Polarization power of a cation increases when

The number of values of c such that st. line y = 4x + c touches the curve $fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus y to the power of 2 end exponent equals 1$ is

Tangents are drawn to the ellipse $fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1$ at the ends of the latus rectum. The are of the quadrilateral so formed is

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

physics

Here are the graphs of x→ t of moving body. which of them is not suitable?

physicsGeneral

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

$I f space a space f u n c t i o n space h a s space a space tan g e n t space a t space a space p o i n t space x equals a space comma space t h e n comma space i t space m e a n s comma space i t space i s space t h e space c r i t i c a l space p o i n t space o f space t h a t space f u n c t i o n space a n d space t h e space d e r i v a t i v e space o f space t h e space f u n c t i o n space i s space z e r o space a t space t h a t space p o i n t. space P e r f o r m space t h e space c a l c u l a t i o n s space c a r e f u l l y comma space t o space a v o i d space s i l l y space m i s t a k e s. space O n e space s h o u l d space k n o w space h o w space t o space r e a d space a space g r a p h space t o space s o l v e space s u c h space q u e s t i o n s.$

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 -