NUVEEN TAX EXEMPT UNIT TRUST SERIES 781
497, 1995-01-27
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<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     MARYLAND
     TRUST 303
              (MARYLAND TRADITIONAL TRUST 303)
 
            Estimated Current Return
            First
            Year: 5.84% to 6.07%
            Subsequent
            Years: 5.87% to 6.10%
            as of 01/25/95
 
            Estimated Long Term Return
            6.04% to 6.28%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds
                  Cusip:
                  67101L 795 Monthly Payment Option
                  67101L 803 Quarterly Payment Option
                  67101L 811 Semi-Annual Payment Option
 
                  Registered in Maryland
                    John Nuveen & Co. Incorporated
                    Investment Bankers
 
<TABLE>
<S>                           <C>
Chicago:                      Atlanta
333 W. Wacker Dr.             Austin
Chicago, Illinois 60606       Boca Raton
Telephone: 312.917.7700       Boston
                              Columbus
New York:                     Dallas/Ft. Worth
Swiss Bank Tower              Irvine
10 East 50th Street           Philadelphia
New York, New York 10022      Phoenix
Telephone: 212.207.2000       San Francisco
                              Seattle
                              Tampa
                              Washington, D.C.
</TABLE>
 
<PAGE>
- --------------------------------------------------------------------------------
 
NUVEEN TAX-EXEMPT UNIT TRUST--MARYLAND TRADITIONAL TRUST 303
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT JANUARY 26, 1995
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                                                             Ratings
                                                                                    Optional         -----------------------
  Aggregate            Name of Issuer and Title of Issue Represented               Redemption        Standard
  Principal               by Sponsor's Contracts to Purchase Bonds                 Provisions        & Poor's       Moody's
  <C>       <C> <S>                                                              <C>                 <C>           <C>
  --------------------------------------------------------------------------------------------------------------------------
  $  350,000    Maryland Health and Higher Educational Facilities Authority,       2003 at 102           A             A
                  Revenue Bonds, Good Samaritan Hospital Issue, Series 1993,
                  5.75% Due 7/1/19.
     350,000    Maryland Health and Higher Educational Facilities Authority,       2003 at 102          AAA           Aaa
                  Project and Refunding Revenue Bonds, Peninsula Regional
                  Medical Center Issue, Series 1993, 5.00% Due 7/1/23.
                  (Original issue discount bonds delivered on or about
                  October 28, 1993 at a price of 93.41% of principal
                  amount.)(MBIA Insured.)
     300,000    Maryland Health and Higher Educational Facilities Authority,       2003 at 102           A            A1
                  Refunding Revenue Bonds, Suburban Hospital Issue, Series
                  1993, 5.125% Due 7/1/21. (Original issue discount bonds
                  delivered on or about October 14, 1993 at a price of
                  94.689% of principal amount.)
     500,000    Anne Arundel County, Maryland, Consolidated General                2005 at 101          AA+           Aa
                  Improvement Bonds, Series 1995, 6.30% Due 8/1/22. (General
                  Obligation Bonds.) (When issued.)
     500,000    Anne Arundel County, Maryland, Pollution Control Revenue           2004 at 102           A            A2
                  Refunding Bonds (Baltimore Gas and Electric Company
                  Project), Series 1994, 6.00% Due 4/1/24.
     500,000    Howard County, Maryland, Mortgage Revenue Refunding Bonds,         2004 at 102          AAA           Aaa
                  Series 1994A (Beech's Farm Apartments Project-FHA Insured
                  Mortgage Loan), 6.50% Due 7/1/24. (MBIA Insured.)
     500,000    Montgomery County, Maryland, Pollution Control Revenue             2004 at 102          A+            A1
                  Refunding Bonds (Potomac Electric Project), 1994 Series,
                  5.375% Due 2/15/24.
     500,000    Industrial Development Authority of Prince George's County,        2003 at 102          AAA           Aaa
                  Maryland, Refunding Lease Revenue Bonds (Upper Marlboro
                  Justice Center Project), Series 1993, 5.25% Due 6/30/19.
                  (Original issue discount bonds delivered on or about
                  February 25, 1993 at a price of 91.667% of principal
                  amount.)(MBIA Insured.)
  ----------
  $3,500,000
  ----------
  ----------
</TABLE>
 
<PAGE>
- --------------------------------------------------------------------------------
UNIT PRICE, ESTIMATED CURRENT RETURN AND ESTIMATED LONG TERM RETURN DEPEND ON
AMOUNT PURCHASED AND PAYMENT OPTION    The sales charges/volume discounts below
apply on all concurrent purchases of any Nuveen trust units, unless any such
purchases are made by a class of investors for which a separate sales charge is
applicable as described more fully in the Prospectus. Estimated Current Return
equals net income divided by offering price. Estimated Long Term Return
represents an average of the yields to maturity (or call) of the Bonds in the
Trust adjusted to reflect expenses and sales charges.
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                              Estimated Current Return (2)
          AMOUNT PURCHASED                         Public      -----------------------------------------------------------
- -------------------------------------  Sales      Offering         Monthly           Quarterly            Semi-Annual
     Units              Dollars        Charge     Price (1)        Payment            Payment               Payment
- ----------------  -------------------  ------    -----------   ---------------    ---------------    ---------------------
<S>               <C>                  <C>       <C>           <C>       <C>      <C>       <C>      <C>       <C>
50-499                 $5,000-$49,999   4.90 %   $     93.63     (5.84%)  5.87%     (5.87%)  5.90%     (5.89%)  5.92%
500-999                 50,000-99,999   4.75           93.48     (5.85)   5.88      (5.88)   5.91      (5.90)   5.93
1,000-2,499           100,000-249,999   4.50           93.24     (5.86)   5.89      (5.90)   5.93      (5.92)   5.95
2,500-4,999           250,000-499,999   4.25           92.99     (5.88)   5.91      (5.91)   5.94      (5.93)   5.96
5,000-9,999           500,000-999,999   3.50           92.27     (5.93)   5.96      (5.96)   5.99      (5.98)   6.01
10,000-24,999     1,000,000- 2,499,999  3.00           91.79     (5.96)   5.99      (5.99)   6.02      (6.01)   6.04
25,000-49,999     2,500,000- 4,999,999  2.50           91.32     (5.99)   6.02      (6.02)   6.05      (6.04)   6.07
50,000 and over    5,000,000 and over   2.00           90.86     (6.02)   6.05      (6.05)   6.08      (6.07)   6.10
</TABLE>
 
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                         Estimated Long Term Return (3)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
- -------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
- ----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     93.63          6.04%            6.08%            6.10%
500-999                 50,000-99,999   4.75           93.48          6.05             6.08             6.10
1,000-2,499           100,000-249,999   4.50           93.24          6.06             6.10             6.12
2,500-4,999           250,000-499,999   4.25           92.99          6.08             6.12             6.13
5,000-9,999           500,000-999,999   3.50           92.27          6.13             6.17             6.19
10,000-24,999     1,000,000- 2,499,999  3.00           91.79          6.16             6.20             6.22
25,000-49,999     2,500,000- 4,999,999  2.50           91.32          6.19             6.23             6.25
50,000 and over    5,000,000 and over   2.00           90.86          6.22             6.26             6.28
</TABLE>
 
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
(1) As of the business day prior to the Date of Deposit. Units are offered at
    the Public Offering Price plus accrued interest.
(2) All figures as of the business day prior to the Date of Deposit. Figures in
    brackets represent the current return. The first year's estimated current
    returns are slightly lower than those for subsequent years because a portion
    of the monies received in the first year only will be treated as a return of
    principal due to the inclusion in the portfolio of "when issued" or other
    Bonds having delivery dates after the date of settlement for a purchase made
    on the Date of Deposit.
(3) In contrast to Estimated Current Return, Estimated Long Term Return reflects
    the amortization of premium or accretion of discount, if any, on the bonds
    in the Trust's portfolio.
 
- --------------------------------------------------------------------------------
 
INTEREST DISTRIBUTIONS TO UNITHOLDERS   Unitholders may elect to have interest
distributions made on a monthly, quarterly, or semi-annual basis. Record Dates
are May 1 and November 1 for semi-annual distributions; February 1, May 1,
August 1 and November 1 for quarterly distributions; and the first of each month
for monthly distributions. Details of interest distributions per unit under the
various plans appear in the following table based upon estimated net annual
interest income at the Date of Deposit:
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                                                      Normal
                                                                                                  Distributions
Maryland Traditional Trust                                        1995                              per Year +
<S>                                     <C>            <C>            <C>            <C>        <C>
- ------------------------------------------------------------------------------------------------  --------------
Record Date*..........................        3/1            5/1            8/1           11/1
Distribution Date.....................       3/15           5/15           8/15          11/15
- ----------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5216(1)                                              $  5.4953
                                                        --------  $.4578 every month  --------
Quarterly Distribution Plan...........  $   .5216(1)   $   .9210(2)   $  1.3815      $  1.3815    $  5.5273
Semi-Annual Distribution Plan.........  $   .5216(1)   $   .9240(3)                  $  2.7720    $  5.5463
- ----------------------------------------------------------------------------------------------------------------
<FN>
  * Record Dates for semi-annual distributions are May 1 and November 1; for quarterly distributions, they are February 1, May 1,
    August 1 and November 1. Record Dates for monthly distributions are the first day of each month.
(1) The first distribution will be paid to all Unitholders, regardless of the distribution plan selected. Such distribution may
    be more or less than a regular monthly distribution.
(2) The second distribution under the quarterly distribution plan represents a 2-month distribution; subsequent quarterly
    distributions will be regular 3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a 2-month distribution; subsequent semi-annual
    distributions will be regular 6-month distributions.
</TABLE>
 
+ Interest for Unitholders of this series began to accrue as of the Date of
Deposit. Units purchased on the Date of Deposit will have $.08 of accrued
interest that will be added to the Public Offering Price on the Settlement Date.
After provision for expenses of the Fund, the daily rate of accrual from the
Date of Deposit to the first Record Date is $.01490 per unit per day.
Consequently, on the first Record Date (03/01/95), accrued interest will total
$0.5216 per unit for the 35-day period. All interest accrued from the Date of
Deposit to the first Record Date, less expenses, will be distributed on the
first Distribution Date to Unitholders of Record as of the first Record Date.
The first payment to all Unitholders of Record on 03/01/95 is $.5216 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01526              Quarterly - $0.01535
                             Semi-Annual - $0.01540
This daily rate of accrual, and the annual distributions shown above, will
remain the same as long as the portfolio size and composition remain the same.
 
- --------------------------------------------------------------------------------
 
                                                          781
<PAGE>
- -------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 27.5 years.
The first bond is scheduled to mature in June, 2019, with the last bond maturity
being July, 2024.
 
- -------------------------------------------------------
 
QUALITY OF PORTFOLIO AS RATED BY
STANDARD & POOR'S CORPORATION
OR MOODY'S INVESTORS SERVICES
- -------------------------------------------------------
 
<TABLE>
<S>                       <C>                    <C>
Rating                    Percent of Portfolio
Category                  Par Value
- --------------------------------------------------------------------
AAA                           39%
AA                            14
A1/A+                         23
A                             24
                             ---
                             100%
</TABLE>
 
- -------------------------------------------------------
 
CALL PROTECTION   Bonds are first subject to optional redemption by the issuers
in the years and at the prices shown under the Redemption Provisions column in
the Schedule of Investments. Unless otherwise stated, in subsequent years, bonds
are redeemable at declining prices, but not usually below par value. Some issues
or some portions of issues may also be subject to sinking fund redemption or
extraordinary redemption without premium prior to the dates shown.
 
- -------------------------------------------------------
 
NO CHARGE FOR REDEMPTION   The Trustee, United States Trust Company of New York,
will redeem units at net asset value. In addition, John Nuveen & Co.
Incorporated intends to maintain a secondary market for this Nuveen Tax-Exempt
Unit Trust. Inasmuch as all securities investments are subject to market price
fluctuation, net asset value at the time of redemption could be more or less
than the initial investment.
 
- -------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
 
- -------------------------------------------------------
 
UNITS OF THE TRUST ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR ENDORSED
BY, ANY BANK AND ARE NOT FEDERALLY INSURED OR OTHERWISE PROTECTED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD OR ANY OTHER AGENCY AND
INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE LOSS OF PRINCIPAL.
 
- -------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES AND
EXPENSES, ON THIS NUVEEN TAX-EXEMPT UNIT TRUST AND ANY OTHER NUVEEN FUND, CALL
YOUR BROKER . . . OR NUVEEN AT
 
                                 1-800-257-8787
 
READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR SEND MONEY.
<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     ARIZONA
     INSURED
     TRUST 37
 
            Estimated Current Return
            5.71% to 5.94%
            as of 01/25/95
 
            Estimated Long Term Return
            5.90% to 6.14%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds rated "AAA"
                  Cusip:
                  67101J 402 Monthly Payment Option
                  67101J 410 Quarterly Payment Option
                  67101J 428 Semi-Annual Payment Option
 
                  Registered in Arizona
                    John Nuveen & Co. Incorporated
                    Investment Bankers
 
<TABLE>
<S>                           <C>
Chicago:                      Atlanta
333 W. Wacker Dr.             Austin
Chicago, Illinois 60606       Boca Raton
Telephone: 312.917.7700       Boston
                              Columbus
New York:                     Dallas/Ft. Worth
Swiss Bank Tower              Irvine
10 East 50th Street           Philadelphia
New York, New York 10022      Phoenix
Telephone: 212.207.2000       San Francisco
                              Seattle
                              Tampa
                              Washington, D.C.
</TABLE>
 
<PAGE>
- --------------------------------------------------------------------------------
 
NUVEEN TAX-EXEMPT UNIT TRUST--INSURED, ARIZONA INSURED TRUST 37
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT JANUARY 26, 1995
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                                                             Ratings
                                                                                    Optional         -----------------------
  Aggregate            Name of Issuer and Title of Issue Represented               Redemption        Standard
  Principal               by Sponsor's Contracts to Purchase Bonds                 Provisions        & Poor's       Moody's
  <C>       <C> <S>                                                              <C>                 <C>           <C>
  --------------------------------------------------------------------------------------------------------------------------
  $  500,000    Arizona Health Facilities Authority, Hospital System Revenue       2003 at 100          AAA           Aaa
                  Refunding Bonds (Phoenix Baptist Hospital and Medical
                  Center, Inc. and Medical Environments, Inc.), Series 1992,
                  6.25% Due 9/1/11.
     500,000    The Industrial Development Authority of the County of              2004 at 102          AAA           Aaa
                  Maricopa, Arizona, Insured Health Facility Refunding
                  Revenue Bonds (Catholic Healthcare West), 1994 Series A,
                  5.00% Due 7/1/15.
     500,000    City of Phoenix (Arizona), Civic Improvement Corporation,          2004 at 102          AAA           Aaa
                  Junior Lien Water System Revenue Bonds, Series 1994, 5.45%
                  Due 7/1/19.
     500,000    City of Phoenix, Arizona, Senior Lien Street and Highway           2003 at 102          AAA           Aaa
                  User Revenue Refunding Bonds, Series 1993, 5.125% Due
                  7/1/11.
     500,000    City of Phoenix Civic Improvement Corporation (Arizona),           2004 at 102          AAA           Aaa
                  Municipal Facilities Subordinated Excise Tax Revenue
                  Bonds, Series 1994, 6.90% Due 7/1/21.
     500,000    Salt River Project Agricultural Improvement and Power              2003 at 102          AAA           Aaa
                  District, Arizona, Salt River Project Electric System
                  Refunding Revenue Bonds, 1993 Series B, 5.25% Due 1/1/19.
     500,000    Commonwealth of Puerto Rico, Public Improvement Bonds of           2004 at 101          AAA           Aaa
                  1994 (General Obligation Bonds), 6.50% Due 7/1/23.                   1/2
  ----------
  $3,500,000
  ----------
  ----------
</TABLE>
 
<PAGE>
- --------------------------------------------------------------------------------
UNIT PRICE, ESTIMATED CURRENT RETURN AND ESTIMATED LONG TERM RETURN DEPEND ON
AMOUNT PURCHASED AND PAYMENT OPTION    The sales charges/volume discounts below
apply on all concurrent purchases of any Nuveen trust units, unless any such
purchases are made by a class of investors for which a separate sales charge is
applicable as described more fully in the Prospectus. Estimated Current Return
equals net income divided by offering price. Estimated Long Term Return
represents an average of the yields to maturity (or call) of the Bonds in the
Trust adjusted to reflect expenses and sales charges.
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                          Estimated Current Return (2)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
- -------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
- ----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     97.20          5.71%            5.74%            5.76%
500-999                 50,000-99,999   4.75           97.05          5.72             5.75             5.77
1,000-2,499           100,000-249,999   4.50           96.80          5.73             5.77             5.79
2,500-4,999           250,000-499,999   4.25           96.54          5.75             5.78             5.80
5,000-9,999           500,000-999,999   3.50           95.79          5.80             5.83             5.85
10,000-24,999     1,000,000- 2,499,999  3.00           95.30          5.82             5.86             5.88
25,000-49,999     2,500,000- 4,999,999  2.50           94.81          5.86             5.89             5.91
50,000 and over    5,000,000 and over   2.00           94.33          5.88             5.92             5.94
</TABLE>
 
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                         Estimated Long Term Return (3)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
- -------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
- ----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     97.20          5.90%            5.93%            5.95%
500-999                 50,000-99,999   4.75           97.05          5.90             5.94             5.96
1,000-2,499           100,000-249,999   4.50           96.80          5.92             5.96             5.98
2,500-4,999           250,000-499,999   4.25           96.54          5.93             5.97             5.99
5,000-9,999           500,000-999,999   3.50           95.79          5.98             6.02             6.04
10,000-24,999     1,000,000- 2,499,999  3.00           95.30          6.01             6.05             6.07
25,000-49,999     2,500,000- 4,999,999  2.50           94.81          6.05             6.08             6.10
50,000 and over    5,000,000 and over   2.00           94.33          6.08             6.12             6.14
</TABLE>
 
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
(1) As of the business day prior to the Date of Deposit. Units are offered at
    the Public Offering Price plus accrued interest.
(2) All figures as of the business day prior to Date of Deposit. The estimated
    current return for purchases made on such date will be as shown, as long as
    the portfolio size and composition remain the same.
(3) In contrast to Estimated Current Return, Estimated Long Term Return reflects
    the amortization of premium or accretion of discount, if any, on the bonds
    in the Trust's portfolio.
 
- --------------------------------------------------------------------------------
 
INTEREST DISTRIBUTIONS TO UNITHOLDERS   Unitholders may elect to have interest
distributions made on a monthly, quarterly, or semi-annual basis. Record Dates
are May 1 and November 1 for semi-annual distributions; February 1, May 1,
August 1 and November 1 for quarterly distributions; and the first of each month
for monthly distributions. Details of interest distributions per unit under the
various plans appear in the following table based upon estimated net annual
interest income at the Date of Deposit:
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                                                      Normal
                                                                                                  Distributions
Arizona Insured Trust                                             1995                              per Year +
<S>                                     <C>            <C>            <C>            <C>        <C>
- ------------------------------------------------------------------------------------------------  --------------
Record Date*..........................        3/1            5/1            8/1           11/1
Distribution Date.....................       3/15           5/15           8/15          11/15
- ----------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5397(1)                                              $  5.5512
                                                        --------  $.4626 every month  --------
Quarterly Distribution Plan...........  $   .5397(1)   $   .9300(2)   $  1.3950      $  1.3950    $  5.5832
Semi-Annual Distribution Plan.........  $   .5397(1)   $   .9336(3)                  $  2.8008    $  5.6022
- ----------------------------------------------------------------------------------------------------------------
<FN>
  * Record Dates for semi-annual distributions are May 1 and November 1; for quarterly distributions, they are February 1, May 1,
    August 1 and November 1. Record Dates for monthly distributions are the first day of each month.
(1) The first distribution will be paid to all Unitholders, regardless of the distribution plan selected. Such distribution may
    be more or less than a regular monthly distribution.
(2) The second distribution under the quarterly distribution plan represents a 2-month distribution; subsequent quarterly
    distributions will be regular 3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a 2-month distribution; subsequent semi-annual
    distributions will be regular 6-month distributions.
</TABLE>
 
+ Interest for Unitholders of this series began to accrue as of the Date of
Deposit. Units purchased on the Date of Deposit will have $.09 of accrued
interest that will be added to the Public Offering Price on the Settlement Date.
After provision for expenses of the Fund, the daily rate of accrual from the
Date of Deposit to the first Record Date is $.01542 per unit per day.
Consequently, on the first Record Date (03/01/95), accrued interest will total
$0.5397 per unit for the 35-day period. All interest accrued from the Date of
Deposit to the first Record Date, less expenses, will be distributed on the
first Distribution Date to Unitholders of Record as of the first Record Date.
The first payment to all Unitholders of Record on 03/01/95 is $.5397 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01542              Quarterly - $0.01550
                             Semi-Annual - $0.01556
This daily rate of accrual, and the annual distributions shown above, will
remain the same as long as the portfolio size and composition remain the same.
 
- --------------------------------------------------------------------------------
 
                                                          781
<PAGE>
- -------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 22.4 years.
The first bond is scheduled to mature in July, 2011, with the last bond maturity
being July, 2023.
 
- -------------------------------------------------------
 
BONDS INSURED BY MBIA   Each bond in this Nuveen Insured series has been
insured* by the Municipal Bond Investors Assurance Corporation, which guarantees
timely payments of principal and interest. Premium payments have been fully paid
by the Date of Deposit.
 
- -------------------------------------------------------
 
CALL PROTECTION   Bonds are first subject to optional redemption by the issuers
in the years and at the prices shown under the Redemption Provisions column in
the Schedule of Investments. Unless otherwise stated, in subsequent years, bonds
are redeemable at declining prices, but not usually below par value. Some issues
or some portions of issues may also be subject to sinking fund redemption or
extraordinary redemption without premium prior to the dates shown.
 
- -------------------------------------------------------
 
NO CHARGE FOR REDEMPTION   The Trustee, United States Trust Company of New York,
will redeem units at net asset value. In addition, John Nuveen & Co.
Incorporated intends to maintain a secondary market for this Nuveen Tax-Exempt
Unit Trust. Inasmuch as all securities investments are subject to market price
fluctuation, net asset value at the time of redemption could be more or less
than the initial investment.
 
- -------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
 
- -------------------------------------------------------
 
UNITS OF THE TRUST ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR ENDORSED
BY, ANY BANK AND ARE NOT FEDERALLY INSURED OR OTHERWISE PROTECTED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD OR ANY OTHER AGENCY AND
INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE LOSS OF PRINCIPAL.
 
- -------------------------------------------------------
* Insurance relates specifically to the bonds and not to the units or to the
  market value of units. Terms of the insurance are more fully described in the
  prospectus. No representation is made as to the insurer's ability to meet its
  commitments. See Section 5 of the prospectus for details.
 
- -------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES AND
EXPENSES, ON THIS NUVEEN TAX-EXEMPT UNIT TRUST AND ANY OTHER NUVEEN FUND, CALL
YOUR BROKER . . . OR NUVEEN AT
 
                                 1-800-257-8787
 
READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR SEND MONEY.
<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     CALIFORNIA
     INSURED
     TRUST 241
 
            Estimated Current Return
            5.99% to 6.22%
            as of 01/25/95
 
            Estimated Long Term Return
            6.14% to 6.39%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds rated "AAA"
                  Cusip:
                  67064U 709 Monthly Payment Option
                  67064U 717 Quarterly Payment Option
                  67064U 725 Semi-Annual Payment Option
 
                  Registered in California
                    John Nuveen & Co. Incorporated
                    Investment Bankers
 
<TABLE>
<S>                           <C>
Chicago:                      Atlanta
333 W. Wacker Dr.             Austin
Chicago, Illinois 60606       Boca Raton
Telephone: 312.917.7700       Boston
                              Columbus
New York:                     Dallas/Ft. Worth
Swiss Bank Tower              Irvine
10 East 50th Street           Philadelphia
New York, New York 10022      Phoenix
Telephone: 212.207.2000       San Francisco
                              Seattle
                              Tampa
                              Washington, D.C.
</TABLE>
 
<PAGE>
- --------------------------------------------------------------------------------
 
NUVEEN TAX-EXEMPT UNIT TRUST--INSURED, CALIFORNIA INSURED TRUST 241
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT JANUARY 26, 1995
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                                                             Ratings
                                                                                    Optional         -----------------------
  Aggregate            Name of Issuer and Title of Issue Represented               Redemption        Standard
  Principal               by Sponsor's Contracts to Purchase Bonds                 Provisions        & Poor's       Moody's
  <C>       <C> <S>                                                              <C>                 <C>           <C>
  --------------------------------------------------------------------------------------------------------------------------
  $  500,000    California Statewide Communities Development Authority,            2003 at 102          AAA           Aaa
                  Certificates of Participation, Sutter Health Obligated
                  Group, 5.50% Due 8/15/23.
     500,000    State Public Works Board of the State of California, Lease         2004 at 102          AAA           Aaa
                  Revenue Bonds (Department of Corrections), 1994 Series A
                  (California State Prison-Monterey County (Soledad II)),
                  7.00% Due 11/1/19.
     500,000    The Regents of the University of California, University of         2003 at 102          AAA           Aaa
                  California Housing System Revenue Bonds, Series A, 5.50%
                  Due 11/1/18.
     500,000    Brea Redevelopment Agency (Orange County, California), 1993        2003 at 102          AAA           Aaa
                  Tax Allocation Refunding Bonds (Redevelopment Project AB),
                  5.50% Due 8/1/17.
     500,000    Fairfield Public Financing Authority (California), 1993            2003 at 102          AAA           Aaa
                  Revenue Bonds, Series B, 5.80% Due 4/1/23.
     500,000    Sacramento Municipal Utility District (California), Electric       2003 at 102          AAA           Aaa
                  Revenue Bonds, 1993 Series E, 5.75% Due 5/15/22.
     500,000    Commonwealth of Puerto Rico, Public Improvement Bonds of           2004 at 101          AAA           Aaa
                  1994 (General Obligation Bonds), 6.50% Due 7/1/23.                   1/2
  ----------
  $3,500,000
  ----------
  ----------
</TABLE>
 
<PAGE>
- --------------------------------------------------------------------------------
UNIT PRICE, ESTIMATED CURRENT RETURN AND ESTIMATED LONG TERM RETURN DEPEND ON
AMOUNT PURCHASED AND PAYMENT OPTION    The sales charges/volume discounts below
apply on all concurrent purchases of any Nuveen trust units, unless any such
purchases are made by a class of investors for which a separate sales charge is
applicable as described more fully in the Prospectus. Estimated Current Return
equals net income divided by offering price. Estimated Long Term Return
represents an average of the yields to maturity (or call) of the Bonds in the
Trust adjusted to reflect expenses and sales charges.
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                          Estimated Current Return (2)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
- -------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
- ----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     95.17          5.99%            6.02%            6.04%
500-999                 50,000-99,999   4.75           95.02          6.00             6.03             6.05
1,000-2,499           100,000-249,999   4.50           94.77          6.01             6.04             6.06
2,500-4,999           250,000-499,999   4.25           94.53          6.03             6.06             6.08
5,000-9,999           500,000-999,999   3.50           93.79          6.07             6.11             6.13
10,000-24,999     1,000,000- 2,499,999  3.00           93.31          6.11             6.14             6.16
25,000-49,999     2,500,000- 4,999,999  2.50           92.83          6.14             6.17             6.19
50,000 and over    5,000,000 and over   2.00           92.36          6.17             6.20             6.22
</TABLE>
 
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                         Estimated Long Term Return (3)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
- -------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
- ----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     95.17          6.14%            6.18%            6.20%
500-999                 50,000-99,999   4.75           95.02          6.15             6.19             6.21
1,000-2,499           100,000-249,999   4.50           94.77          6.17             6.21             6.23
2,500-4,999           250,000-499,999   4.25           94.53          6.18             6.22             6.24
5,000-9,999           500,000-999,999   3.50           93.79          6.23             6.27             6.29
10,000-24,999     1,000,000- 2,499,999  3.00           93.31          6.27             6.31             6.32
25,000-49,999     2,500,000- 4,999,999  2.50           92.83          6.30             6.34             6.36
50,000 and over    5,000,000 and over   2.00           92.36          6.33             6.37             6.39
</TABLE>
 
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
(1) As of the business day prior to the Date of Deposit. Units are offered at
    the Public Offering Price plus accrued interest.
(2) All figures as of the business day prior to Date of Deposit. The estimated
    current return for purchases made on such date will be as shown, as long as
    the portfolio size and composition remain the same.
(3) In contrast to Estimated Current Return, Estimated Long Term Return reflects
    the amortization of premium or accretion of discount, if any, on the bonds
    in the Trust's portfolio.
 
- --------------------------------------------------------------------------------
 
INTEREST DISTRIBUTIONS TO UNITHOLDERS   Unitholders may elect to have interest
distributions made on a monthly, quarterly, or semi-annual basis. Record Dates
are May 1 and November 1 for semi-annual distributions; February 1, May 1,
August 1 and November 1 for quarterly distributions; and the first of each month
for monthly distributions. Details of interest distributions per unit under the
various plans appear in the following table based upon estimated net annual
interest income at the Date of Deposit:
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                                                      Normal
                                                                                                  Distributions
California Insured Trust                                          1995                              per Year +
<S>                                     <C>            <C>            <C>            <C>        <C>
- ------------------------------------------------------------------------------------------------  --------------
Record Date*..........................        3/1            5/1            8/1           11/1
Distribution Date.....................       3/15           5/15           8/15          11/15
- ----------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5537(1)                                              $  5.6966
                                                        --------  $.4746 every month  --------
Quarterly Distribution Plan...........  $   .5537(1)   $   .9546(2)   $  1.4319      $  1.4319    $  5.7286
Semi-Annual Distribution Plan.........  $   .5537(1)   $   .9576(3)                  $  2.8728    $  5.7476
- ----------------------------------------------------------------------------------------------------------------
<FN>
  * Record Dates for semi-annual distributions are May 1 and November 1; for quarterly distributions, they are February 1, May 1,
    August 1 and November 1. Record Dates for monthly distributions are the first day of each month.
(1) The first distribution will be paid to all Unitholders, regardless of the distribution plan selected. Such distribution may
    be more or less than a regular monthly distribution.
(2) The second distribution under the quarterly distribution plan represents a 2-month distribution; subsequent quarterly
    distributions will be regular 3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a 2-month distribution; subsequent semi-annual
    distributions will be regular 6-month distributions.
</TABLE>
 
+ Interest for Unitholders of this series began to accrue as of the Date of
Deposit. Units purchased on the Date of Deposit will have $.09 of accrued
interest that will be added to the Public Offering Price on the Settlement Date.
After provision for expenses of the Fund, the daily rate of accrual from the
Date of Deposit to the first Record Date is $.01582 per unit per day.
Consequently, on the first Record Date (03/01/95), accrued interest will total
$0.5537 per unit for the 35-day period. All interest accrued from the Date of
Deposit to the first Record Date, less expenses, will be distributed on the
first Distribution Date to Unitholders of Record as of the first Record Date.
The first payment to all Unitholders of Record on 03/01/95 is $.5537 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01582              Quarterly - $0.01591
                             Semi-Annual - $0.01596
This daily rate of accrual, and the annual distributions shown above, will
remain the same as long as the portfolio size and composition remain the same.
 
- --------------------------------------------------------------------------------
 
                                                          781
<PAGE>
- -------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 26.2 years.
The first bond is scheduled to mature in August, 2017, with the last bond
maturity being August, 2023.
 
- -------------------------------------------------------
 
BONDS INSURED BY MBIA   Each bond in this Nuveen Insured series has been
insured* by the Municipal Bond Investors Assurance Corporation, which guarantees
timely payments of principal and interest. Premium payments have been fully paid
by the Date of Deposit.
 
- -------------------------------------------------------
 
CALL PROTECTION   Bonds are first subject to optional redemption by the issuers
in the years and at the prices shown under the Redemption Provisions column in
the Schedule of Investments. Unless otherwise stated, in subsequent years, bonds
are redeemable at declining prices, but not usually below par value. Some issues
or some portions of issues may also be subject to sinking fund redemption or
extraordinary redemption without premium prior to the dates shown.
 
- -------------------------------------------------------
 
NO CHARGE FOR REDEMPTION   The Trustee, United States Trust Company of New York,
will redeem units at net asset value. In addition, John Nuveen & Co.
Incorporated intends to maintain a secondary market for this Nuveen Tax-Exempt
Unit Trust. Inasmuch as all securities investments are subject to market price
fluctuation, net asset value at the time of redemption could be more or less
than the initial investment.
 
- -------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
 
- -------------------------------------------------------
 
UNITS OF THE TRUST ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR ENDORSED
BY, ANY BANK AND ARE NOT FEDERALLY INSURED OR OTHERWISE PROTECTED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD OR ANY OTHER AGENCY AND
INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE LOSS OF PRINCIPAL.
 
- -------------------------------------------------------
 
* Insurance relates specifically to the bonds and not to the units or to the
  market value of units. Terms of the insurance are more fully described in the
  prospectus. No representation is made as to the insurer's ability to meet its
  commitments. See Section 5 of the prospectus for details.
 
- -------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES AND
EXPENSES, ON THIS NUVEEN TAX-EXEMPT UNIT TRUST AND ANY OTHER NUVEEN FUND, CALL
YOUR BROKER . . . OR NUVEEN AT
 
                                 1-800-257-8787
 
READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR SEND MONEY.


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