A particle is projected with an initial velocity at an angle of $45 ^ { \circ }$ to the horizontal. It reaches its maximum height at $\mathrm { t } = 2 \mathrm {~s}$ and passes the top of a building at $\mathrm { t } = 3 \mathrm {~s}$ after projection. Find the height of the building. (A) 10 m (B) 15 m (C) 20 m (D) 25 m
$f ( x ) = \frac { e ^ { x } \left( e ^ { \tan x - x } - 1 \right) + \log ( \sec x + \tan x ) - x } { \tan x - x }$ If $\mathrm { f } ( \mathrm { x } )$ is continuous at $\mathrm { x } = 0$, then find $\mathrm { f } ( 0 )$
$\int _ { 0 } ^ { 36 } \mathbf { f } \left( \frac { \mathbf { t x } } { 36 } \right) \mathbf { d t } = \mathbf { 4 \alpha f } ( \mathbf { x } )$ If the curve represented by $\mathrm { y } = \mathrm { f } ( \mathrm { x } )$ is a standard parabola passing through $( 2,1 )$ and $( - 4 , \beta )$ then find
A bag contains 100 balls in which 10 are defective and 90 are nondefective balls. Find the number of ways to select 8 balls without replacement in which at least 7 balls should be defective?
Consider 10 data such that their mean is 10 and variance is 2. If one of the data $\alpha$ is removed and new data entry $\beta$ is inserted. Now new mean is 10.1 and new variance is 1.99 then $( \alpha + \beta )$ is equal to (A) $10 \bar { x } _ { \text {new } }$ (B) $20 \quad \sigma _ { \text {new } } ^ { 2 }$ (C) 1 (D) 2
Number of matrices A of order $3 \times 2$ such that all of its elements are from the set $\{ - 2 , - 1,0,1,2 \}$ such that trace of $\mathrm { AA } ^ { \mathrm { T } }$ is 5 , is equal to (A) 120 (B) 192 (C) 312 (D) 126
Let a circle passes through origin and the points $\mathrm { A } ( - \sqrt { 2 } \alpha , 0 ) , \mathrm { B } ( 0, \sqrt { 2 } \beta )$, where $\alpha$ and $\beta$ are non zero real parameters, such that its radius is 4 . Then the radius of locus of centroid of triangle $O A B$ is (A) $\frac { 2 } { 3 }$ (B) $\frac { 4 } { 3 }$ (C) $\frac { 11 } { 3 }$