THE FIRST TRUST COMBINED SERIES 501 TRUST AGREEMENT Dated: December 29, 2015

THE FIRST TRUST COMBINED SERIES 501

TRUST AGREEMENT

Dated: December 29, 2015

This Trust Agreement among First Trust Portfolios L.P., as Depositor, The Bank of New York Mellon, as Trustee, First Trust Advisors L.P., as Evaluator, First Trust Advisors L.P., as Portfolio Supervisor, and FTP Services LLC, as FTPS Unit Servicing Agent sets forth certain provisions in full and incorporates other provisions by reference to the document entitled "Standard Terms and Conditions of Trust for The First Trust Combined Series 283 and subsequent Series, effective February 19, 2009" (herein called the "Standard Terms and Conditions of Trust"), and such provisions as are set forth in full and such provisions as are incorporated by reference constitute a single instrument. All references herein to Articles and Sections are to Articles and Sections of the Standard Terms and Conditions of Trust.

WITNESSETH THAT:

In consideration of the premises and of the mutual agreements herein contained, the Depositor, the Trustee, the Evaluator, the Portfolio Supervisor and FTPS Unit Servicing Agent agree as follows:

PART I

STANDARD TERMS AND CONDITIONS OF TRUST

Subject to the Provisions of Part II and Part III hereof, all the provisions contained in the Standard Terms and Conditions of Trust are herein incorporated by reference in their entirety and shall be deemed to be a part of this instrument as fully and to the same extent as though said provisions had been set forth in full in this instrument.

PART II

SPECIAL TERMS AND CONDITIONS OF TRUST

TAX EXEMPT MUNICIPAL INCOME TRUST, SERIES 290

The following special terms and conditions are hereby agreed to:

A. The Securities defined in Section 1.01(5) listed in Schedule A hereto have been deposited in trust under this Trust Agreement.

B. The fractional undivided interest in and ownership of the Trust Fund represented by each Unit for a Trust on the Initial Date of Deposit is the amount set forth under the caption "Fractional Undivided Interest in the Trust per Unit" in the section entitled "Summary of Essential Information" in the Prospectus.

C. The number of units in a Trust on the Initial Date of Deposit referred to in Section 2.03 is set forth under the caption "Initial Number of Units" in the section entitled "Summary of Essential Information" in the Prospectus.

D. The approximate amount, if any, which the Trustee shall be required to advance out of its own funds and cause to be paid to the Depositor pursuant to the second sentence of Section 3.05 shall be the amount per Unit for each Trust that the Trustee agreed to reduce its fee or pay Trust Fund expenses set forth in the footnotes to the "Fee Table" for each Trust in the Prospectus times the number of units for such Trust referred to in Part II H. of this Trust Agreement.

E. For each Trust the First General Record Date and the amount of the second distribution of funds from the Interest Account shall be the record date for the Interest Account and the amount set forth under "Summary of Essential Information" in the Prospectus.

F. For each Trust the "First Settlement Date" is the date set forth under "Summary of Essential Information-First Settlement Date" for such Trust in the Prospectus.

G. First Trust Advisors L.P.’s compensation as referred to in Section 4.03 of the Standard Terms and Conditions of Trust and FTP Services LLC's compensation as referred to in Section 3.15 of the Standard Terms and Conditions of Trust shall collectively be an annual fee in the amount of $.81 Per Unit, payable to such of First Trust Advisors L.P. and/or FTP Services LLC as they, or either of them, shall from time to time direct by written notice to the Trustee.

H. The Trustee's compensation as referred to in Section 6.04 of the Standard Terms and Conditions of Trust shall be an annual fee in the amount of $.98 per Unit for Trusts with monthly distribution plans, calculated based on the largest number of Units outstanding during the calendar year except during the initial offering period as determined in Section 4.01 of this Indenture, in which case the fee is calculated based on the largest number of Units outstanding during the period for which the compensation is paid (such annual fee to be pro rated for any calendar year in which the Trustee provides service during less than the whole of such year). However, in no event, except as may otherwise be provided in the Standard Terms and Conditions of Trust, shall the Trustee receive compensation in any one year from any Trust of less than $2,000 for such annual compensation.

I. The Initial Date of Deposit for the Trust is December 29, 2015.

J. No Unit holder will be eligible for an in-kind distribution of Securities pursuant to Section 5.02.

K. No Unit holder will be eligible for an in-kind distribution of Securities pursuant to Section 8.02.

PART III

A. Article IV of the Standard Terms and Conditions of Trust shall be amended to add the following:

"Section 4.06. Liability of Portfolio Supervisor. The Portfolio Supervisor shall be under no liability to the Unit holders for any action taken or for refraining from the taking of any action in good faith pursuant to this Indenture or for errors in judgment, but shall be liable only for its own willful misfeasance, bad faith or gross negligence in the performance of its duties or by reason of its reckless disregard of its obligations and duties hereunder."

B. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, the last sentence of Section 3.01 shall be replaced with the following:

"As used herein, the Depositor's reimbursable expenses of organizing the Trust shall include the cost of the initial preparation and typesetting of the registration statement, prospectuses (including preliminary prospectuses), the indenture, and other documents relating to the Trust, SEC and state blue sky registration fees, the cost of the initial valuation of the portfolio and audit of the Trust, the costs of a portfolio consultant, and licensing fees required for the establishment of the Trust under license agreements which provide for full payment of the licensing fees not later than the conclusion of the Organization Expense Period if any, the initial fees and expenses of the Trustee, and legal and other out-of-pocket expenses related thereto, but not including the expenses incurred in the printing of preliminary prospectuses and prospectuses, expenses incurred in the preparation and printing of brochures and other advertising materials and any other selling expenses."

C. Section 3.15 of the Standard Terms and Conditions of Trust is hereby amended by adding the following as paragraph (a)(5) and renumbering the subsequent subparagraphs:

"(5) The FTPS Unit Servicing Agent shall be responsible for all tax reporting required from time to time by applicable law and regulations with respect to holders of FTPS Units, and reporting of cost basis in respect of the FTPS Units of such holders (including, without limitation, reporting required by Section 6045(g) of the Internal Revenue Code of 1986, as amended)."

D. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, Section 2.03 is restated in full as follows:

"Section 2.03. Issuance of Units. The Trustee hereby acknowledges receipt of the deposit referred to in Section 2.01. Notwithstanding any provisions of the Indenture to the contrary, Units shall be held solely in uncertificated form evidenced by appropriate notation in the registration books of the Trustee, and no Unit holder shall be entitled to the issuance of a Certificate evidencing the Units owned by such Unit holder. The only permitted registered holders of Units shall be (i) Depository Trust Company (or its nominee, Cede & Co.), (ii) the FTPS Unit Servicing Agent or (iii) Unit holders who purchase or otherwise hold their Units through Advisor Direct ("Advisor Direct holders"); consequently, individuals who are not Advisor Direct holders or holders of FTPS Units must hold their Units through an entity which is a participant in Depository Trust Company. Except as provided by the preceding provisions of this paragraph, the rights specified in this Indenture of holders of Units evidenced by a Certificate shall apply to holders of Units held in uncertificated form."

E. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, Section 6.02 of the Standard Terms is amended to add the following as the penultimate paragraph:

"Cost-basis reporting for Unit holders who purchase or hold their Units through the First Trust Advisor Direct system ("Advisor Direct"). The Depositor shall maintain information required for the reporting of the cost basis of Advisor Direct holders (as defined in section 2.03) as may be required from time to time by applicable law (including, without limitation, Section 6045(g) of the Internal Revenue Code of 1986, as amended) and regulations, and the Depositor shall be responsible for the reporting of such information to the Advisor Direct holders, or if reporting by the Depositor is not permitted by applicable law or regulation or if the Depositor and Trustee otherwise agree that the Trustee shall report such information, the Depositor shall provide the Trustee such information as will permit the Trustee to provide required cost-basis information to the Advisor Direct holders and shall provide the information at such times and in such form as the Trustee may reasonably request. The Depositor will be solely responsible for the accuracy of such cost-basis information and the reporting thereof to Advisor Direct holders   as provided above. The Trustee may rely conclusively upon the cost-basis information provided by the Depositor with respect to Advisor Direct holders, and shall be indemnified in accordance with Section 6.04 of the Indenture against any loss or liability, including any penalty or other charge imposed by any taxing authority in respect of such cost-basis information or reporting thereof made by the Depositor as provided in this paragraph."

F. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, Section 3.07 shall be amended by adding the following immediately after Section 3.07(j):

"(k) that such sale is necessary for the Trust to comply with such federal and/or state securities laws, regulations and/or regulatory actions and interpretations which may be in effect from time to time."

G. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, Section 1.01 (8) shall be replaced in its entirety with the following:

"(8) "Securities" shall mean such of the income-bearing, tax-exempt or taxable obligations, including delivery statements relating to "when-issued" and/or "regular-way" contracts, if any, for the purchase of certain obligations and certified or bank check(s) or letter(s) of credit sufficient in amount or availability required for such purchase, deposited in irrevocable trust and listed in Schedule A of the Trust Agreement, additional Securities deposited pursuant to Section 2.01 hereof, and any obligations received in exchange, substitution or replacement for such obligations pursuant to Sections 3.08 and 3.14 hereof, as may from time to time continue to be held as part of the Trust Fund."

H. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, Section 3.14 (a) shall be replaced in its entirety with the following:

"(a) The New Securities (i) shall have a fixed maturity date (whether or not entitled to the benefits of any sinking, redemption, purchase or similar fund) not exceeding the date of maturity of the Special Securities they replace and not less than ten years after the date of purchase or, in the case of an Intermediate Trust, or a Short Intermediate Trust, not less than 5 years and 3 years, respectively, from the Date of Deposit, (ii) must be purchased at a price that results in a current return as of the Date of Deposit at least equal to that of the Special Securities they replace, (iii) must be purchased at a price that results in a yield to maturity as of the Date of Deposit at least equal to the Special Securities they replace, (iv) shall be payable as to principal and interest in United States currency, (v) shall not be a "when, as and if issued" Security, (vi) shall be issued after July 18, 1984 and (vi) shall have the benefit of exemption from state and/or federal taxation on interest to an equal or greater extent than the Special Securities they replace."

I. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, Section 3.07(i) shall be replaced in its entirety with the following:

"(i) that the Federal tax exemption, if applicable, on such Securities has been lost; or"

J. Section 3.06 of the Standard Terms and Conditions of Trust shall be amended to include the following paragraph at the end of such section:

"With respect to any Trust which has elected to be taxed as a regulated investment company, amounts distributable from the Interest Account upon termination of the Trust pursuant to Section 8.02 shall be treated as transferred to the Principal Account and included in the dollar amount reported as distributed from the Principal Account for all purposes of this Section 3.06."

K. Notwithstanding anything to the contrary in the Standard Terms and Conditions of Trust, the fourth paragraph of Section 3.05 shall be replaced in its entirety with the following:

"For monthly distributions, the share of the balance in the Interest Account to be distributed to a Certificateholder shall be computed as of the tenth day of each month, commencing with the first such day subsequent to the First General Record Date (the "Monthly Record Date"). The Trustee shall distribute to each Certificateholder of record as of the close of business on such Monthly Record Date such Certificateholder's pro rata share of the balance of the Interest Account as computed herein on or shortly after the twenty-fifth day of such month (the "Monthly Distribution Date"). Such Computation shall be an amount equal to the estimated amount of interest accrued on the Bonds from and including the immediately preceding Monthly Record Date through but not including the Monthly Record Date on which such calculation is made, less (i) the estimated costs and expenses attributable to such period (ii) interest attributable to such period paid or payable in connection with redemption of Units and (iii) amounts previously advanced by the Trustee pursuant to this Section 3.05 which are now deemed to be uncollectible, divided by the number of Units outstanding on such Monthly Record Date. In the event the amount on deposit in the Interest Account on a Monthly Distribution Date is not sufficient for the payment of the amount of interest to be distributed on the basis of the aforesaid computation, the Trustee shall advance out of its own funds and cause to be deposited in and credited to the Interest Account such amount as may be required to permit payment of the monthly interest distribution to be made on such Monthly Distribution Date and shall be entitled to be reimbursed, without interest, out of interest received by the Trust on the first Monthly Record Date following the date of such advance on which such reimbursement may be made without reducing the amount in the Interest Account to an amount less than that required for the next ensuing monthly interest distribution except where advances were made by the Trustee on Bonds which have defaulted or on which any payment has been recovered from the Trustee by a trustee in bankruptcy and the interest on which cannot currently be collected (either from the issuer of the Bonds or the Insurer), in which case the Trustee may reimburse itself for such advances and reduce, if necessary, the amount of the interest distribution. The Trustee shall be deemed to be the beneficial owner of the income of the Trust to the extent such income is required to reimburse the Trustee for amounts advanced by it pursuant to this Section 3.05; amounts payable to the Trustee in respect of such advances shall be secured by a lien on the Trust prior to the interests of Certificateholders."

IN WITNESS WHEREOF, First Trust Portfolios L.P., The Bank of New York Mellon, First Trust Advisors L.P. and FTP Services LLC have each caused this Trust Agreement to be executed and the respective corporate seal to be hereto affixed and attested (if applicable) by authorized officers; all as of the day, month and year first above written.

FIRST TRUST PORTFOLIOS L.P.,
Depositor

By Xxxxxxxxx X. Xxxx
Senior Vice President

THE BANK OF NEW YORK MELLON,
Trustee

By Xxxxxxx X. Xxxxxxx
Managing Director

[SEAL]

ATTEST:

Xxxxxxxxx X. Xxxxxxxxx

Vice President

FIRST TRUST ADVISORS L.P.,
Evaluator

By Xxxxxxxxx X. Xxxx
Senior Vice President

FIRST TRUST ADVISORS L.P.,
Portfolio Supervisor

By Xxxxxxxxx X. Xxxx
Senior Vice President

FTP Services LLC,
FTPS Unit Servicing Agent

By Xxxxxxxxx X. Xxxx
Senior Vice President

SCHEDULE A TO TRUST AGREEMENT

SECURITIES INITIALLY DEPOSITED

IN

THE FIRST TRUST COMBINED SERIES 501

(Note: Incorporated herein and made a part hereof is the "Portfolio" as set forth for each Trust in the Prospectus.)