If p ^4 + q ^3 + r ^2 + s + t = | , * 20 c ^2 + 3 & - 1 & + 3 + 1… - Vidyadip

Question

If $p{\lambda ^4} + q{\lambda ^3} + r{\lambda ^2} + s\lambda + t = $ $\left| {\,\begin{array}{*{20}{c}}{{\lambda ^2} + 3\lambda }&{\lambda - 1}&{\lambda + 3}\\{\lambda + 1}&{2 - \lambda }&{\lambda - 4}\\{\lambda - 3}&{\lambda + 4}&{3\lambda }\end{array}\,} \right|,$ the value of $t$ is

✓

Answer

b
(b) Since it is an identity in $\lambda $ so satisfied by every value of $\lambda $.

Now put $\lambda = 0 $ in the given equation, we have $t = \left| {\,\begin{array}{*{20}{c}}0&{ - 1}&3\\1&2&{ - 4}\\{ - 3}&4&0\end{array}\,} \right|\, = - 12 + 30 = 18$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\omega $ is a complex cube root of unity, then $225 + $${(3\omega + 8{\omega ^2})^2}$$ + {(3{\omega ^2} + 8\omega )^2} = $

$arg\left( {\frac{{3 + i}}{{2 - i}} + \frac{{3 - i}}{{2 + i}}} \right)$ is equal to

If the lines $x -2y = 12$ is tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ at the point $\left( {3,\frac{-9}{2}} \right)$, then the length of the latus rectum of the ellipse is

Let $A = \{1, 2, 3,....7\}$ and let $P(1)$ denote the power set of $A.$ If the number of functions $f : A\rightarrow P(A)$ such that $a \in f ( a ), \forall a \in A$ is $m ^{ n }, m$ and $n \in N$ and $m$ is least, then $m + n$ is equal to $...........$

If $\alpha , \beta $ are two real numbers satisfying $\alpha^2 + \beta^2$ = $ 5$ and $3(\alpha^5 + \beta^5) = 11$$(\alpha^3 + \beta^3)$, then $\alpha \beta$ is

A two-digit number $\overline{a b}$ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits $a$ and $b$. (For example, $18$ is an almost prime number because $13$ is a prime number). Then the number of almost prime two-digit numbers is

If the quadratic equation ${x^2} + \left( {2 - \tan \theta } \right)x - \left( {1 + \tan \theta } \right) = 0$ has $2$ integral roots, then sum of all possible values of $\theta $ in interval $(0, 2\pi )$ is $k\pi $, then $k$ equals

The expression ${[x + {({x^3} - 1)^{1/2}}]^5} + {[x - {({x^3} - 1)^{1/2}}]^5}$ is a polynomial of degree

Let the normals at all the points on a given curve pass through a fixed point $(a, b) .$ If the curve passes through $(3,-3)$ and $(4,-2 \sqrt{2}),$ and given that $a-2 \sqrt{2} b=3,$ then $\left(a^{2}+b^{2}+a b\right)$ is equal to ..... .

Let $f(x) = \left\{ \begin{array}{l}{x^2} + k,\;\;\;\;{\rm{when}}\;\;x \ge 0\\ - {x^2} - k,\;\;{\rm{when\,\, }}x < 0\end{array} \right.$. If the function $f(x)$ be continuous at $x = 0$, then $k =$