If f(x)=∣∣ ∣ ∣∣1xx+12xx(x−1)x(x+1)3x(x

Sail E0 Webinar

Question

If

f (x) = ∣ ∣∣∣ ∣ \begin{matrix} 1 & x & x + 1 2 x & x (x - 1) & x (x + 1) 3 x (x - 1) & x (x - 1) (x - 2) & x (x^{2} - 1) \end{matrix} ∣ ∣∣∣ ∣

, then f(200) is equal to

Options:

A . 1

B . 0

C . 200

D . -200

Answer: Option B
:
B

f (X) = x (x + 1) ∣ ∣∣ ∣ \begin{matrix} 1 & 1 & 1 2 x & x - 1 & x 3 x (x - 1) & (x - 1) (x - 2) & x (x - 1) \end{matrix} ∣ ∣∣ ∣ = x (x + 1) (x - 1) ∣ ∣∣ ∣ \begin{matrix} 1 & 1 & 1 2 x & x - 1 & x 3 x & x - 2 & x \end{matrix} ∣ ∣∣ ∣

Applying

C_{2} \to C_{2} - C_{1}

and

C_{3} \to C_{3} - C_{1}

then

f (x) = x (x + 1) (x - 1) ∣ ∣∣ ∣ \begin{matrix} 1 & 0 & 0 2 x & - x - 1 & - x 3 x & - 2 x - 2 & - 2 x \end{matrix} ∣ ∣∣ ∣ = x^{2} (x + 1)^{2} (x - 1) ∣ ∣∣ ∣ \begin{matrix} 1 & 0 & 0 2 x & - 1 & - 1 3 x & - 2 & - 2 \end{matrix} ∣ ∣∣ ∣ = 0 ∴ f (200) = 0

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. X + ky − z = 0, 3x − ky −z = 0 and....x + ky − z = 0, 3x − ky −z = 0 and x − 3y + z = 0 has non-zero solution for k =

Question 2. The number of values of k for which the system of equations (k+1)x + 8y = 4k, kx + (k....the system of equations (k+1)x + 8y = 4k, kx + (k+3)y = 3k−1 has infinitely many solutions, is

Question 3. If a, b, c are sides of a triangle and ∣∣ ∣ ∣∣a2b2c2(a+1)2(b+1)2(c+1)2(a−1)2(b....b, c are sides of a triangle and ∣∣ ∣ ∣∣a2b2c2(a+1)2(b+1)2(c+1)2(a−1)2(b−1)2(c−1)2∣∣ ∣ ∣∣=0, then

Question 4. If Δ1=∣∣ ∣∣111abca2b2c2∣∣ ∣∣,Δ2=∣∣ &#x....If Δ1=∣∣ ∣∣111abca2b2c2∣∣ ∣∣,Δ2=∣∣ ∣∣1bca1cab1abc∣∣ ∣∣, then

Question 5. If sin 2x = 1, then ∣∣ ∣∣0cosx−sinxsinx0cosxcosxsinx0∣∣ ∣&#....If sin 2x = 1, then ∣∣ ∣∣0cosx−sinxsinx0cosxcosxsinx0∣∣ ∣∣2 equals

Question 6. If α,β are non real numbers satisfying x3−1=0 then the value of ∣∣ ∣∣....satisfying x3−1=0 then the value of ∣∣ ∣∣λ+1αβαλ+β1β1λ+α∣∣ ∣∣ is equal to

Question 7. Let f(x)=∣∣ ∣∣cosxsinxcosxcox2xsin2x2cos2xcos3xsin3x3cos3x∣∣ ∣∣,....Let f(x)=∣∣ ∣∣cosxsinxcosxcox2xsin2x2cos2xcos3xsin3x3cos3x∣∣ ∣∣, then f′(π2) is equal to

Question 8. ∣∣ ∣∣1ab−a1c−b−c1∣∣ ∣∣=....

Question 9. If a,b,c are non – zero real numbers and if the equations (a-1) x = y + z, (b -1)y = z + x, (c - 1)z = x + ....solution, then ab + bc + ca is equal to

Question 10. If Dk=∣∣ ∣ ∣∣1nn2kn2+n+1n2+n2k−1n2n2+n+1∣∣ ∣ ∣....If Dk=∣∣ ∣ ∣∣1nn2kn2+n+1n2+n2k−1n2n2+n+1∣∣ ∣ ∣∣ and ∑nk=1Dk=56, then n equals

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

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0