COFFEY, Circuit Judge.

The appellant Rick Serola appeals his convictions for two counts of giving false testimony before a Grand Jury in violation of 18 U.S.C. § 1623. We affirm.

I.

On July 20 and October 4, 1983, Serola was subpoenaed to testify under a grant of immunity before a grand jury investigating a marijuana distribution ring in Milwaukee, Wisconsin operating from 1977 through 1979. On July 20, during the course of his testimony, the government prosecutor asked Serola whether he was familiar with an individual named Douglas Lane and whether he knew of or participated in a marijuana distribution ring involving Lane. Serola admitted that he knew Lane; but, he claimed that he could not recall whether Lane was involved in any marijuana transactions. During Serola's grand jury testimony on October 4, 1983, he was asked about his relationship with a John Tamarri and his familiarity with Tamarri's marijuana distribution activities; Serola denied any knowledge of Tamarri's involvement in any marijuana distribution ring. On January 3, 1984, Serola was indicated on two counts of perjury on the basis of the answers given to the grand jury on July 20 and October 4, 1983 regarding his claimed lack of knowledge of Lane's and Tamarri's marijuana sales activities. The indictment charged:

COUNT I

"THE GRAND JURY CHARGES:

"On the 4th day of October, 1983, at Milwaukee, within the State and Eastern District of Wisconsin,

RICHARD SEROLA

while under oath as a witness in proceedings before a grand jury of the United States of America did knowingly make false material declaration in that he did falsely answer questions as follows:

Q "Now, did Tamarri have any other involvement in your marijuana business?

A "Well, he was just kind of like — not really, no. He was just kind of there to — you know, I may have led them to believe that he did because I wanted to be, you know, — when you don't know a person very well and you don't know much about them, you don't know how to get ahold (sic) of them and all that stuff, you want to kind of — and you're trying to get them to front you a lot of weed, you want to be on some kind of social level with them so that's what I tried to do and that's how John fit into it.

Q "Other than helping introduce you to Kirk, did Tamarri have anything else to do with your marijuana business?

A "No.

* * * * * *

Q "So Tamarri never delivered any marijuana to Lane for you?

A. "I guess that's right.

Q. "Were you and Tamarri ever together at Lane's farm when large bales of marijuana which were delivered were there waiting to be distributed?

A. "I can't recall anything like that, no.

"All of which the said Richard Serola did then and there know to be false, in violation of 18 U.S.C. § 1623.

COUNT 2

"THE GRAND JURY FURTHER CHARGES:

"On the 20th day of July, 1983, at Milwaukee, within the State and Eastern District of Wisconsin,

RICHARD SEROLA

while under oath as a witness in proceedings before a grand jury of the United States of America did knowingly make false material declarations in that he did falsely answer questions as follows:

Q. "Did you ever front marijuana to Douglas Lane?

A. "No, not that I can recall.

Q. "Did you ever sell marijuana to Douglas Lane?

A. "Not that I can recall.

Q. "Did you ever transfer marijuana to Douglas Lane?

A. "You mean quantities?

Q. "I mean marijuana, any quantity.

A. "I can't recall.

Q. "By that you mean as you sit here this afternoon, you can recall no occasion when you caused marijuana to be transported, given, transferred in any way to Douglas Lane, is that right?

A. "Right.

* * * * * *

Q. "Now, during the time when you lived at the Pompano Beach address, you caused cars and a truck and a motor home to transport marijuana from your Pompano Beach address to Mr. Lane's farmhouse outside of Milwaukee, Wisconsin, isn't that right.

A. "I know that I had some cars leave the house. Where they went, I don't know, you know. I do — my job is to get it out and when they come down, they come back to me with the money, usually, you know, the people who I give the vehicle to.

* * * * * *

Q. "Do you know whether Doug Lane has ever trafficked in marijuana?

A. "No.

Q. "Do you know whether he has ever bought or sold marijuana?

A. "No.

Q. "Have you ever seen Doug Lane with large quantities of marijuana?

A. "No, not that I can recall.

"All of which the said Richard Serola did then and there know to be false, in violation of 18 U.S.C. § 1623."

Michael Colella, the first witness called by the government at Serola's perjury trial, testified that Lane, Tamarri and Serola, former college friends, convinced him in early 1977 to act as a courier for a shipment of marijuana from Florida to Wisconsin. Colella testified that his first trip as a courier occurred in May of 1977 after Tamarri directed Colella to meet Serola in Florida; Serola in turn provided him with an automobile to transport the marijuana to Wisconsin. Subsequently, in July, 1977, Lane again called Colella, directed him to fly to Florida to pick up a shipment of marijuana from Serola and transport the load to Wisconsin. Colella stated that although he could not be sure of the particular location where he transported each of these loads, he was sure he delivered one of the loads of marijuana at Lane's farm in Wisconsin. Colella further testified that in the fall of 1977 he traveled with Tamarri by automobile to Boston, Massachusetts in order to retrieve a truck containing marijuana. Colella testified that while in Massachusetts, Tamarri made several telephone calls and during one of the conversations he overheard Tamarri call a person named "Rick" to discuss their progress in transporting the marijuana. Before leaving Boston, Tamarri told Colella to deliver the marijuana to a Tom Monahan who lived in Milwaukee. When Colella arrived at Monahan's address, both Monahan and Serola were waiting for him. Monahan testified that before Colella arrived at his house Lane called and told him that the load would be arriving shortly. After Colella arrived at Monahan's house, Lane and Tamarri appeared and joined Serola and Monahan in inventorying the marijuana. In March of 1978, Colella under Lane's direction once more made a trip to Florida and this time Lane supplied him with cash and a camper, which he drove to Serola's residence in Florida. On his return trip, Serola instructed Colella to deliver a load of marijuana to Tamarri's cousin in Chicago. In April of 1978, Colella also accompanied Tamarri as they transported a load of marijuana from Florida to Lane's farm in Wisconsin. Colella testified that his expenses for all of these trips were covered by either Tamarri or Lane.

In June, 1978, during another courier trip between Florida and Wisconsin, Colella was arrested by Florida authorities for possession of marijuana after they discovered his illegal cache when Colella was forced to stop at an agricultural inspection station. Colella testified that Lane, Tamarri and Serola agreed to pay Colella $15,000 in exchange for Colella's promise not to disclose their involvement with the marijuana. Subsequently, Colella was called before a grand jury in August of 1982. Prior to his testimony, he met with Lane to discuss how he should couch his testimony so as not to incriminate Lane, Tamarri, or Serola. Since Serola was also scheduled to testify before the grand jury, Colella met with Serola and Lane at Lane's farm subsequent to Colella's grand jury testimony in order that they might coordinate their stories. Lloyd Kissick, Serola's former business partner, also testified that Serola had told him that when he (Serola) left to testify before the grand jury, Serola stated that he would be staying at Lane's farm to "go over his testimony." (Tr. 31). Kissick also recounted a conversation between himself and Serola wherein Serola told him that he (Serola) answered most of the grand jury questions by stating that he did not recall the events and that the reason he did so was to avoid answering questions he did not wish to answer or was in doubt about the answer.

Finally, Joseph Kirk and Martin Plambeck, both of whom admitted they were marijuana traffickers in the late 1970's, also testified on behalf of the government. Kirk testified that both Tamarri and Serola had told him of a man named Doug Lane who could financially back Tamarri and Serola in larger drug transactions, while Plambeck stated that he had extensive marijuana dealings during the late 1970's with Tamarri and a man named "Rick."

In his defense, Serola presented four witnesses before offering the testimony of Al Hoover, who was called to impeach portions of Kissick's testimony regarding Kissick's claimed business dealings with Hoover. The district court, however, excluded Hoover's testimony on the grounds that it constituted collateral impeachment. After the defense rested its case, the jury returned a verdict finding Serola guilty on both perjury counts.

On appeal, Serola claims that the district court committed reversible error when it (1) failed to dismiss the indictment; (2) failed to make an explicit ruling on the record regarding the admissibility of co-conspirator hearsay statements; (3) asked Joseph Kirk a series of improper questions thus prejudicing his case; and (4) excluded the testimony of Al Hoover. He further claims that the evidence presented is insufficient to support the verdict.

II.

Initially, Serola complains that because of the number of questions contained in the indictment, he lacked sufficient notice as to which statements the government was relying on to establish its perjury charge; he further asserts that the government should have included a "truth paragraph" in the indictment setting forth what the government believed to be the "objective truth" of Serola's testimony.

It has long been held that in reviewing the sufficiency of an indictment the court should be guided by practical rather than technical considerations. See, e.g., United States v. Gironda, 758 F.2d 1201, 1209 (7th Cir. 1985); United States v. Brack, 747 F.2d 1142, 1147 (7th Cir. 1984), cert. denied ___ U.S. ___, 105 S.Ct. 1193, 84 L.Ed.2d 339 (1985). In Gironda, this court addressed the factors used in assessing the sufficiency of an indictment:

"First, it should state all of the elements of the offense charged; second, it should inform the defendant of the nature of the charge so that he may prepare a defense; and third, it must enable the defendant to plead the judgment as the bar to any later prosecution for the same offense."

Gironda, 758 F.2d at 1209. In order to prosecute a person for perjury under 18 U.S.C. § 1623, the government must establish that the defendant's answers dealt with a material fact in the grand jury investigation and that the answers given were knowingly false. See United States v. Martellano, 675 F.2d 940, 942 (7th Cir. 1982).

The only issue raised by Serola in challenging the sufficiency of the indictment is whether Serola had adequate notice of the charge of perjury so as to enable him to prepare his defense. After reviewing the indictment, we are convinced that the questions recited therein are clear, direct and unambiguous. Count I clearly sets forth specific questions in which the prosecution inquires as to the extent of Tomarri's involvement in the marijuana distribution ring, while Count II details with specificity questions concerning Serola's involvement with Lane in distributing the marijuana. In response, Serola answered the questions with a "no" or replied that he could not recall Tamarri's or Lane's involvement. Since the questions and answers in the indictment are complete, direct and clearly stated, Serola was adequately notified of the charges brought by the government. See United States v. Ras, 713 F.2d 311, 318-19 (7th Cir. 1983). Indeed, in his brief to this court, Serola never discusses how his ability to prepare his defense against the perjury charges was hampered by the questions and answers contained in the indictment.

Serola cites several cases from the Third and Ninth Circuits to support his argument that an indictment for perjury is insufficient unless the indictment contains a "truth paragraph" detailing what the government believes to be the objective truth of the accused perjuror's testimony. See United States v. Slawik, 548 F.2d 75, 83-84 (3rd Cir. 1977); see also United States v. Tonelli, 577 F.2d 194, 196 (3rd Cir. 1978); United States v. Cowley, 720 F.2d 1037 (9th Cir. 1983). The Second and Fifth Circuits, however, have rejected the theory that a truth paragraph must be included. See United States v. Marchisio, 344 F.2d 653, 662 (2d Cir. 1965); United States v. Oberski, 734 F.2d 1034, 1035 n. 1 (5th Cir. 1984); United States v. Crippen, 579 F.2d 340, 342 (5th Cir. 1978), cert. denied, 439 U.S. 1069, 99 S.Ct. 837, 59 L.Ed.2d 34 (1979). Indeed, the precise holding in Slawik, concerned the fact that the questions and answers contained in the indictment were too ambiguous to determine which interpretation of the defendant's answers the grand jury charged or meant to charge as false. See Slawik, 548 F.2d at 83-84, 86, citing Bronston v. United States, 409 U.S. 352, 362, 93 S.Ct. 595, 601, 34 L.Ed.2d 568 (1973). This same concern over the ambiguity of the questions asked and the answers given pervaded the Cowley decision. Cowley, 720 F.2d at 1042-43. However, when an indictment, such as the one at issue in this case, contains clear, direct, unambiguous and precise questions and answers that the nature and extent of the alleged falsity is fairly self-evident, the defendant has had adequate notice and a "truth paragraph" is not required.

Serola further contends that the district court also erred in refusing to entertain his motion requesting that the government respond to his request for a bill of particulars, disclosing what the government believed to be the "objective truth" of the statements made by Serola contained in the perjury indictment. The district court denied this motion, along with other portions of Serola's bill of particulars, requesting details of times and dates. Both parties recognize that consideration of a bill of particulars rests within the sound discretion of the trial court and its decision can be reversed only upon a showing of an abuse of discretion. See United States v. Kendall, 665 F.2d 126, 134 (7th Cir. 1981), cert. denied, 455 U.S. 1021, 102 S.Ct. 1719, 72 L.Ed.2d 140 (1982). The test for determining whether a bill of particulars is needed is, in part: "`whether the indictment . . . sufficiently apprises the defendant of the charges to enable him to prepare for trial.'" (citations omitted). Id. As noted in our discussion concerning the sufficiency of Serola's indictment, the nature and particulars of the charge lodged against Serola were adequately set forth in the indictment so as to allow Serola to prepare a defense for trial. Thus, the district court did not abuse its discretion in denying Serola's motion for a bill of particulars. See United States v. Matlock, 675 F.2d 981, 986 (8th Cir. 1982).

III.

Serola next argues that his case was prejudiced by several rulings made by the district court during the course of the trial; however, only one of these rulings merits extended discussion.

Serola challenges the admissibility of certain co-conspirator statements contending that the district court did not make any specific finding as to the existence of a conspiracy between Colella, Lane, Tamarri, and Serola to warrant the admission of portions of Colella's testimony. Colella, the government's first witness at trial, testified that in 1977 he reached an agreement with Lane, Tamarri and Serola to distribute marijuana. At the beginning of Colella's testimony, he detailed several conversations with each individual (Tamarri, Serola and Lane); for example, he recounted Tamarri directing him to go to Florida as "the load was ready, to come on down and pick it up." This statement was objected to by defense counsel, but the district court overruled the objection and admitted the evidence pursuant to the co-conspirator exception to the hearsay rule codified in Fed.R.Evid. Rule 801(d)(2)(E). Describing another drug-running trip to Boston, Colella testified that Tamarri made several telephone calls, and in one phone call he overheard him speak to a man named "Rick." The district court again admitted this evidence under Rule 801(d)(2)(E), subject to the government establishing the existence of the conspiracy by independent evidence. Colella also recounted other statements, such as Doug Lane's statements directing him to pick up a load of marijuana in Florida from Serola, and discussions he had with Serola, Lane, and Tamarri concerning payments made to him in exchange for his silence after he (Colella) was arrested for transporting marijuana. However, Colella also recalled his contracts with Serola, Tamarri and Lane which did not involve any allegedly hearsay statements. As an example, he recited that on his return trip back to Wisconsin from Boston with Tamarri, Colella described how he dropped off the marijuana at Monahan's house and that Monahan and Serola were there to greet him. Also, Colella testified that he had given money to Serola in exchange for marijuana to be delivered to Lane's farm in Wisconsin. Monahan, testifying for the government, verified that Colella had made a delivery to his house and that Serola, Tamarri and Lane helped Monahan inventory it. Other witnesses also testified during the trial as to their contacts and experiences with the marijuana trafficking of Lane Tamarri and Serola.

At the end of the government's case, defense counsel moved to dismiss the indictment on the basis that the government had failed to adduce sufficient evidence to sustain a charge of perjury, but the court denied this motion. At this time, Serola's counsel neither made a motion to strike the co-conspirator's statements for failure of the government to establish the conspiracy by independent evidence, nor did he request the court to make a specific finding regarding the establishment of a conspiracy. After the defense rested its case, the court asked the parties if they had any objections to the jury instructions. Defense counsel noted only that he objected to the form of one of the co-conspirator instructions, but he did not move to strike the co-conspirator statements. Defense counsel then stated:

"I lodged an objection to the co-conspirator, that it didn't meet the standard, the Court made its ruling, I assume that the Court had made at the close of the Government's case by denying my motion, implicit in this is that you have found that there was sufficient evidence to justify or to consist of a foundation for that."

In response, the district court noted:

"Let the record show that the Court did deny the motion for directed verdict of acquittal at the conclusion of the Government's case, and implicit in that denial was the finding by the Court that there had been an existence of a conspiracy established by the actions and statements of the declarants themselves, such that the Court felt that pursuant to the general rules of law, case law and otherwise hearsay declarations of co-conspirators were admissible."

Although Serola claims in one sentence of his brief that no independent evidence existed to sustain any finding of a conspiracy, see appellant's brief at 18, he does not press the point on appeal, obviously because he realizes the record contains more than sufficient independent evidence to establish the existence of a conspiracy. Rather, Serola contends that the district court committed reversible error when it failed to make a specific finding that independent evidence existed establishing the presence of a conspiracy by a preponderance of the evidence to justify admission of the co-conspirators' out-of-court statements.

In United States v. Nicosia, 638 F.2d 970 (7th Cir. 1980), cert. denied, 452 U.S. 961, 101 S.Ct. 3110, 69 L.Ed.2d 972 (1981), our court declined to follow the Third Circuit's decision in United States v. Continental Group, Inc., 603 F.2d 444, 457 (3d Cir. 1979), cert. denied, 444 U.S. 1032, 100 S.Ct. 703, 62 L.Ed.2d 668 (1980), which held that the district court's denial of the defendant's motion to strike co-conspirators' statements fulfilled the obligations of the district court to make a specific finding that independent evidence existed to establish the conspiracy. Nicosia, 638 F.2d at 974 n. 2. However, Nicosia noted that our decision in United States v. Santiago, 582 F.2d 1128 (7th Cir. 1978) does not require that a district court make specific findings concerning the existence of the conspiracy as a "necessary predicate for admission of such co-conspirator's statements," Nicosia, 638 F.2d at 974, but nevertheless we stated that "we believe the record entry of such a finding is the better practice and exercise for the district court to follow when confronted with an objection to or motion to strike a co-conspirator's testimony relating to out-of-court statements. . . ." Id. Our court concluded, however, that the district court's failure to make such a specific finding was at most harmless error. Id.

In this case, the defendant failed to make a motion to strike portions of Colella's testimony regarding statements made by Serola, Lane, and Tamarri. Further, the district court, unlike the situation in Nicosia, did make a finding on the record at the end of the trial that the government did prove the existence of a conspiracy. Under these circumstances, the district court's finding of a conspiracy was sufficient to fulfill its obligation under Santiago.

Serola also argues that the district court committed reversible error when it questioned a government witness, Joseph Kirk, sua sponte, about the rehabilitative effect of an earlier stay in jail on a charge related to Kirk's prior marijuana distribution activities. Our review of the record reveals that Serola failed to object during trial to this question as required by Fed.R.Evid. Rule 614(a), (c). Failure to make a timely objection waives any right to appellate review unless the court's questioning constitutes plain error. See, e.g., Czajku v. Hickman, 703 F.2d 317, 320 (8th Cir. 1983); United States v. Billups, 692 F.2d 320, 327 (4th Cir. 1982). Given that the record contains substantial evidence of guilt and the court's questioning occurred only briefly during this week-long trial, the court's questioning, while irrelevant to the issues presented, does not rise to a level of plain error as the question was not so "conspicuous" that it "probably changed the outcome of the trial." United States v. Silverstein, 732 F.2d 1338, 1349 (7th Cir. 1984).

Serola also contends that the district court improperly limited the cross-examination of Lloyd Kissick, Serola's former business partner in the Balancing Act Scales Company, as to his bias and motive for testifying, and improperly excluded the testimony of Al Hoover, a former business associate of Kissick and Serola. After reviewing the record, we are unable to discover an instance where the district court made an evidentiary ruling that could be properly construed as limiting Serola's right to cross-examine Kissick. Further, we point out that the district court properly excluded Hoover's testimony as it was extrinsic evidence addressing only the collateral issue of Kissick's proper ownership percentage in the company. See, e.g., United States v. Taylor, 728 F.2d 864 (7th Cir. 1984) (reciting the well-established rule that "a witness `may not be impeached by contradiction as to collateral . . . matters elicited on cross-examination.'" Id. at 874); see also United States v. Carter, 720 F.2d 941, 949 (7th Cir. 1983).

IV.

Finally, Serola challenges the sufficiency of the evidence supporting his conviction for perjury. He points out that each count in the indictment listed a series of questions and concluded with the phrase "[a]ll of which the said Richard Serola did then and there know to be false. . . ." Serola now attacks the third and fourth questions in Count I and the first, second, and sixth questions in Count II of the indictment alleging that there was insufficient evidence to demonstrate that he had perjured himself when he gave these answers.

In a perjury case the government must prove beyond a reasonable doubt that: (1) the questions and answers contained in the indictment were material to the grand jury investigation; and (2) at least one of the questions in the particular indictment was answered by the defendant knowing the answer to be false. See, e.g., United States v. Kehoe, 562 F.2d 65, 69 (1st Cir. 1977) (single-count indictment, containing six questions and answers, alleging that "all of [defendant's] testimony" was given knowing it to be false); see also, United States v. Caucci, 635 F.2d 441, 444 (5th Cir. 1981); United States v. Bonacorsa, 528 F.2d 1218, 1221-22 (2d Cir. 1976); Vitello v. United States, 425 F.2d 416, 422 (9th Cir.), cert. denied, 400 U.S. 822, 91 S.Ct. 43, 27 L.Ed.2d 50 (1970). In this case, the jury was instructed, in part, that the government must prove beyond a reasonable doubt that the defendant knowingly "made one or more false declarations as charged in the indictment." The district court also instructed the jury that it must reach a unanimous verdict and "deliberate with the goal of reaching an agreement which is consistent with the individual judgment of each juror." Thus, the jury was instructed that it must reach a unanimous verdict on at least one of the questions contained in each of the two indictments. At trial, Serola never objected to the district court's instruction that it must find that the defendant "made one or more false declarations as charged in the indictment." This failure to object at trial to the jury instruction reciting that the government need only prove that Serola gave an answer to at least one question knowing the answer to be false waives his right to appellate review of this instruction. See Singer v. United States, 380 U.S. 24, 38, 85 S.Ct. 783, 13 L.Ed.2d 630 (1965); Fed.R.Crim.P. Rule 30.

Thus, since the jury was instructed that it could find the defendant guilty if he answered at least one question in each indictment knowing the answer to be false and there was more than sufficient direct evidence to sustain the jury's verdict on each particular question not challenged by Serola here on appeal, we affirm the jury's verdict.