , x = $4 t squared space plus space 3$ meets the curve again at $t subscript 1$ and is normal to the curve at that point, then value of t must be -

The tangent at ( $t$ , $t squared$ – $t cubed$ ) on the curve y = $x squared$ – $x cubed$ meets the curve again at Q, then abscissa of Q must be -

If $fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction$ = 1 is a tangent to the curve x = 4t,y = $fraction numerator 4 over denominator t end fraction$ , t $element of$ R then -

The line $fraction numerator x over denominator a end fraction$ + $fraction numerator y over denominator b end fraction$ = 1 touches the curve $y space equals space b e to the power of negative x over a end exponent$ at the point :