If Δ(x) = ∣∣ ∣ ∣∣xnsin x

Sail E0 Webinar

Question

If

Δ (x) = ∣ ∣∣∣ ∣ \begin{matrix} x^{n} & s i n x & c o s x n! & s i n \frac{n π}{2} & c o s \frac{n π}{2} a & a^{2} & a^{3} \end{matrix} ∣ ∣∣∣ ∣

, then the value of

\frac{d^{n}}{d x^{n}} [Δ (x)] a t x = 0

is

Options:

A . -1

B . 0

C . 1

D . Dependent of a

Answer: Option B
:
B

\frac{d^{n}}{d x^{n}} [Δ (x)] = ∣ ∣∣∣∣ ∣ \begin{matrix} \frac{d^{n}}{d x^{n}} x^{n} & \frac{d^{n}}{d x^{n}} s i n x & \frac{d^{n}}{d x^{n}} c o s x n! & s i n (\frac{n π}{2}) & c o s (\frac{n π}{2}) a & a^{2} & a^{3} \end{matrix} ∣ ∣∣∣∣ ∣ = ∣ ∣∣∣∣ ∣ \begin{matrix} n! & s i n (x + \frac{n π}{2}) & c o s (x + \frac{n π}{2}) n! & s i n (\frac{n π}{2}) & c o s (\frac{n π}{2}) a & a^{2} & a^{3} \end{matrix} ∣ ∣∣∣∣ ∣ \Rightarrow [Δ^{n} (x)]_{x = 0} = ∣ ∣∣∣∣ ∣ \begin{matrix} n! & s i n (0 + \frac{n π}{2}) & c o s (0 + \frac{n π}{2}) n! & s i n (\frac{n π}{2}) & c o s (\frac{n π}{2}) a & a^{2} & a^{3} \end{matrix} ∣ ∣∣∣∣ ∣ = 0 {S i n c e R_{1} \equiv R_{2}} .

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If a,b and care non zero numbers, then Δ=∣∣ ∣ ∣∣b2c2bcb+cc2a2cac+aa2b2aba+b....and care non zero numbers, then Δ=∣∣ ∣ ∣∣b2c2bcb+cc2a2cac+aa2b2aba+b∣∣ ∣ ∣∣ is equal to

Question 2. The cofactor of the element '4' in the determinant ∣∣ ∣ ∣ ∣∣13512342....cofactor of the element '4' in the determinant ∣∣ ∣ ∣ ∣∣1351234280110211∣∣ ∣ ∣ ∣∣ is

Question 3. If pλ4+qλ3+rλ+5λ+t=∣∣ ∣∣λ2+3λλ−1λ+3&#....If pλ4+qλ3+rλ+5λ+t=∣∣ ∣∣λ2+3λλ−1λ+3λ+12−λλ−4λ−3λ+43λ∣∣ ∣∣, the value of t is

Question 4. If f(n)=αn+βn and ∣∣ ∣ ∣∣31+f(1)1+f(2)1+f(1)1+f(2)1+f(3)1+f(2)1+f(3)1+f(4....If f(n)=αn+βn and ∣∣ ∣ ∣∣31+f(1)1+f(2)1+f(1)1+f(2)1+f(3)1+f(2)1+f(3)1+f(4)∣∣ ∣ ∣∣=k(1−α)2(1−β)2(α−β)2, then k is equal to

Question 5. If the system of linear equation x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a ....x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a non zero solution, then a, b, c

Question 6. If A1, B1, C1.... are respectively the co-factors of the elements a1, b1, c1.... of the determinant ....of the elements a1, b1, c1.... of the determinant Δ = ∣∣ ∣∣a1b1c1a2b2c2a3b3c3∣∣ ∣∣, then ∣∣∣B2C2B3C3∣∣∣ =

Question 7. ....

Question 8. If Δ1 = ∣∣∣10ab∣∣∣ and Δ2 = ∣∣&#....If Δ1 = ∣∣∣10ab∣∣∣ and Δ2 = ∣∣∣10cd∣∣∣, then Δ2Δ1 is equal to

Question 9. If the system of linear equation x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a ....x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a non zero solution, then a, b, c

Question 10. If Δ(x) = ∣∣ ∣ ∣∣xnsin xcos xn!sinnπ2cosnπ2aa2a....If Δ(x) = ∣∣ ∣ ∣∣xnsin xcos xn!sinnπ2cosnπ2aa2a3∣∣ ∣ ∣∣, then the value of dndxn[Δ(x)] at x=0 is

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0