| 2023-07-03 | Evaluate \( \lim _{x \rightarrow 1 / 2} \frac{4 x^{2}-1}{2 x-1} \) |
| 2023-07-03 | If \( f(x)=x^{100}+x^{99}+\ldots+x+1 \), then \( f^{\prime}(1) \) is equal to
(a) 5050
(b) 5049
... |
| 2023-07-03 | If \( f(x)=\frac{x^{n}-a^{n}}{x-a} \) for some constant a, then \( f^{\prime}(a) \) is equal to
... |
| 2023-07-03 | If \( f(x)=1+x+\frac{x^{2}}{2}+\ldots+\frac{x^{100}}{100} \), then \( f^{\prime}(1) \) is equal ... |
| 2023-07-03 | Determine the points in (i) \( x y \)-plane (ii) \( y z \)-plane and (iii) \( z x \)-plane which... |
| 2023-07-03 | Verify the following
\( (5,-1,1),(7,-4,7),(1,-6,10) \) and \( (-1,-3,4) \) are the vertices
of a... |
| 2023-07-03 | \[
\lim _{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos 2 x)}}{x}=
\]
(a) 1
(b) -1
(c) 0
(d) l... |
| 2023-07-03 | The mid-points of the sides of a triangle \( A B C \) are given by \( (-2,3,5),(4,-1,7) \) and \... |
| 2023-07-03 | Using section formula, show that the points \( A(2,-3,4), B(-1 \), \( 2,1) \) and \( C(0,1 / 3,2... |
| 2023-07-03 | \[
\lim _{x \rightarrow a} \frac{(x+2)^{5 / 3}-(a+2)^{5 / 3}}{x-a}=
\]
-(a) \( \frac{5}{3}(a+2)^... |
| 2023-07-03 | Find the coordinates of the points which tisect the line segment joining the points \( P(4,2,-6)... |
| 2023-07-03 | Find the ratio in which the sphere \( x^{2}+y^{2}+z^{2}=504 \) divides the line joining the poin... |
| 2023-07-03 | Using section formula, Prove that the three points \( A(-2,3,5), B(1,2,3) \) and \( C(7,0,-1) \)... |
| 2023-07-03 | Show that the plane \( a x+b y+c z+d=0 \) divides the line joining the points \( \left(x_{1}, y_... |
| 2023-07-03 | Find the ratio in which the line segment joining the points \( (4,8,10) \) and \( (6,10,-8) \) i... |
| 2023-07-03 | If \( A(-2,2,3) \) and \( B(13,-3,13) \) are two points. Find the locus of a point \( P \) which... |
| 2023-07-03 | Show that the three points \( A(2,3,4), B(-1,2-3) \) and \( C(-4,1,-10) \) are collinear and fin... |
| 2023-07-03 | Show that the points \( A(1,3,4), B(-1,6,10), C(-7,4,7) \) and \( D(-5,1,1) \) are the vertices ... |
| 2023-07-03 | Prove that the tetrahedron with vertices at the points \( O(0,0,0) \), \( A(0,1,1), B(1,0,1) \) ... |
| 2023-07-03 | Show that the points \( (3,2,2),(-1,4,2),(0,5,6),(2,1,2) \) lie on a sphere whose centre is \( (... |
| 2023-07-03 | Prove that the point \( A(1,3,0), B(-5,5,2), C(-9,-1,2) \) and \( D(-3,-3,0) \) taken is order a... |
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