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533
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The correct statement(s) regarding defects in solids is(are)
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Related Questions
Let
$f:[0,∞)→R$
be a continuous function such that
$f(x)=1−2x+∫_{0}e_{x−t}f(t)dt$
for all
$x∈[0,∞)$
. Then, which of the following statement(s) is (are) TRUE?The curve
$y=f(x)$
passes through the point
$(1,2)$
(b) The curve
$y=f(x)$
passes through the point
$(2,−1)$
(c) The area of the region
${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$
is
$4π−2 $
(d) The area of the region
${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$
is
$4π−1 $
A circle S passes through the point (0, 1) and is orthogonal to the circles
$(x−1)_{2}+y_{2}=16$
and
$x_{2}+y_{2}=1$
. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)
Let
$F_{1}(x_{1},0)$
and
$F_{2}(x_{2},0)$
, for
$x_{1}<0$
and
$x_{2}>0$
, be the foci of the ellipse
$9x_{2} +8y_{2} =1$
Suppose a parabola having vertex at the origin and focus at
$F_{2}$
intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral
$MF_{1}NF_{2}$
is
Three randomly chosen nonnegative integers
$x,yandz$
are found to satisfy the equation
$x+y+z=10.$
Then the probability that
$z$
is even, is:
$125 $
(b)
$21 $
(c)
$116 $
(d)
$5536 $
Let x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.
Let PQ be a focal chord of the parabola
$y_{2}=4ax$
The tangents to the parabola at P and Q meet at a point lying on the line
$y=2x+a,a>0$
. Length of chord PQ is
Let
$g:R→R$
be a differentiable function with
$g(0)=0,g_{′}(1)=0,g_{′}(1)=0$
.Let
$f(x)={∣x∣x g(x),0=0and0,x=0$
and
$h(x)=e_{∣x∣}$
for all
$x∈R$
. Let
$(foh)(x)$
denote
$f(h(x))and(hof)(x)$
denote
$h(f(x))$
. Then which of thx!=0 and e following is (are) true?
Let
$p,q$
be integers and let
$α,β$
be the roots of the equation,
$x_{2}−x−1=0,$
where
$α=β$
. For
$n=0,1,2,,leta_{n}=pα_{n}+qβ_{n}˙$
FACT : If
$aandb$
are rational number and
$a+b5 =0,thena=0=b˙$
If
$a_{4}=28,thenp+2q=$
7 (b) 21 (c) 14 (d) 12
Related Questions
Let
$f:[0,∞)→R$
be a continuous function such that
$f(x)=1−2x+∫_{0}e_{x−t}f(t)dt$
for all
$x∈[0,∞)$
. Then, which of the following statement(s) is (are) TRUE?The curve
$y=f(x)$
passes through the point
$(1,2)$
(b) The curve
$y=f(x)$
passes through the point
$(2,−1)$
(c) The area of the region
${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$
is
$4π−2 $
(d) The area of the region
${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$
is
$4π−1 $
A circle S passes through the point (0, 1) and is orthogonal to the circles
$(x−1)_{2}+y_{2}=16$
and
$x_{2}+y_{2}=1$
. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)
Let
$F_{1}(x_{1},0)$
and
$F_{2}(x_{2},0)$
, for
$x_{1}<0$
and
$x_{2}>0$
, be the foci of the ellipse
$9x_{2} +8y_{2} =1$
Suppose a parabola having vertex at the origin and focus at
$F_{2}$
intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral
$MF_{1}NF_{2}$
is
Three randomly chosen nonnegative integers
$x,yandz$
are found to satisfy the equation
$x+y+z=10.$
Then the probability that
$z$
is even, is:
$125 $
(b)
$21 $
(c)
$116 $
(d)
$5536 $
Let x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.
Let PQ be a focal chord of the parabola
$y_{2}=4ax$
The tangents to the parabola at P and Q meet at a point lying on the line
$y=2x+a,a>0$
. Length of chord PQ is
Let
$g:R→R$
be a differentiable function with
$g(0)=0,g_{′}(1)=0,g_{′}(1)=0$
.Let
$f(x)={∣x∣x g(x),0=0and0,x=0$
and
$h(x)=e_{∣x∣}$
for all
$x∈R$
. Let
$(foh)(x)$
denote
$f(h(x))and(hof)(x)$
denote
$h(f(x))$
. Then which of thx!=0 and e following is (are) true?
Let
$p,q$
be integers and let
$α,β$
be the roots of the equation,
$x_{2}−x−1=0,$
where
$α=β$
. For
$n=0,1,2,,leta_{n}=pα_{n}+qβ_{n}˙$
FACT : If
$aandb$
are rational number and
$a+b5 =0,thena=0=b˙$
If
$a_{4}=28,thenp+2q=$
7 (b) 21 (c) 14 (d) 12
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